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2017
  1. Pierre Aboulker, Nick Brettell, Frédéric Havet, Dániel Marx, and Nicolas Trotignon. Colouring graphs with constraints on connectivity. Journal of Graph Theory, 85(4):814-838, 2017. [WWW ] [PDF ]
    Keywords: colouring, local connectivity, local edge-connectivity, Brooks' theorem, minimally k-connected, vertex degree.
     
  2. Julien Bensmail, Mohammed Senhaji, and Kasper Szabo Lyngsie. On a combination of the 1-2-3 Conjecture and the Antimagic Labelling Conjecture. Discrete Mathematics and Theoretical Computer Science, 19(1), August 2017. [WWW ] [PDF ]
    Keywords: equitable edge-weightings, 1-2-3 Conjecture, Antimagic Labelling Conjecture.
     
  3. Lélia Blin, Janna Burman, and Nicolas Nisse. Exclusive Graph Searching. Algorithmica, 77(3):942-969, 2017. [WWW ] [PDF ]
     
  4. Nathann Cohen, David Coudert, Guillaume Ducoffe, and Aurélien Lancin. Applying clique-decomposition for computing Gromov hyperbolicity. Theoretical Computer Science, 2017. [WWW ] [PDF ]
    Keywords: outerplanar graphs, Gromov hyperbolicity, graph algorithms, clique-decomposition.
     
  5. Gianlorenzo D 'angelo, Alfredo Navarra, and Nicolas Nisse. A unified approach for Gathering and Exclusive Searching on rings under weak assumptions. Distributed Computing, 30(1):17-48, 2017. [WWW ] [PDF ]
     
  6. Rennan Dantas, Frédéric Havet, and Rudini M Sampaio. Identifying codes for infinite triangular grids with a finite number of rows. Discrete Mathematics, 340:1584 - 1597, 2017. [WWW ] [PDF ]
     
  7. Euripides Markou, Nicolas Nisse, and Stéphane Pérennes. Exclusive graph searching vs. pathwidth. Information and Computation, 252:243 - 260, 2017. [WWW ] [PDF ]
    Keywords: graph searching, pathwidth.
     
  8. Myriana Rifai, Nicolas Huin, Christelle Caillouet, Frédéric Giroire, Joanna Moulierac, Dino Lopez Pacheco, and Guillaume Urvoy-Keller. Minnie : An SDN world with few compressed forwarding rules. Computer Networks, 121:185 - 207, July 2017. [WWW ] [PDF ]
    Keywords: Software Defined Networks, data center networks, routing tables, compression, TCAM.
     
  9. Sahel Sahhaf, Wouter Tavernier, Dimitri Papadimitriou, Davide Careglio, Alok Kumar, Christian Glacet, David Coudert, Nicolas Nisse, Lluis Fàbrega, Pere Vilà, Miguel Camelo, Pieter Audenaert, Didier Colle, and Piet Demeester. Routing at Large Scale: Advances and Challenges for Complex Networks. IEEE Network, pp 12 - 22, 2017. [WWW ] [PDF ]
    Keywords: Complex networks, Geometric routing, Compact routing, Algebraic routing, Path-vector routing.
     
  10. Julien Bensmail, Valentin Garnero, Nicolas Nisse, Alexandre Salch, and Valentin Weber. Recovery of disrupted airline operations using k-Maximum Matching in graphs. In IX Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS), IX Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS), Marseille, France, September 2017. [WWW ] [PDF ]
    Keywords: Graph, Matching, Augmenting paths, Complexity, Trees.
     
  11. Christelle Caillouet and Tahiry Razafindralambo. Efficient Deployment of Connected Unmanned Aerial Vehicles for Optimal Target Coverage. In IEEE, editor, GIIS 2017 - Global Information Infrastructure and Networking Symposium, Saint-Pierre, France, October 2017. [WWW ] [PDF ]
     
  12. Nathann Cohen, Frédéric Havet, Dorian Mazauric, Ignasi Sau, and Rémi Watrigant. Complexity Dichotomies for the Minimum F -Overlay Problem. In IWOCA 2017 - 28th International Workshop on Combinatorial Algorithms, Newcastle, Australia, pages 12, July 2017. [WWW ] [PDF ]
    Keywords: Hypergraph, Minimum F-Overlay Problem, NP-completeness, Fixed-parameter tractability.
     
  13. Nathann Cohen, Nìcolas Martins, Fionn Mc Inerney, Nicolas Nisse, Stéphane Pérennes, and Rudini Sampaio. Enquêter dans les graphes. In ALGOTEL 2017 - 19èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Quiberon, France, May 2017. [WWW ] [PDF ]
    Keywords: Programmation Linéaire, Mots-clefs : Jeux combinatoires à deux joueurs dans les graphes, Jeu de Gendarmes et Voleur.
     
  14. Nathann Cohen, Fionn Mc Inerney, Nicolas Nisse, and Stéphane Pérennes. Study of a combinatorial game in graphs through Linear Programming. In 28th International Symposium on Algorithms and Computation (ISAAC 2017), Phuket, Thailand, 2017. [WWW ] [PDF ]
    Keywords: Turn-by-turn games in graphs, Graph algorithms, Linear Programming.
     
  15. David Coudert and Guillaume Ducoffe. A simple approach for lower-bounding the distortion in any Hyperbolic embedding. In EUROCOMB'17 -- The European Conference on Combinatorics, Graph Theory and Applications, volume 61, Vienna, Austria, pages 293 - 299, August 2017. Elsevier. [WWW ] [PDF ]
    Keywords: Gromov hyperbolicity, Hyperbolic space, Cop and Robber games.
     
  16. David Coudert, James Luedtke, Eduardo Moreno, and Konstantinos Priftis. Computing and maximizing the exact reliability of wireless backhaul networks. In International Network Optimization Conference, Lisbon, Portugal, February 2017. [WWW ] [PDF ]
    Keywords: Network design, Backhaul network, Reliability, Optimization.
     
  17. Nicolas Huin, Brigitte Jaumard, and Frédéric Giroire. Optimization of Network Service Chain Provisioning. In IEEE International Conference on Communications 2017, Paris, France, May 2017. [WWW ] [PDF ]
    Keywords: service function chaining, SFC, column generation.
     
  18. Nicolas Huin, Myriana Rifai, Frédéric Giroire, Dino Lopez Pacheco, Guillaume Urvoy-Keller, and Joanna Moulierac. Bringing Energy Aware Routing closer to Reality with SDN Hybrid Networks. In GLOBECOM 2017 - IEEE Global Communications Conference, Singapore, Singapore, pages 7, December 2017. [WWW ] [PDF ]
     
  19. Nicolas Huin, Andrea Tomassilli, Frédéric Giroire, and Brigitte Jaumard. Energy-Efficient Service Function Chain Provisioning. In International Network Optimization Conference 2017, Lisbonne, Portugal, February 2017. [WWW ] [PDF ]
    Keywords: Network Function Virtualization, Service Function Chains, Software Defined Networks, Energy Efficiency, Optimization, Column Generation.
     
  20. Julien Bensmail, Valentin Garnero, and Nicolas Nisse. On improving matchings in trees, via bounded-length augmentations. Research Report, Université Côte d'Azur, July 2017. [WWW ] [PDF ]
    Keywords: trees, bounded-length augmentations, maximum matchings.
     
  21. Nathann Cohen, Nìcolas Martins, Fionn Mc Inerney, Nicolas Nisse, Stéphane Pérennes, and Rudini Sampaio. Spy-Game on graphs: complexity and simple topologies. Research Report, Inria Sophia Antipolis, 2017. [WWW ] [PDF ]
    Keywords: Cops and Robber games, graphs, PSPACE-hard.
     
  22. Nathann Cohen, Fionn Mc Inerney, Nicolas Nisse, and Stéphane Pérennes. Study of a combinatorial game in graphs through Linear Programming. Research Report, Inria Sophia Antipolis, 2017. [WWW ] [PDF ]
    Keywords: Linear Programming, Cops and Robber games, Graphs.
     
  23. David Coudert, Guillaume Ducoffe, and Alexandru Popa. Fully polynomial FPT algorithms for some classes of bounded clique-width graphs. Research Report, Inria - Sophia antipolis ; Universite Cote d'Azur ; University of Bucharest, Faculty of Mathematics and Computer Science ; National Institute for Research and Development in Informatics, Romania, July 2017. [WWW ] [PDF ]
    Keywords: Neighbourhood diversity, Primeval decomposition, Clique-width, Modular decomposition, Split decomposition, Hardness in P, Fully polynomial FPT, Graph algorithms.
     
  24. Guillaume Ducoffe, Ruxandra Marinescu-Ghemeci, and Alexandru Popa. On the (di)graphs with (directed) proper connection number two. Research Report, Université Côte d’Azur, Inria, CNRS, I3S, France ; University of Bucharest, Faculty of Mathematics and Computer Science ; National Institute for Research and Development in Informatics, Romania ; The Research Institute of the University of Bucharest ICUB, Romania, March 2017. [WWW ] [PDF ]
     
  25. Guillaume Ducoffe. Finding cut-vertices in the square roots of a graph. Research Report, Université Côte d’Azur, Inria, CNRS, I3S, France, February 2017. [WWW ] [PDF ]
    Keywords: square root, biconnected components, clique cutset, cactus-block graph, Gallai tree, cycle-power graph, circular-arc graph.
     
  26. Frédéric Giroire, Nicolas Huin, and Andrea Tomassilli. The Structured Way of Dealing with Heterogeneous Live Streaming Systems. Research Report RR-9070, Inria Sophia Antipolis ; Cnrs ; Universite Cote d'Azur, June 2017. [WWW ] [PDF ]
    Keywords: distributed algorithms, reliability, diffusion tree, protocols, churn, peer-to-peer, video streaming, pair-à-pair, diffusion video en direct, protocoles, fiabilité, arbre de diffusion, algorithmes distribués.
     
  27. Nicolas Huin, Myriana Rifai, Frédéric Giroire, Dino Lopez Pacheco, Guillaume Urvoy-Keller, and Joanna Moulierac. Bringing Energy Aware Routing closer to Reality with SDN Hybrid Networks. Research Report RR-9020, INRIA Sophia Antipolis - I3S ; I3S, January 2017. [WWW ] [PDF ]
    Keywords: Software Defined Network, energy saving, energy aware routing, hybrid network, packet loss.
     
  28. Kolja Knauer and Nicolas Nisse. Computing metric hulls in graphs. Research Report, Inria - Sophia Antipolis, 2017. [WWW ] [PDF ]
     
  29. Olivier Baudon, Julien Bensmail, Mohammed Senhaji, and Eric Sopena. Neighbour-Sum-2-Distinguishing Edge-Weightings: Doubling the 1-2-3 Conjecture.
    Note: Working paper or preprint, May 2017. [WWW ] [PDF ]
    Keywords: 1-2-3 Conjecture, Difference-2 distinction, Bipartite graphs.
     
  30. Julien Bensmail. A 1-2-3-4 result for the 1-2-3 Conjecture in 5-regular graphs.
    Note: Working paper or preprint, April 2017. [WWW ] [PDF ]
    Keywords: 1-2-3 Conjecture, four weights, 5-regular graphs.
     
2016
  1. Fedor V. Fomin, Pierre Fraigniaud, Nicolas Nisse, and Dimitrios M. Thilikos. Forewords: Special issue on Theory and Applications of Graph Searching Problems, volume 655:1 of Theoretical Computer Science - Special Issue on Theory and Applications of Graph Searching Problems. December 2016. [WWW ]
     
  2. Guillaume Ducoffe. Metric properties of large graphs. Theses, Université Côte d'Azur, December 2016. [WWW ] [PDF ]
    Keywords: Graph, Algorithms, Complexity in P, Gromov Hyperbolicity, Treelength, Treebreadth, Treewidth, Coloring games, Nash equilibrium, Boolean function learning, Algorithmes, Complexité dans P, Hyperbolicité, Jeux de coloration, Équilibre de Nash, Apprentissage de fonction booléenne, Graphe.
     
  3. J Araujo, Frédéric Giroire, J Moulierac, Yi Liu, and R Modrzejewski. Energy Efficient Content Distribution. The Computer Journal, 59(2):192-207, February 2016. [WWW ] [PDF ]
    Keywords: Energy Efficiency, Integer Linear Programming, Content Deliv-ery Network, In-network Caching, Future Internet.
     
  4. Julio Araujo, Frédéric Havet, Claudia Linhares Sales, and Ana Silva. Proper orientation of cacti. Journal of Theoretical Computer Science (TCS), 639:14-25, 2016. [WWW ] [PDF ]
    Keywords: proper orientation, graph coloring, cactus graph, claw-free graph, planar graph, block graph.
     
  5. Julio Araujo, Gregory Morel, Leonardo Sampaio, Ronan Soares, and Valentin Weber. Hull number: P5-free graphs and reduction rules. Discrete Applied Mathematics, 210:171 - 175, September 2016. [WWW ]
     
  6. Joergen Bang-Jensen, Nathann Cohen, and Frédéric Havet. Finding good 2-partitions of digraphs II. Enumerable properties. Journal of Theoretical Computer Science (TCS), 640:1-19, August 2016. [WWW ] [PDF ]
    Keywords: Feedback vertex set, Out-branching, Tournament, Oriented, NP-complete, Polynomial, Partition, Splitting digraphs, Acyclic, Semicomplete digraph, 2-Partition, Minimum degree.
     
  7. J Bang-Jensen, Frédéric Havet, and Anders Yeo. The complexity of finding arc-disjoint branching flows. Discrete Applied Mathematics, 209:16-26, 2016. [WWW ] [PDF ]
     
  8. J Bang-Jensen and Frédéric Havet. Finding good 2-partitions of digraphs I. Hereditary properties. Journal of Theoretical Computer Science (TCS), 636:85--94, 2016. [WWW ] [PDF ]
    Keywords: minimum degree, 2-partition, tournament, out-branching, feedback vertex set, oriented, NP-complete, polynomial, partition, splitting digraphs, acyclic, semicomplete digraph.
     
  9. Jean-Claude Bermond, Cristiana Gomes Huiban, and Patricio Reyes. Round weighting problem and gathering in radio networks with symmetrical interference. Discrete Mathematics, Algorithms and Applications, 8(2):1650035 57 pages, 2016. [WWW ]
    Keywords: Radio networks, wireless networks, interference, grids, gathering, bounds, approximation algorithms..
     
  10. Jean-Claude Bermond, Alain Jean-Marie, Dorian Mazauric, and Joseph Yu. Well Balanced Designs for Data Placement. Journal of Combinatorial Designs, 24(2):55-76, February 2016. [WWW ] [PDF ]
     
  11. David Coudert and Guillaume Ducoffe. On the hyperbolicity of bipartite graphs and intersection graphs. Discrete Applied Mathematics, 214:187-195, 2016. [WWW ] [PDF ]
    Keywords: biclique graph, line graph, clique graph, Gromov hyperbolicity, bipartite graph, intersection graph, graph power.
     
  12. David Coudert, Guillaume Ducoffe, and Nicolas Nisse. To Approximate Treewidth, Use Treelength!. Siam Journal on Discrete Mathematics, 30(3):13, 2016. [WWW ] [PDF ]
    Keywords: Graph, Treewidth, Treelength, Cycle basis, Genus.
     
  13. David Coudert and Guillaume Ducoffe. Data center interconnection networks are not hyperbolic. Theoretical Computer Science, 639:72-90, 2016. [WWW ] [PDF ]
    Keywords: interconnection network, data center, Cayley graph, greedy routing scheme, metric embedding, graph endomorphism, Gromov hy-perbolicity.
     
  14. David Coudert, Dorian Mazauric, and Nicolas Nisse. Experimental Evaluation of a Branch and Bound Algorithm for Computing Pathwidth and Directed Pathwidth. ACM Journal of Experimental Algorithmics, 21(1):23, 2016. [WWW ] [PDF ]
     
  15. David Coudert, Stéphane Pérennes, Hervé Rivano, and Marie-Emilie Voge. Combinatorial optimization in networks with Shared Risk Link Groups. Discrete Mathematics and Theoretical Computer Science, Vol. 18, no 3:25, May 2016. [WWW ] [PDF ]
    Keywords: colored graphs, Shared Risk Link Group, complexity, algorithms, Multi-layer networks.
     
  16. Nicolas Nisse and Ronan Pardo Soares. On the Monotonicity of Process Number. Discrete Applied Mathematics, 210:103-111, 2016. [WWW ] [PDF ]
    Keywords: Graph Searching, Process Number, Monotonicity.
     
  17. Jean-Claude Bermond, Nathann Cohen, David Coudert, Dimitrios Letsios, Ioannis Milis, Stéphane Pérennes, and Vassilis Zissimopoulos. Bin Packing with Colocations. In Klaus Jansen and Monaldo Mastrolilli, editors, 14th International Workshop on Approximation and Online Algorithms (WAOA), volume 10138, Aarhus, Denmark, pages 40-51, August 2016. Springer. [WWW ] [PDF ]
     
  18. Marwane Bouznif, Frédéric Havet, and Myriam Preissmann. Minimum-Density Identifying Codes in Square Grids. In 11th International Conference, AAIM 2016, volume 9778 of Lecture Notes in Computer Science, Bergamo, Italy, pages 77-88, July 2016. Riccardo Dondi, Springer. [WWW ] [PDF ]
    Keywords: identifying code, square grid, discharging method.
     
  19. Nathann Cohen, Frédéric Havet, William Lochet, and Nicolas Nisse. Subdivisions of oriented cycles in digraphs with large chromatic number. In Bordeaux Graph Wokshop 2016, Bordeaux, France, pages 85-88, November 2016. [WWW ] [PDF ]
     
  20. Nathann Cohen, Mathieu Hilaire, Nicolas Martins, Nicolas Nisse, and Stéphane Pérennes. Spy-Game on graphs. In Erik D. Demaine and Fabrizio Grandoni, editors, 8th International Conference on Fun with Algorithms, FUN 2016, volume 49 of Leibniz International Proceedings in Informatics (LIPIcs), La Maddalena, Maddalena Islands, Italy, 2016. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. [WWW ] [PDF ]
     
  21. David Coudert and Guillaume Ducoffe. Liens entre symétries et étirements de routages dans les réseaux d'interconnexions de centres de données. In ALGOTEL 2016 - 18èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Bayonne, France, May 2016. [WWW ] [PDF ]
    Keywords: Mots-clefs : Graphe, Centre de données, Routage géométrique, Endomorphisme de graphe, Hyperbolicité.
     
  22. Rennan Dantas, Frédéric Havet, and Rudini M Sampaio. Identifying codes for infinite triangular grids with a finite number of rows. In Bordeaux Graph Workshop 2016, Bordeaux, France, November 2016. [WWW ] [PDF ]
     
  23. Guillaume Ducoffe. The Parallel Complexity of Coloring Games. In Martin Gairing and Rahul Savani, editors, 9th International Symposium, SAGT 2016, number 9928 of Algorithmic Game Theory, Liverpool, United Kingdom, pages 27-39, September 2016. Springer International Publishing. [WWW ] [PDF ]
     
  24. Guillaume Ducoffe, Sylvain Legay, and Nicolas Nisse. On the Complexity of Computing Treebreadth. In Veli Mäkinen, Simon J. Puglisi, and Leena Salmela, editors, 27th International Workshop on Combinatorial Algorithms, IWOCA 2016, number 9843 of Combinatorial Algorithms, Helsinki, Finland, pages 3-15, August 2016. Springer International Publishing. [WWW ] [PDF ]
     
  25. Frédéric Giroire and Nicolas Huin. Étude d'un système distribué de diffusion de vidéo en direct. In ALGOTEL 2016 - 18èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Bayonne, France, May 2016. [WWW ] [PDF ]
    Keywords: pair-à-pair.
     
  26. Myriana Rifai, Nicolas Huin, Christelle Caillouet, Frédéric Giroire, Joanna Moulierac, Dino Lopez Pacheco, and Guillaume Urvoy-Keller. MINNIE : enfin un monde SDN sans (trop de) règles. In ALGOTEL 2016 - 18èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Bayonne, France, May 2016. [WWW ] [PDF ]
     
  27. Julio Araujo, Guillaume Ducoffe, Nicolas Nisse, and Karol Suchan. On interval number in cycle convexity. Research Report, Inria Sophia Antipolis ; I3S, 2016. [WWW ] [PDF ]
    Keywords: graph, convexity, complexity, dominating set.
     
  28. Julio Araujo, Frédéric Giroire, Yaning Y.L. Liu, Remigiusz Modrzejewski, and Joanna Moulierac. Energy Efficient Content Distribution. Research Report RR-8091, INRIA, January 2016. [WWW ] [PDF ]
    Keywords: Energy Efficiency, Integer Linear Programming, Content Delivery Network, Net- work Cache, Future Internet.
     
  29. Jorgen Bang-Jensen, Nathann Cohen, and Frédéric Havet. Finding good 2-partitions of digraphs II. Enumerable properties. Research Report RR-8868, INRIA Sophia Antipolis - I3S, February 2016. [WWW ] [PDF ]
     
  30. Jorgen Bang-Jensen and Frédéric Havet. Finding good 2-partitions of digraphs I. Hereditary properties. Research Report RR-8867, INRIA Sophia Antipolis - I3S, February 2016. [WWW ] [PDF ]
     
  31. Olivier Baudon, Julien Bensmail, Hervé Hocquard, Mohammed Senhaji, and Eric Sopena. On locally irregular decompositions of subcubic graphs. Research Report, Université de bordeaux ; Université de Nice - Sophia Antipolis, 2016. [WWW ] [PDF ]
     
  32. Olivier Baudon, Julien Bensmail, Jakub Przybylo, and Mariusz Wozniak. On locally irregular decompositions and the 1-2 Conjecture in digraphs. Research Report, Inria, CNRS, Université de Bordeaux, AGH University, September 2016. [WWW ] [PDF ]
     
  33. Jean-Claude Bermond, Nathann Cohen, David Coudert, Dimitrios Letsios, Ioannis Milis, Stéphane Pérennes, and Vassilis Zissimopoulos. Bin packing with colocations. Research Report, Inria ; I3S, October 2016. [WWW ] [PDF ]
     
  34. Marwane Bouznif, Frédéric Havet, and Myriam Preissmann. Minimum-density identifying codes in square grids. Research Report RR-8845, INRIA Sophia Antipolis - I3S, January 2016. [WWW ] [PDF ]
     
  35. Nathann Cohen, Frédéric Havet, William Lochet, and Nicolas Nisse. Subdivisions of oriented cycles in digraphs with large chromatic number. Research Report RR-8865, LRI - CNRS, University Paris-Sud ; LIP - ENS Lyon ; INRIA Sophia Antipolis - I3S, February 2016. [WWW ] [PDF ]
     
  36. Nathann Cohen, Mathieu Hilaire, Nicolas Martins, Nicolas Nisse, and Stéphane Pérennes. Spy-Game on graphs. Research Report RR-8869, Inria, February 2016. [WWW ] [PDF ]
     
  37. David Coudert and Guillaume Ducoffe. Clique-decomposition revisited. Research Report, INRIA Sophia Antipolis - I3S, February 2016. [WWW ] [PDF ]
    Keywords: planar graphs, treewidth, clique-decomposition, minimal triangulation, clique-number, bounded-degree graphs.
     
  38. David Coudert. A note on Integer Linear Programming formulations for linear ordering problems on graphs. Research Report, Inria ; I3S ; Universite Nice Sophia Antipolis ; CNRS, February 2016. [WWW ] [PDF ]
     
  39. David Coudert, Guillaume Ducoffe, Nicolas Nisse, and Mauricio Soto. Distance-preserving orderings in graphs. Research Report RR-8973, Inria Sophia Antipolis, 2016. [WWW ] [PDF ]
    Keywords: bounded treewidth, distance-preserving elimination ordering, metric graph theory, NP-complete, exact expo- nential algorithm, integer linear programming.
     
  40. David Coudert, James Luedtke, Eduardo Moreno, and Konstantinos Priftis. Computing and maximizing the exact reliability of wireless backhaul networks. Research Report, Inria Sophia Antipolis ; I3S, November 2016. [WWW ] [PDF ]
    Keywords: Network design, Backhaul network, Reliability, Optimization.
     
  41. Rennan Dantas, Frédéric Havet, and Rudini Sampaio. Identifying codes for infinite triangular grids with a finite number of rows. Research Report RR-8951, INRIA Sophia Antipolis - I3S, August 2016. [WWW ] [PDF ]
    Keywords: identifying code, grid, discharging method, méthode de déchargement, grille, code identifiant.
     
  42. Guillaume Ducoffe, Sylvain Legay, and Nicolas Nisse. On computing tree and path decompositions with metric constraints on the bags. Research Report RR-8842, INRIA Sophia Antipolis - Méditerranée ; LRI - CNRS, University Paris-Sud, January 2016. [WWW ] [PDF ]
    Keywords: path-breadth, k-good tree decompositions, tree-length, tree-breadth, path-length.
     
  43. Frédéric Giroire, Nicolas Huin, Joanna Moulierac, and Khoa Phan. Energy-Aware Routing in Software-Defined Networks with Table Compression (using Wildcard Rules). Research Report RR-8897, INRIA Sophia Antipolis - I3S, April 2016. [WWW ] [PDF ]
    Keywords: energy savings, backbone networks, Software Defined Networks, data center networks, routing tables, compression, TCAM memory, réseaux programmables, réseaux de centre de données, table de routage, mémoire TCAM, économie d'énergie, réseau backbone.
     
  44. Frédéric Giroire and Juan-Carlos Maureira. Analysis of the Failure Tolerance of Linear Access Networks. Research Report RR-8903, CNRS, University of Nice Sophia Antipolis, I3S, UMR 7271, COATI, Inria, 06900 Sophia Antipolis, France ; Center of Mathematical Modeling, University of Chile, Chile ; Inria Sophia Antipolis, April 2016. [WWW ] [PDF ]
    Keywords: Access networks, failure tolerance, telecommuting, connectivity analysis, maintenance cost.
     
  45. Nicolas Huin, Andrea Tomassilli, Frédéric Giroire, and Brigitte Jaumard. Energy-Efficient Service Function Chain Provisioning. Research Report RR-8980, Inria Sophia Antipolis ; Université Côte d'Azur ; Cnrs ; Concordia University, November 2016. [WWW ] [PDF ]
    Keywords: Column Generation, Network Function Virtualization, Service Function Chains, Software Defined Networks, Energy Efficiency, Optimization, Optimisation, Efficacité énergétique, Réseaux logiciels, Virtualisation des fonctions réseaux, Chaînes de fonctions de service, Génération de Colonnes.
     
  46. Myriana Rifai, Nicolas Huin, Christelle Caillouet, Frédéric Giroire, Joanna Moulierac, Dino Lopez Pacheco, and Guillaume Urvoy-Keller. MINNIE: an SDN World with Few Compressed Forwarding Rules. Research Report RR-8848, INRIA Sophia-Antipolis ; I3S, January 2016. [WWW ] [PDF ]
    Keywords: Software Defined Networks, data center networks, routing tables, compression, TCAM memory.
     
  47. Andrea Tomassilli, Nicolas Huin, Frédéric Giroire, and Brigitte Jaumard. Energy-Efficient Service Chains with Network Function Virtualization. Research Report RR-8979, Inria Sophia Antipolis ; Université Côte d'Azur ; Cnrs ; Concordia University, October 2016. [WWW ] [PDF ]
    Keywords: Optimization, Energy Efficiency, Network Function Virtualization, Service Function Chains, Software Defined Networks, Chaînes de fonctions de service, Virtualisation des fonctions réseaux, Réseaux logiciels, Efficacité énergétique, Optimisation.
     
  48. Luc Hogie, Michel Syska, and Nicolas Chleq. BigGraphs: distributed graph computing, September 2016. [WWW ]
     
  49. Pierre Aboulker, Jorgen Bang-Jensen, Nicolas Bousquet, Pierre Charbit, Frédéric Havet, Frédéric Maffray, and Jose Zamora. $\chi$-bounded families of oriented graphs.
    Note: Working paper or preprint, 2016. [WWW ] [PDF ]
     
  50. Seong-Gyun Jeong, Yuliya Tarabalka, Nicolas Nisse, and Josiane Zerubia. Progressive Tree-like Curvilinear Structure Reconstruction with Structured Ranking Learning and Graph Algorithm.
    Note: Working paper or preprint, December 2016. [WWW ] [PDF ]
     
2015
  1. Mohamed Amine BERGACH. Adaptation of the Fast Fourier Transform processing on hybride integrated CPU/GPU architecture. Theses, Université Nice Sophia Antipolis, October 2015. [WWW ] [PDF ]
    Keywords: FFT, GPGPU, CPU, SIMD, SIMT, AAA, OpenCL.
    Abstract:
    Les architectures multi-c{\oe}urs Intel Core (IvyBridge, Haswell,...) contiennent {\`a} la fois des c{\oe}urs CPU g{\'e}n{\'e}ralistes (4), mais aussi des c{\oe}urs d{\'e}di{\'e}s GPU embarqu{\'e}s sur cette m{\^e}me puce (16 et 40 respectivement). Dans le cadre de l'activit{\'e} de la soci{\'e}t{\'e} Kontron (qui participe {\`a} ce financement de nature CIFRE) un objectif important est de calculer efficacement sur cette architecture des tableaux et s{\'e}quences de transform{\'e}es de Fourier rapides (FFT), comme par exemple on en trouve dans des applications radar. Alors que des biblioth{\`e}ques natives (mais propri{\'e}taires) existent chez Intel pour les CPU, rien de tel n'est actuellement disponible pour la partie GPU. L'objectif de la th{\`e}se {\'e}tait donc de d{\'e}finir le placement efficace de modules FFT, en {\'e}tudiant au niveau th{\'e}orique la forme optimale permettant de regrouper des {\'e}tages de calcul d'une telle FFT en fonction de la localit{\'e} des donn{\'e}es sur un c{\oe}ur de calcul unique. Ce choix a priori permet d'esp{\'e}rer une efficacit{\'e} des traitements, en ajustant la taille de la m{\'e}moire disponible {\`a} celles des donn{\'e}es n{\'e}cessaires. Ensuite la multiplicit{\'e} des c{\oe}urs reste exploitable pour disposer plusieurs FFT calcul{\'e}es en parall{\`e}le, sans interf{\'e}rence (sauf contention du bus entre CPU et GPU). Nous avons obtenu des r{\'e}sultats significatifs, tant au niveau de l'implantation d'une FFT (1024 points) sur un c{\oe}ur CPU SIMD, exprim{\'e}e en langage C, que pour l'implantation d'une FFT de m{\^e}me taille sur un c{\oe}ur GPU SIMT, exprim{\'e}e alors en OpenCL. De plus nos r{\'e}sultats permettent de d{\'e}finir des r{\`e}gles pour synth{\'e}tiser automatiquement de telles solutions, en fonction uniquement de la taille de la FFT son nombre d'{\'e}tages plus pr{\'e}cis{\'e}ment), et de la taille de

     
  2. Fatima Zahra Moataz. Towards efficient and fault-tolerant optical networks : complexity and algorithms. Theses, Université Nice Sophia Antipolis, October 2015. [WWW ] [PDF ]
    Keywords: Routing and spectrum assignment, Tree-decomposition, Complexity, Asymmetric nodes, Forbidden transitions, Shared risk link group, Noeuds asymétriques, Transitions interdites, Groupe de liens partageant un risque, Routage et allocation de spectre, Décomposition arborescente, Complexité.
    Abstract:
    Nous {\'e}tudions dans cette th{\`e}se des probl{\`e}mes d’optimisation avec applications dans les r{\'e}seaux optiques. Les probl{\`e}mes {\'e}tudi{\'e}s sont li{\'e}s {\`a} la tol{\'e}rance aux pannes et {\`a} l’utilisation efficace des ressources. Les r{\'e}sultats obtenus portent principalement sur la complexit{\'e} de calcul de ces probl{\`e}mes. La premi{\`e}re partie de cette th{\`e}se est consacr{\'e}e aux probl{\`e}mes de trouver des chemins et des chemins disjoints. La recherche d’un chemin est essentielle dans tout type de r{\'e}seaux afin d’y {\'e}tablir des connexions et la recherche de chemins disjoints est souvent utilis{\'e}e pour garantir un certain niveau de protection contre les pannes dans les r{\'e}seaux. Nous {\'e}tudions ces probl{\`e}mes dans des contextes diff{\'e}rents. Nous traitons d’abord les probl{\`e}mes de trouver un chemin et des chemins lien ou n{\oe}ud- disjoints dans des r{\'e}seaux avec n{\oe}uds asym{\'e}triques, c’est-{\`a}-dire des n{\oe}uds avec restrictions sur leur connectivit{\'e} interne. Ensuite, nous consid{\'e}rons les r{\'e}seaux avec des groupes de liens partageant un risque (SRLG) en {\'e}toile : ensembles de liens qui peuvent tomber en panne en m{\^e}me temps suite {\`a} un {\'e}v{\'e}nement local. Dans ce type de r{\'e}seaux, nous examinons le probl{\`e}me de recherche des chemins SRLG-disjoints. La deuxi{\`e}me partie de cette th{\`e}se est consacr{\'e}e au probl{\`e}me de routage et d’allocation de spectre (RSA) dans les r{\'e}seaux optiques {\'e}lastiques (EONs). Les EONs sont propos{\'e}s comme la nouvelle g{\'e}n{\'e}ration des r{\'e}seaux optiques et ils visent une utilisation plus efficace et flexible des ressources optiques. Le probl{\`e}me RSA est central dans les EONs. Il concerne l’allocation de ressources aux requ{\^e}tes sous plusieurs contraintes.

     
  3. Deepesh Agarwal, Christelle Caillouet, David Coudert, and Frédéric Cazals. Unveiling Contacts within Macro-molecular assemblies by solving Minimum Weight Connectivity Inference Problems. Molecular and Cellular Proteomics, 14:2274-2284, April 2015. [WWW ] [PDF ]
    Keywords: Biophysics, Bioinformatics, Mathematical Modeling, connectivity inference, Algorithms, Mass Spectrometry, Structural Biology.
    Abstract:
    Consider a set of oligomers listing the subunits involved in sub-complexes of a macro-molecular assembly, obtained e.g. using native mass spectrometry or affinity purification. Given these oligomers, connectivity inference (CI) consists of finding the most plausible contacts between these subunits, and minimum connectivity inference (MCI) is the variant consisting of finding a set of contacts of smallest cardinality. MCI problems avoid speculating on the total number of contacts, but yield a subset of all contacts and do not allow exploiting a priori information on the likelihood of individual contacts. In this context, we present two novel algorithms, MILP-W and MILP-WB. The former solves the minimum weight connectivity inference (MWCI), an optimization problem whose criterion mixes the number of contacts and their likelihood. The latter uses the former in a bootstrap fashion, to improve the sensitivity and the specificity of solution sets. Experiments on three systems (yeast exosome, yeast proteasome lid, human eiF3), for which reference contacts are known (crystal structure, cryo electron microscopy, cross-linking), show that our algorithms predict contacts with high specificity and sensitivity, yielding a very significant improvement over previous work, typically a twofold increase in sensitivity. The software accompanying this paper is made available, and should prove of ubiquitous interest whenever connectivity inference from oligomers is faced.

     
  4. Omid Amini, David Coudert, and Nicolas Nisse. Non-deterministic graph searching in trees. Journal of Theoretical Computer Science (TCS), 580:101-121, May 2015. [WWW ] [PDF ]
    Keywords: Pathwidth, Trees, Graph Searching, Treewidth.
    Abstract:
    Non-deterministic graph searching was introduced by Fomin et al. to provide a unified approach for pathwidth, treewidth, and their interpretations in terms of graph searching games. Given q $\ge$ 0, the q-limited search number, s q (G), of a graph G is the smallest number of searchers required to capture an invisible fugitive in G, when the searchers are allowed to know the position of the fugitive at most q times. The search parameter s 0 (G) corresponds to the pathwidth of a graph G, and s $\infty$ (G) to its treewidth. Determining s q (G) is NP-complete for any fixed q $\ge$ 0 in general graphs and s 0 (T) can be computed in linear time in trees, however the complexity of the problem on trees has been unknown for any q \textgreater{} 0. We introduce a new variant of graph searching called restricted non-deterministic. The corresponding parameter is denoted by rs q and is shown to be equal to the non-deterministic graph searching parameter s q for q = 0, 1, and at most twice s q for any q $\ge$ 2 (for any graph G). Our main result is a polynomial time algorithm that computes rs q (T) for any tree T and any q $\ge$ 0. This provides a 2-approximation of s q (T) for any tree T , and shows that the decision problem associated to s 1 is polynomial in the class of trees. Our proofs are based on a new decomposition technique for trees which might be of independent interest.

     
  5. Julio Araujo, Nathann Cohen, Susanna F. De Rezende, Frédéric Havet, and Phablo Moura. On the proper orientation number of bipartite graphs. Journal of Theoretical Computer Science (TCS), 566:59-75, February 2015. [WWW ]
    Abstract:
    An {\it orientation} of a graph $G$ is a digraph $D$ obtained from $G$ by replacing each edge by exactly one of the twopossible arcs with the same endvertices.For each $v \in V(G)$, the \emph{indegree} of $v$ in $D$, denoted by $d^-\_D(v)$, is the number of arcs with head $v$ in $D$.An orientation $D$ of $G$ is \emph{proper} if $d^-\_D(u)\neq d^-\_D(v)$, for all $uv\in E(G)$.The \emph{proper orientation number} of a graph $G$, denoted by $po(G)$, is the minimum of the maximumindegree over all its proper orientations. In this paper, we prove that $po(G) \leq \left(\Delta(G) + \sqrt{\Delta(G)}\right)/2 + 1$ if $G$ is a bipartite graph, and $po(G)\leq 4$ if $G$ is a tree.% Moreover, we show that deciding whether the proper orientation number is at most~2 and at most~3 0s an $NP$-complete problem for planar subcubic graphs and planar bipartite graphs, respectively. It is well-known that $po(G)\leq \Delta(G)$, for every graph $G$.However, we prove that deciding whether $po(G)\leq \Delta(G)-1$ is already an $NP$-complete problem on graphs with $\Delta(G) = k$, for every $k \geq 3$.We also show that it is $NP$-complete to decide whether $po(G)\leq 2$, for planar \emph{subcubic} graphs $G$. Moreover, we prove that it is $NP$-complete to decide whether $po(G)\leq 3$, for planar bipartite graphs $G$ with maximum degree 5.

     
  6. Julio Araujo, Frédéric Havet, and Mathieu Schmitt. Steinberg-like theorems for backbone colouring. Electronic Notes in Discrete Mathematics, pp 223-229, December 2015. [WWW ] [PDF ]
    Keywords: Graph Colouring, Planar Graph, Backbone Colouring, Steinberg's Conjecture.
    Abstract:
    A function f:V(G)$\rightarrow${1,…,k}f:V(G)$\rightarrow${1,…,k} is a (proper) k-colouring of G if |f(u)--f(v)|$\ge$1|f(u)--f(v)|$\ge$1, for every edge uv$\in$E(G)uv$\in$E(G). The chromatic number $\chi$(G)$\chi$(G) is the smallest integer k for which there exists a proper k-colouring of G.Given a graph G and a subgraph H of G, a circular q-backbone k-colouring c of (G, H) is a k-colouring of G such that q$\le$|c(u)--c(v)|$\le$k--qq$\le$|c(u)--c(v)|$\le$k--q, for each edge uv$\in$E(H)uv$\in$E(H). The circular q-backbone chromatic number of a graph pair (G, H ), denoted CBCq(G,H)CBCq(G,H), is the minimum k such that (G, H) admits a circular q-backbone k-colouring.In this work, we first show that if G is a planar graph containing no cycle on 4 or 5 vertices and H$\subseteq$GH$\subseteq$G is a forest, then CBC2(G,H)$\le$7CBC2(G,H)$\le$7. Then, we prove that if H$\subseteq$GH$\subseteq$G is a forest whose connected components are paths, then CBC2(G,H)$\le$6CBC2(G,H)$\le$6.

     
  7. Jorgen Bang-Jensen, Frédéric Havet, and Ana Karolinna MAIA DE OLIVEIRA. Finding a subdivision of a digraph. Theoretical Computer Science, 562:20, 2015. [WWW ] [PDF ]
    Abstract:
    We consider the following problem for oriented graphs and digraphs: Given a directed graph D, does it contain a subdivision of a prescribed digraph F? We give a number of examples of polynomial instances, several NP-completeness proofs as well as a number of conjectures and open problems.

     
  8. Florent Becker, Adrian Kosowski, Martin Matamala, Nicolas Nisse, Ivan Rapaport, Karol Suchan, and Ioan Todinca. Allowing each node to communicate only once in a distributed system: shared whiteboard models. Distributed Computing, 28(3):189-200, 2015. [WWW ] [PDF ]
    Abstract:
    In this paper we study distributed algorithms on massive graphs where links represent a particular relationship between nodes (for instance, nodes may represent phone numbers and links may indicate telephone calls). Since such graphs are massive they need to be processed in a distributed way. When computing graph-theoretic properties, nodes become natural units for distributed computation. Links do not necessarily represent communication channels between the computing units and therefore do not restrict the communication flow. Our goal is to model and analyze the computational power of such distributed systems where one computing unit is assigned to each node. Communication takes place on a whiteboard where each node is allowed to write at most one message. Every node can read the contents of the whiteboard and, when activated, can write one small message based on its local knowledge. When the protocol terminates its output is computed from the final contents of the whiteboard. We describe four synchronization models for accessing the whiteboard. We show that message size and synchronization power constitute two orthogonal hierarchies for these systems.We exhibit problems that separate these models, i.e., that can be solved in one model but not in a weaker one, even with increased message size. These problems are related to maximal independent set and connectivity. We also exhibit problems that require a given message size independently of the synchronization model.

     
  9. Jean-Claude Bermond, David Coudert, Gianlorenzo D 'angelo, and Fatima Zahra Moataz. Finding disjoint paths in networks with star shared risk link groups. Journal of Theoretical Computer Science (TCS), 579:74-87, May 2015. [WWW ] [PDF ]
    Keywords: Diverse routing, Shared Risk Link Group, Complexity, Algorithms, Disjoint paths, Colored graph.
    Abstract:
    The notion of Shared Risk Link Groups (SRLG) has been introduced to capture surviv-ability issues where some links of a network fail simultaneously. In this context, the k-diverse routing problem is to find a set of k pairwise SRLG-disjoint paths between a given pair of end nodes of the network. This problem has been proven NP-complete in general and some polynomial instances have been characterized. In this paper, we investigate the k-diverse routing problem in networks where the SRLGs are localized and satisfy the star property. This property states that a link may be subject to several SRLGs, but all links subject to a given SRLG are incident to a common node. We first provide counterexamples to the polynomial time algorithm proposed by X. Luo and B. Wang (DRCN'05) for computing a pair of SRLG-disjoint paths in networks with SRLGs satisfying the star property, and then prove that this problem is in fact NP-complete. We then characterize instances that can be solved in polynomial time or are fixed parameter tractable, in particular when the number of SRLGs is constant, the maximum degree of the vertices is at most 4, and when the network is a directed acyclic graph. Finally we consider the problem of finding the maximum number of SRLG-disjoint paths in networks with SRLGs satisfying the star property. We prove that this problem is NP-hard to approximate within O(|V | 1--$\epsilon$) for any 0 \textless{} $\epsilon$ \textless{} 1, where V is the set of nodes in the network. Then, we provide exact and approximation algorithms for relevant subcases.

     
  10. Jean-Claude Bermond, Bi Li, Nicolas Nisse, Hervé Rivano, and Min-Li Yu. Data gathering and personalized broadcasting in radio grids with interference. Journal of Theoretical Computer Science (TCS), 562:453-475, 2015. [WWW ] [PDF ]
    Keywords: Gathering, Personalized broadcasting, Interference, Grid, Radio networks.
    Abstract:
    In the gathering problem, a particular node in a graph, the base station , aims at receiving messages from some nodes in the graph. At each step, a node can send one message to one of its neighbors (such an action is called a call ). However, a node cannot send and receive a message during the same step. Moreover, the communication is subject to interference constraints, more precisely, two calls interfere in a step, if one sender is at distance at most dI from the other receiver. Given a graph with a base station and a set of nodes having some messages, the goal of the gathering problem is to compute a schedule of calls for the base station to receive all messages as fast as possible, i.e., minimizing the number of steps (called makespan). The gathering problem is equivalent to the personalized broadcasting problem where the base station has to send messages to some nodes in the graph, with same transmission constraints.In this paper, we focus on the gathering and personalized broadcasting problem in grids. Moreover, we consider the non-buffering model: when a node receives a message at some step, it must transmit it during the next step. In this setting, though the problem of determining the complexity of computing the optimal makespan in a grid is still open, we present linear (in the number of messages) algorithms that compute schedules for gathering with dI$\in${0,1,2}. In particular, we present an algorithm that achieves the optimal makespan up to an additive constant 2 when dI=0. If no messages are "close" to the axes (the base station being the origin), our algorithms achieve the optimal makespan up to an additive constant 1 when dI=0, 4 when dI=2, and 3 when both dI=1 and the base station is in a corner. Note that, the approximation algorithms that we present also provide approximation up to a ratio 2 for the gathering with buffering. All our results are proved in terms of personalized broadcasting.

     
  11. Nathann Cohen, David Coudert, and Aurélien Lancin. On computing the Gromov hyperbolicity. ACM Journal on Experimental Algorithmics, 20(1):18, 2015. [WWW ] [PDF ]
    Keywords: Algorithms, Gromov Hyperbolicity, Networks.
    Abstract:
    The Gromov hyperbolicity is an important parameter for analyzing complex networks which expresses how the metric structure of a network looks like a tree. It is for instance used to provide bounds on the expected stretch of greedy-routing algorithms in Internet-like graphs. However, the best known theoretical algorithm computing this parameter runs in O(n^3.69) time, which is prohibitive for large-scale graphs. In this paper, we propose an algorithm for determining the hyperbolicity of graphs with tens of thousands of nodes. Its running time depends on the distribution of distances and on the actual value of the hyperbolicity. Although its worst case runtime is O(n^4), it is in practice much faster than previous proposals as observed in our experimentations. Finally, we propose a heuristic algorithm that can be used on graphs with millions of nodes. Our algorithms are all evaluated on benchmark instances.

     
  12. David Coudert, Alvinice Kodjo, and Truong Khoa Phan. Robust Energy-aware Routing with Redundancy Elimination. Computers and Operations Research, 64:21, December 2015. [WWW ] [PDF ]
    Keywords: Robust Network Optimization, Green Networking, Energy-aware Routing, Redundancy Elimination.
    Abstract:
    Many studies in literature have shown that energy-aware routing (EAR) can significantly reduce energy consumption for backbone networks. Also, as an arising concern in networking research area, the protocol-independent traffic redundancy elimination (RE) technique helps to reduce (a.k.a compress) traffic load on backbone network. Motivation from a formulation perspective, we first present an extended model of the classical multi-commodity flow problem with compressible flows. Moreover, our model is robust with fluctuation of traffic demand and compression rate. In details, we allow any set of a predefined size of traffic flows to deviate simultaneously from their nominal volumes or compression rates. As an applicable example, we use this model to combine redundancy elimination and energy-aware routing to increase energy efficiency for a backbone network. Using this extra knowledge on the dynamics of the traffic pattern, we are able to significantly increase energy efficiency for the network. We formally define the problem and model it as a Mixed Integer Linear Program (MILP). We then propose an efficient heuristic algorithm that is suitable for large networks. Simulation results with real traffic traces on Abilene, Geant and Germany50 networks show that our approach allows for 16-28 4.689922e-262xtra energy saving with respect to the classical EAR model.

     
  13. Gianlorenzo d'Angelo, Gabriele Di Stefano, Alfredo Navarra, Nicolas Nisse, and Karol Suchan. Computing on rings by oblivious robots: a unified approach for different tasks. Algorithmica, 72(4):1055-1096, 2015. [WWW ] [PDF ]
    Abstract:
    A set of autonomous robots have to collaborate in order to accomplish a common task in a ring-topology where neither nodes nor edges are labeled (that is, the ring is anonymous). We present a unified approach to solve three important problems: the exclusive perpetual exploration, the exclusive perpetual clearing, and the gathering problems. In the first problem, each robot aims at visiting each node infinitely often while avoiding that two robots occupy a same node (exclusivity property); in exclusive perpetual clearing (also known as searching), the team of robots aims at clearing the whole ring infinitely often (an edge is cleared if it is traversed by a robot or if both its endpoints are occupied); and in the gathering problem, all robots must eventually occupy the same node. We investigate these tasks in the Look-Compute-Move model where the robots cannot communicate but can perceive the positions of other robots. Each robot is equipped with visibility sensors and motion actuators, and it operates in asynchronous cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it eventually moves to this neighbor (Move). Moreover, robots are endowed with very weak capabilities. Namely, they are anonymous, asynchronous, oblivious, uniform (execute the same algorithm) and have no common sense of orientation. In this setting, we devise algorithms that, starting from an exclusive and rigid (i.e. aperiodic and asymmetric) configuration, solve the three above problems in anonymous ring-topologies.

     
  14. Olivier Delmas, Frédéric Havet, and Mickaël Montassier. Design of fault-tolerant on-board networks with variable switch sizes. Theoretical Computer Science, 562:15, 2015. [WWW ]
    Abstract:
    An \emph{$(n,k,r)$-network} is a triple $N=(G,\inp,\outp)$ where $G=(V,E)$is a graph and $\inp,\outp$ are non-negative integer functions defined on $V$ calledthe \emph{input} and \emph{output} functions, such that for any $v \in V$,$\inp(v)+\outp(v)+ \degree(v)\leq 2r$ where $\degree(v)$ is the degree of $v$ in thegraph $G$. The total number of inputs is $\inp(V)=\sum\_{v\in V}\inp(v)=n$, and the total number of outputs is $\outp(V)=\sum\_{v\in V}\outp(v)=n+k$.An $(n,k,r)$-network is \emph{valid}, if for any \emph{faulty} outputfunction $\outp'$ (that is such that $0\leq \outp'(v) \leq \outp(v)$ for any $v\in V$, and $\outp'(V) = n$), there are $n$ edge-disjoint paths in $G$such that each vertex $v\in V$ is the initial vertex of $\inp(v)$ pathsand the terminal vertex of $\outp'(v)$ paths.We investigate the design problem of determining the minimum number ${\cal N}(n,k,r)$ ofvertices in a valid $(n,k,r)$-network and of constructing minimum$(n,k,r)$-networks, or at least valid $(n,k,r)$-networks with a numberof vertices close to the optimal value.We first give some upper bounds on ${\cal N}(n,k,r)$.We show ${\cal N}(n,k,r)\leq \left\lceil \frac{k+2}{2r-2}\right\rceil \left\lceil\frac{n}{2}\right\rceil$. When $r\geq k/2$, we prove a better upper bound: ${\cal N}(n,k,r) \leq \frac{r-2+k/2}{r^2-2r+k/2} n + O(1)$.Next, we establish some lower bounds. We show that if $k\geq r$, then${\cal N}(n,k,r) \geq \frac{3n+k}{2r}$. We improve this bound when $k\geq 2r$:$\displaystyle {\cal N}(n,k,r) \geq \formule$.Finally, we determine ${\cal N}(n,k,r)$ up to additive constants for $k\leq 6$.

     
  15. Frédéric Giroire, Ioannis Lamprou, Dorian Mazauric, Nicolas Nisse, Stéphane Pérennes, and Ronan Soares. Connected Surveillance Game. Journal of Theoretical Computer Science (TCS), 584:131-143, June 2015. [WWW ] [PDF ]
    Keywords: Surveillance game, Cops and robber games, Prefetching, Online strategy, Competitive ratio, Cost of connectivity.
    Abstract:
    The surveillance game [Fomin et al., 2012] models the problem of web-page prefetching as a pursuit evasion game played on a graph. This two-player game is played turn-by-turn. The first player, called the observer, can mark a fixed amount of vertices at each turn. The second one controls a surfer that stands at vertices of the graph and can slide along edges. The surfer starts at some initially marked vertex of the graph, its objective is to reach an unmarked node before all nodes of the graph are marked. The surveillance number sn(G) of a graph G is the minimum amount of nodes that the observer has to mark at each turn ensuring it wins against any surfer in G. Fomin et al. also defined the connected surveillance game where the observer must ensure that marked nodes always induce a connected subgraph. They ask what is the cost of connectivity, i.e., is there a constant c \textgreater{} 0 such that the ratio between the connected surveillance number csn(G) and sn(G) is at most c for any graph G. It is straightforward to show that csn(G) $\le$ ∆ sn(G) for any graph G with maximum degree ∆. Moreover, it has been shown that there are graphs G for which csn(G) = sn(G) + 1. In this paper, we investigate the question of the cost of the connectivity. We first provide new non-trivial upper and lower bounds for the cost of connectivity in the surveillance game. More precisely, we present a family of graphs G such that csn(G) \textgreater{} sn(G) + 1. Moreover, we prove that csn(G) $\le$ sn(G)n for any n-node graph G. While the gap between these bounds remains huge, it seems difficult to reduce it. We then define the online surveillance game where the observer has no a priori knowledge of the graph topology and discovers it little-by-little. This variant, which fits better the prefetching motivation, is a restriction of the connected variant. Unfortunately, we show that no algorithm for solving the online surveillance game has competitive ratio better than Ω(∆). That is, while interesting, this variant does not help to obtain better upper bounds for the connected variant. We finally answer an open question [Fomin et al., 2012] by proving that deciding if the surveillance number of a digraph with maximum degree 6 is at most 2 is NP-hard.

     
  16. Frédéric Giroire, Joanna Moulierac, Truong Khoa Phan, and frederic roudaut. Minimization of network power consumption with redundancy elimination. Computer Communications, 59:98--105, March 2015. [WWW ] [PDF ]
    Abstract:
    Recently, energy-aware routing (EAR) has gained an increasing popularity in the networking research community. The idea is that traffic demands are redirected over a subset of the network links, allowing other links to sleep to save energy. In this paper, we propose GreenRE -- a new EAR model with the support of data redundancy elimination (RE). This technique, enabled within routers, can virtually increase the capacity of network links. Based on real experiments on Orange Labs platform, we show that performing RE increases the energy consumption for routers. Therefore, it is important to determine which routers should enable RE and which links to put into sleep mode so that the power consumption of the network is minimized. We model the problem as Mixed Integer Linear Program and propose greedy heuristic algorithms for large networks. Simulations on several network topologies show that the GreenRE model can gain further 370f energy savings compared to the classical EAR model.

     
  17. Frédéric Giroire, Stéphane Pérennes, and Issam Tahiri. On the complexity of equal shortest path routing. Networks, 2015. [WWW ] [PDF ]
    Keywords: shortest path, routing, OSPF-ECMP protocol, maximum flow, NP-hard, approximation algorithms, inverse shortest path.
    Abstract:
    In telecommunication networks packets are carried from a source s to a destination t on a path determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from s to t follows a shortest path according to these lengths. For better protection and efficiency, one wishes to use multiple (shortest) paths between two nodes. Therefore the routing protocol must determine how the traffic from s to t is distributed among the shortest paths. In the protocol called OSPF-ECMP (for Open Shortest Path First-Equal Cost Multiple Path) the traffic incoming at every node is uniformly balanced on all outgoing links that are on shortest paths. In that context, the operator task is to determine the '' best '' link lengths, toward a goal such as maximizing the network throughput for given link capacities. In this work, we show that the problem of maximizing even a single commodity flow for the OSPF-ECMP protocol cannot be approximated within any constant factor ratio. Besides this main theorem, we derive some positive results which include polynomial-time approximations and an exponential-time exact algorithm.

     
  18. Frédéric Havet, A Karolinna Maia, and Min-Li Yu. Complexity of greedy edge-colouring. Journal of the Brazilian Computer Society, 21(18), 2015. [WWW ] [PDF ]
    Abstract:
    The Grundy index of a graph G = (V, E) is the greatest number of colours that the greedy edge-colouring algorithm can use on G. We prove that the problem of determining the Grundy index of a graph G = (V, E) is NP-hard for general graphs. We also show that this problem is polynomial-time solvable for caterpillars. More specifically, we prove that the Grundy index of a caterpillar is (G) or (G) + 1 and present a polynomial-time algorithm to determine it exactly.

     
  19. Adrian Kosowski, Bi Li, Nicolas Nisse, and Karol Suchan. k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth. Algorithmica, 72(3):758-777, 2015. [WWW ] [PDF ]
    Abstract:
    Cops and robber games, introduced by Winkler and Nowakowski [41] and independently defined by Quilliot [43], concern a team of cops that must capture a robber moving in a graph. We consider the class of k-chordal graphs, i.e., graphs with no induced (chordless) cycle of length greater than k, k $\ge$ 3. We prove that k -- 1 cops are always sufficient to capture a robber in k-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including k-chordal graphs. We present a polynomial-time algorithm that, given a graph G and k $\ge$ 3, either returns an induced cycle larger than k in G, or computes a tree-decomposition of G, each bag of which contains a dominating path with at most k -- 1 vertices. This allows us to prove that any k-chordal graph with maximum degree ∆ has treewidth at most (k --1)(∆ --1) +2, improving the O(∆ (∆ --1) k--3) bound of Bodlaender and Thilikos (1997). Moreover, any graph admitting such a tree-decomposition has small hyperbolicity. As an application, for any n-vertex graph admitting such a tree-decomposition, we propose a compact routing scheme using routing tables, addresses and headers of size O(k log ∆ + log n) bits and achieving an additive stretch of O(k log ∆). As far as we know, this is the first routing scheme with O(k log ∆ + log n)-routing tables and small additive stretch for k-chordal graphs.

     
  20. Joanna Moulierac and Truong Khoa Phan. Optimizing IGP link weights for energy-efficiency in multi-period traffic matrices. Computer Communications, 61:11, May 2015. [WWW ] [PDF ]
    Abstract:
    Recently, due to the increasing power consumption and worldwide gases emissions in ICT (Information and Communication Technology), energy efficient ways to design and operate backbone networks are becoming a new concern for network operators. Since these networks are usually overprovisioned and since traffic load has a small influence on power consumption of network equipments, the most common approach to save energy is to put unused line cards that drive links between neighboring routers into sleep mode. To guarantee QoS, all traffic demands should be routed without violating capacity constraints and the network should keep its connectivity. From the perspective of traffic engineering, we argue that stability in routing configuration also plays an important role in QoS. In details, frequent changes in network configuration (link weights, slept and activated links) to adapt with traffic fluctuation in daily time cause network oscillations. In this work, we propose a novel optimization method to adjust the link weights of Open Shortest Path First (OSPF) protocol while limiting the changes in network configurations when multi-period traffic matrices are considered. We formally define the problem and model it as Mixed Integer Linear Program (MILP). We then propose an efficient heuristic algorithm that is suitable for large networks. Simulation results with real traffic traces on three different networks show that our approach achieves high energy saving while keeping the networks in stable state (less changes in network configuration).

     
  21. Michele Borassi, David Coudert, Pierluigi Crescenzi, and Andrea Marino. On Computing the Hyperbolicity of Real-World Graphs. In 23rd Annual European Symposium on Algorithms (ESA), volume 9294 of Lecture Notes in Computer Science, Patras, Greece, pages 215-226, September 2015. Springer. [WWW ] [PDF ]
    Keywords: Hyperbolicity, Graph, Algorithm.
    Abstract:
    The (Gromov) hyperbolicity is a topological property of a graph, which has been recently applied in several different contexts, such as the design of routing schemes, network security, computational biology, the analysis of graph algorithms, and the classification of complex networks. Computing the hyperbolicity of a graph can be very time consuming: indeed, the best available algorithm has running-time O(n^{3.69}), which is clearly prohibitive for big graphs. In this paper, we provide a new and more efficient algorithm: although its worst-case complexity is O(n^4), in practice it is much faster, allowing, for the first time, the computation of the hyperbolicity of graphs with up to 200,000 nodes. We experimentally show that our new algorithm drastically outperforms the best previously available algorithms, by analyzing a big dataset of real-world networks. Finally, we apply the new algorithm to compute the hyperbolicity of random graphs generated with the Erd{\"o}s-Renyi model, the Chung-Lu model, and the Configuration Model.

     
  22. Augustin Chaintreau, Guillaume Ducoffe, Roxana Geambasu, and Mathias Lécuyer. Vers une plus grande transparence du Web. In ALGOTEL 2015 - 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Beaune, France, June 2015. [WWW ] [PDF ]
    Keywords: Algorithmes d'apprentissage, Formes normales disjonctives monotones, Annonces publicitaires ciblées, Sécurité de l'information (Privacy).
    Abstract:
    De plus en plus les g{\'e}ants du Web (Amazon, Google et Twitter en t{\^e}te) recourent a la manne des " Big data " : ils collectent une myriade de donn{\'e}es qu'ils exploitent pour leurs algorithmes de recommandation personnalis{\'e}e et leurs campagnes publicitaires. Pareilles m{\'e}thodes peuvent consid{\'e}rablement am{\'e}liorer les services rendus a leurs utilisateurs, mais leur opacit{\'e} fait d{\'e}bat. En effet, il n'existe pas a ce jour d'outil suffisamment robuste qui puisse tracer sur le Web l'usage des donn{\'e}es et des informations sur un utilisateur par des services en ligne. Motiv{\'e}s par ce manque de transparence, nous avons d{\'e}velopp{\'e} un prototype du nom d'XRay, et qui peut pr{\'e}dire quelle donn{\'e}e parmi toutes celles pr{\'e}sentes dans un compte utilisateur est responsable de la r{\'e}ception d'une publicit{\'e}. Dans cet article, nous pr{\'e}sentons son principe ainsi que les r{\'e}sultats de nos premi{\`e}res exp{\'e}rimentations. Nous introduisons dans le m{\^e}me temps le tout premier mod{\`e}le th{\'e}orique pour le probl{\`e}me de la transparence du Web, et nous interpr{\'e}tons les performances d'Xray a la lumi{\`e}re de nos r{\'e}sultats obtenus dans ce mod{\`e}le. En particulier, nous d{\'e}montrons qu'un nombre $\\theta$(log N) de comptes utilisateurs auxiliaires, remplis selon un proc{\'e}d{\'e} al{\'e}atoire , suffisent a d{\'e}terminer quelle donn{\'e}e parmi les N en pr{\'e}sence a caus{\'e} la r{\'e}ception d'une publicit{\'e}. Nous aborderons bri{\`e}vement les extensions possibles, et quelques probl{\`e}mes ouverts.

     
  23. David Coudert, Guillaume Ducoffe, and Nicolas Nisse. Structure vs métrique dans les graphes. In ALGOTEL 2015 - 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Beaune, France, June 2015. [WWW ] [PDF ]
    Keywords: Genre, Hyperbolicité, Graphe, Largeur arborescente (Treewidth), Longueur arborescente (Treelength).
    Abstract:
    L'{\'e}mergence de r{\'e}seaux de tr{\`e}s grande taille oblige {\`a} repenser de nombreux probl{\`e}mes sur les graphes : en apparence simples, mais pour lesquels les algorithmes de r{\'e}solution connus ne passent plus a l'{\'e}chelle. Une approche possible est de mieux comprendre les propri{\'e}t{\'e}s de ces r{\'e}seaux complexes, et d'en d{\'e}duire de nouvelles m{\'e}thodes plus efficaces. C'est dans ce but que nous d{\'e}montrons des relations g{\'e}n{\'e}rales entre les propri{\'e}t{\'e}s structurelles des graphes et leurs propri{\'e}t{\'e}s m{\'e}triques. Nos relations se d{\'e}duisent de nouvelles bornes serr{\'e}es sur le diam{\`e}tre des s{\'e}parateurs minimaux dans un graphe. Plus pr{\'e}cis{\'e}ment , nous prouvons que dans tout graphe G le diam{\`e}tre d'un s{\'e}parateur minimal S dans G est au plus (l(G)/2) · (|S| -- 1), avec l(G) la plus grande taille d'un cycle isom{\'e}trique dans G. Nos preuves reposent sur des propri{\'e}t{\'e}s de connexit{\'e} dans les puissances d'un graphe. Une cons{\'e}quence de nos r{\'e}sultats est que pour tout graphe G, sa longueur arborescente (treelength) est au plus l(G)/2 fois sa largeur arborescente (treewidth). En compl{\'e}ment de cette relation, nous bornons la largeur arborescente par une fonction de la longueur arborescente et du genre du graphe. Cette borne se g{\'e}n{\'e}ralise {\`a} la famille des graphes qui excluent un apex-graph H comme mineur. Par cons{\'e}quent , nous obtenons un algorithme tr{\`e}s simple qui, {\'e}tant donn{\'e} un graphe excluant un apex-graph fix{\'e} comme mineur, calcule sa largeur arborescente en temps O(n${}^2$) et avec facteur d'approximation O(l(G)).

     
  24. Frédéric Giroire, Frédéric Havet, and Joanna Moulierac. Compressing two-dimensional routing tables with order. In INOC (International Network Optimization Conference), Varsovie, Poland, May 2015. [WWW ] [PDF ]
    Abstract:
    A communication in a network is a pair of nodes (s, t). The node s is called the source source and t the destination. A communication set is a set of distinct communications, i.e. two communications might have the same source or the same destination, but they cannot have both same source and same destination. A routing of a communication (s, t) is a path in the network from s to t. A routing of a communication set is a union of routings of its communications. At each node, there is a set X of communications whose routing path goes through this node. The node needs to be able to find for each communication (s,t) in X, the port that the routing path of (s,t) uses to leave it. An easy way of doing it is to store the list of all triples (s,t,k), where (s, t) $\in$ X and k is the port used by the (s, t)-path to leave the node. Such triples are called communication triples. However, such a list might be very large. Motivated by routing in telecommunication network using Software Defined Network Technologies, we consider the problem of compacting this list using aggregation rules. Indeed, SDN routers use specific memory which is expensive and of small capacity. Hence, in addition, we can use some additional triples, called $\star$-triples. As an example, a t-destination triple ($\star$, t, p), means that every communication with destination t leaves on port p. We carry out in this work a study of the problem complexity, providing results of NP-completeness, of Fixed-Parameter Tractability and approximation algorithms.

     
  25. Frédéric Giroire and Nicolas Huin. Study of Repair Protocols for Live Video Streaming Distributed Systems. In IEEE GLOBECOM 2015 - Global Communications Conference, San Diego, United States, December 2015. [WWW ] [PDF ]
    Abstract:
    -We study distributed systems for live video streaming. These systems can be of two types: structured and un-structured. In an unstructured system, the diffusion is done opportunistically. The advantage is that it handles churn, that is the arrival and departure of users, which is very high in live streaming systems, in a smooth way. On the opposite, in a structured system, the diffusion of the video is done using explicit diffusion trees. The advantage is that the diffusion is very efficient, but the structure is broken by the churn. In this paper, we propose simple distributed repair protocols to maintain, under churn, the diffusion tree of a structured streaming system. We study these protocols using formal analysis and simulation. In particular, we provide an estimation of the system metrics, bandwidth usage, delay, or number of interruptions of the streaming. Our work shows that structured streaming systems can be efficient and resistant to churn.

     
  26. Frédéric Giroire, Stephane Perennes, and Issam Tahiri. Grid spanners with low forwarding index for energy efficient networks. In International Network Optimization Conference (INOC), Electronic Notes in Discrete Mathematics, Warsaw, Poland, May 2015. [WWW ] [PDF ]
    Keywords: spanning subgraphs, forwarding index, energy saving, routing, grid.
    Abstract:
    A routing R of a connected graph G is a collection that contains simple paths connecting every ordered pair of vertices in G. The edge-forwarding index with respect to R (or simply the forwarding index with respect to R) $\pi$(G, R) of G is the maximum number of paths in R passing through any edge of G. The forwarding index $\pi$(G) of G is the minimum $\pi$(G, R) over all routings R's of G. This parameter has been studied for different graph classes [12], [1], [5], [4]. Motivated by energy efficiency, we look, for different numbers of edges, at the best spanning graphs of a square grid, namely those with a low forwarding index.

     
  27. Frédéric Giroire, Stéphane Pérennes, and Issam Tahiri. How to design graphs with low forwarding index and limited number of edges. In 26th International Workshop on Combinatorial Algorithms (IWOCA 2015), Verona, Italy, October 2015. [WWW ] [PDF ]
    Keywords: graphs, forwarding index, routing, design problem, energy efficiency, extremal graphs.
    Abstract:
    The (edge) forwarding index of a graph is the minimum, over all possible rout-ings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question: Given a number e of edges and a number n of vertices, what is the least congested graph that we can construct? and what forwarding-index can we achieve? Our problem has some distant similarities with the well-known (∆, D) problem, and we sometimes build upon results obtained on it. The goal of this paper is to study how to build graphs with low forwarding indices and to understand how the number of edges impacts the forwarding index. We answer here these questions for different families of graphs: general graphs, graphs with bounded degree, sparse graphs with a small number of edges by providing constructions, most of them asymptotically optimal. For instance, we provide an asymptotically optimal construction for (n, n + k) cubic graphs-its forwarding index is $\sim$ n 2 3k log 2 (k). Our results allow to understand how the forwarding-index drops when edges are added to a graph and also to determine what is the best (i.e least congested) structure with e edges. Doing so, we partially answer the practical problem that initially motivated our work: If an operator wants to power only e links of its network, in order to reduce the energy consumption (or wiring cost) of its networks, what should be those links and what performance can be expected?

     
  28. Frédéric Havet, Nicolas Huin, Joanna Moulierac, and Khoa Phan. Routage vert et compression de règles SDN. In ALGOTEL 2015 - 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Beaune, France, June 2015. [WWW ] [PDF ]
    Abstract:
    La technologie SDN permet de s{\'e}parer le plan de contr{\^o}le et le plan de donn{\'e}es qui cohabitent actuellement sur les routeurs dans les architectures r{\'e}seaux classiques et de r{\'e}aliser le routage par un ou plusieurs contr{\^o}leur(s) centralis{\'e}(s). Nos travaux portent sur l'utilisation de cette technologie pour minimiser la consommation d'{\'e}nergie dans les r{\'e}seaux, notamment en permettant au contr{\^o}leur d'{\'e}teindre {\`a} distance des liens non utilis{\'e}s. Une des probl{\'e}matiques est que les tables de routage SDN ne peuvent contenir qu'un nombre tr es limit{\'e} de r{\`e}gles. Ceci est d{\^u} au type particulier de m{\'e}moire utilis{\'e} pour permettre l'ajout a distance de r{\`e}gles de routage par le contr{\^o}leur SDN. Dans ce papier, nous {\'e}tudions le probl{\`e}me de compression de tables de routage bidimensionnelles avec priorit{\'e}, en particulier la complexit{\'e} algorithmique et proposons des algorithmes d'approximation. Nous proposons ensuite des algorithmes de routage vert qui effectuent en m{\^e}me temps le choix des routes, la compression des tables de routages et la mise en veille des liens non utilis{\'e}s. Ces algorithmes sont test{\'e}s sur les r{\'e}seaux de la librairie SNDLib.

     
  29. Mamadou Moustapha Kanté, Fatima Zahra Moataz, Benjamin Momège, and Nicolas Nisse. Finding Paths in Grids with Forbidden Transitions. In WG 2015, 41st International Workshop on Graph-Theoretic Concepts in Computer Science, Munich, Germany, June 2015. [WWW ] [PDF ]
    Abstract:
    A transition in a graph is a pair of adjacent edges. Given a graph G = (V, E), a set of forbidden transitions F $\subseteq$ E × E and two vertices s, t $\in$ V , we study the problem of finding a path from s to t which uses none of the forbidden transitions of F. This means that it is forbidden for the path to consecutively use two edges forming a pair in F. The study of this problem is motivated by routing in road networks in which forbidden transitions are associated to prohibited turns as well as routing in optical networks with asymmetric nodes, which are nodes where a signal on an ingress port can only reach a subset of egress ports. If the path is not required to be elementary, the problem can be solved in polynomial time. On the other side, if the path has to be elementary, the problem is known to be NP-complete in general graphs [Szeider 2003]. In this paper, we study the problem of finding an elementary path avoiding forbidden transitions in planar graphs. We prove that the problem is NP-complete in planar graphs and particularly in grids. In addition, we show that the problem can be solved in polynomial time in graphs with bounded treewidth. More precisely, we show that there is an algorithm which solves the problem in time O((3∆(k + 1)) 2k+4 n)) in n-node graphs with treewidth at most k and maximum degree ∆.

     
  30. Mamadou Moustapha Kanté, Fatima Zahra Moataz, Benjamin Momège, and Nicolas Nisse. On paths in grids with forbidden transitions. In ALGOTEL 2015 - 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Beaune, France, June 2015. [WWW ] [PDF ]
    Keywords: Forbidden transitions, planar graph, grid, asymmetric nodes.
    Abstract:
    Une transition dans un graphe est une paire d'ar{\^e}tes incidentes {\`a} un m{\^e}me sommet. Etant donn{\'e}s un graphe G = (V, E), deux sommets s,t $\in$ V et un ensemble associ{\'e} de transitions interdites F $\subseteq$ E × E, le probl{\`e}me de chemin {\'e}vitant des transitions interdites consiste {\`a} d{\'e}cider s'il existe un chemin {\'e}l{\'e}mentaire de s {\`a} t qui n'utilise aucune des transitions de F. C'est-{\`a}-dire qu'il est interdit d'emprunter cons{\'e}cutivement deux ar{\^e}tes qui soient une paire de F. Ce probl{\`e}me est motiv{\'e} par le routage dans les r{\'e}seaux routiers (o{\`u} une transition interdite repr{\'e}sente une interdiction de tourner) ainsi que dans les r{\'e}seaux optiques avec des noeuds asym{\'e}triques. Nous prouvons que le probl{\`e}me est NP-difficile dans les graphes planaires et plus particuli{\`e}rement dans les grilles. Nous montrons {\'e}galement que leprobl{\`e}me peut {\^e}tre r{\'e}solu en temps polynomial dans la classe des graphes de largeur arborescente born{\'e}e.

     
  31. Alvinice Kodjo, Brigitte Jaumard, Napoleão Nepomuceno, Mejdi Kaddour, and David Coudert. Dimensioning microwave wireless networks. In ICC 2015 : IEEE International Conference on Communications, London, United Kingdom, pages 2803 - 2809, June 2015. IEEE. [WWW ] [PDF ]
    Abstract:
    We aim at dimensioning fixed broadband microwave wireless networks under unreliable channel conditions. As the transport capacity of microwave links is prone to variations due to, e.g., weather conditions, such a dimensioning requires special attention. It can be formulated as the determination of the minimum cost bandwidth assignment of the links in the network for which traffic requirements can be met with high probability, while taking into account that transport link capacities vary depending on channel conditions. The proposed optimization model represents a major step forward since we consider dynamic routing. Experimental results show that the resulting solutions can save up to 450f the bandwidth cost compared to the case where a bandwidth over-provisioning policy is uniformly applied to all links in the network planning. Comparisons with previous work also show that we can solve much larger instances in significantly shorter computing times, with a comparable level of reliability.

     
  32. Bi Li, Fatima Zahra Moataz, Nicolas Nisse, and Karol Suchan. Minimum Size Tree-decompositions. In LAGOS 2015 -- VIII Latin-American Algorithms, Graphs and Optimization Symposium, Beberibe, Ceará, Brazil, May 2015. [WWW ] [PDF ]
    Keywords: Minimum size tree-decomposition, treewidth, NP-hard.
    Abstract:
    Tree-decompositions are the cornerstone of many dynamic programming algorithms for solving graph problems. Since the complexity of such algorithms generally depends exponentially on the width (size of the bags) of the decomposition, much work has been devoted to compute tree-decompositions with small width. However, practical algorithms computing tree-decompositions only exist for graphs with treewidth less than 4. In such graphs, the time-complexity of dynamic programming algorithms is dominated by the size (number of bags) of the tree-decompositions. It is then interesting to minimize the size of the tree-decompositions. In this extended abstract, we consider the problem of computing a tree-decomposition of a graph with width at most k and minimum size. We prove that the problem is NP-complete for any fixed k $\ge$ 4 and polynomial for k $\le$ 2; for k = 3, we show that it is polynomial in the class of trees and 2-connected outerplanar graphs.

     
  33. Nicolas Nisse, Alexandre Salch, and Valentin Weber. Comment appliquer les chaînes augmentantes pour atterrir a l'heure ?. In ALGOTEL 2015 - 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Beaune, France, June 2015. [WWW ] [PDF ]
    Abstract:
    Lorsqu'un avion approche d'un a{\'e}roport , il dispose d'un intervalle de temps (slot) tr{\`e}s limit{\'e} (une vingtaine de minutes) pour atterrir. Si l'avion a du retard {\`a} cause des conditions m{\'e}t{\'e}orologiques ({\`a} cause du retard d'autres avions, ou si lui-m{\^e}me a eu du retard au d{\'e}collage), il perd son slot et il faut qu'un nouveau slot lui soit attribu{\'e} par les contr{\^o}leurs des op{\'e}rations de la compagnie a{\'e}rienne. Cependant, les slots d'atterrissage sont une denr{\'e}e rare et, pour qu'un avion A puisse atterrir a l'heure, les contr{\^o}leurs doivent r{\'e}gul{\`i}{\`e}rement modifier l'attribution des slots d'autres avions afin d'affecter un slot compatible avec l'heure d'arriv{\'e}e de l'avion A. Ce probl{\`e}me peut ais{\'e}ment etre mod{\'e}lis{\'e} comme un probl{\`e}me de couplage dans un graphe biparti. Malheureusement, d{\^u} au syst{\`e}me mis en place pour permettre ces {\'e}changes, les contr{\^o}leurs a{\'e}riens ne peuvent effectuer leurs modifications qu'en effectuant deux types d'op{\'e}rations : soit attribuer {\`a} l'avion A un slot libre, soit donner {\`a} l'avion A le slot d'un avion B et attribuer un slot libre {\`a} ce dernier. Le probl{\`e}me devient donc le suivant. Soit G un graphe et M un couplage (ensemble d'ar{\^e}tes deux-{\`a}-deux disjointes) de G. Comment calculer un couplage maximum pouvant etre obtenu {\`a} partir de M en utilisant uniquement des chemins augmentants de longueur au plus k ? Ce probl{\`e}me a d{\'e}j{\`a} {\'e}t{\'e} {\'e}tudi{\'e} dans le cadre des r{\'e}seaux sans-fil car il fournit une simple approximation au probl{\`e}me de couplage maximum. Nous prouvons que, pour k = 3, ce probl{\`e}me peut {\^e}tre r{\'e}solu en temps polynomial, fournissant ainsi un algorithme efficace pour les contr{\^o}leurs a{\'e}riens. Nous prouvons ensuite que, pour tout entier impair k $\ge$ 5, le probl{\`e}me est NP-complet dans les graphes bipartis planaires de degr{\'e} au plus 3.

     
  34. Myriana Rifai, Nicolas Huin, Christelle Caillouet, Frédéric Giroire, Dino Lopez Pacheco, Joanna Moulierac, and Guillaume Urvoy-Keller. Too many SDN rules? Compress them with MINNIE. In IEEE GLOBECOM, San diego, United States, December 2015. IEEE. [WWW ] [PDF ]
    Keywords: Software defined networks, experimentation, TCAM, number of rules.
    Abstract:
    Software Defined Networking (SDN) is gaining momentum with the support of major manufacturers. While it brings flexibility in the management of flows within the data center fabric, this flexibility comes at the cost of smaller routing table capacities. In this paper, we investigate compression techniques to reduce the forwarding information base (FIB) of SDN switches. We validate our algorithm, called MINNIE, on a real testbed able to emulate a 20 switches fat tree architecture. We demonstrate that even with a small number of clients, the limit in terms of number of rules is reached if no compression is performed, increasing the delay of all new incoming flows. MINNIE, on the other hand, reduces drastically the number of rules that need to be stored with a limited impact on the packet loss rate. We also evaluate the actual switching and reconfiguration times and the delay introduced by the communications with the controller.

     
  35. Fatima Zahra Moataz. On Spectrum Assignment in Elastic Optical Tree-Networks. In ALGOTEL 2015 - 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Beaune, France, June 2015. [WWW ] [PDF ]
    Keywords: interval coloring, routing and spectrum assignment, optical networks, Approximation algorithms.
    Abstract:
    Pour r{\'e}pondre {\`a} la demande croissante du trafic d'Internet, une nouvelle g{\'e}n{\'e}ration de r{\'e}seaux optiques est en cours de d{\'e}veloppement ; les r{\'e}seaux optiques {\'e}lastiques (EONs). La technologie EON permet d'utiliser le spectre optique de mani{\`e}re efficace et flexible. Cette flexibilit{\'e} promet de r{\'e}soudre les difficult{\'e}s li{\'e}es {\`a} la croissance et l'h{\'e}t{\'e}rog{\'e}n{\'e}it{\'e} du trafic. Toutefois, elle rend le probl{\`e}me d'allocation de ressources plus complexe. Dans ce papier, nous traitons le probl{\`e}me d'allocation de spectre dans les r{\'e}seaux optiques {\'e}lastiques en arbre. Dans ce type de r{\'e}seau , bien que le routage soit fix{\'e}, l'allocation de spectre est NP-difficile. Nous pr{\'e}sentons des r{\'e}sultats de difficult{\'e} et d'approximation pour des cas sp{\'e}ciaux o{\`u} le r{\'e}seau est une {\'e}toile ou un arbre binaire.

     
  36. Julio Araujo, Frédéric Havet, Claudia Linhares Sales, and Ana Silva. Proper orientation of cacti. Research Report RR-8833, INRIA Sophia Antipolis - Méditerranée, December 2015. [WWW ] [PDF ]
    Keywords: proper orientation, graph coloring, cactus graph, claw-free graph.
    Abstract:
    An orientation of a graph is proper if two adjacent vertices have different indegrees. We prove that every cactus admits a proper orientation with maximum indegree at most 7. We also prove that the bound 7 is tight by showing a cactus having no proper orientation with maximum indegree less than 7. We also prove that any planar claw-free graph has a proper orientation with maximum indegree at most 6 and that this bound can also be attained.

     
  37. Jean-Claude Bermond and Fatima Zahra Moataz. On Spectrum Assignment in Elastic Optical Tree-Networks. Research Report, Inria Sophia Antipolis ; Université Nice Sophia Antipolis, February 2015. [WWW ] [PDF ]
    Keywords: Approximation algorithms, routing and spectrum assignment, optical networks, interval coloring.
    Abstract:
    To face the explosion of the Internet traffic, a new generation of optical networks is being developed; the Elastic optical Networks (EONs). The aim with EONs is to use the optical spectrum efficiently and flexibly. The benefit of the flexibility is, however, accompanied by more difficulty in the resource allocation problems. In this report, we study the problem of Spectrum Allocation in Elastic Optical Tree-Networks. In trees, even though the routing is fixed, the spectrum allocation is NP-hard. We survey the complexity and approximability results that have been established for the SA in trees and prove new results for stars and binary trees.

     
  38. David Coudert and Guillaume Ducoffe. Data center interconnection networks are not hyperbolic. Research Report, Inria Sophia Antipolis ; I3S ; Université Nice Sophia Antipolis ; CNRS, May 2015. [WWW ] [PDF ]
    Abstract:
    Topologies for data center networks have been proposed in the literature through various graph classes and operations. A common trait to most existing designs is that they enhance the symmetric properties of the underlying graphs. Indeed, symmetry is a desirable property for interconnection networks because it minimizes congestion problems and it allows each entity to run the same routing protocol. However, despite sharing similarities these topologies all come with their own routing protocol. Recently, generic routing schemes have been introduced which can be implemented for any interconnection networks. The performances of such universal routing schemes are intimately related to the hyperbolicity of the topology. Roughly, graph hyperbolicity is a metric parameter which measures how close is the shortest-path metric of a graph from a tree metric (the smaller gap the better). Motivated by the good performances in practice of these new routing schemes, we propose the first general study of the hyperbolicity of data center interconnection networks. Our findings are disappointingly negative: we prove that the hyperbolicity of most data center topologies scales linearly with their diameter, that it the worst-case possible for hyperbolicity. To obtain these results, we introduce original connection between hyperbolicity and the properties of the endomorphism monoid of a graph. In particular, our results extend to all vertex and edge-transitive graphs. Additional results are obtained for de Bruijn and Kautz graphs, grid-like graphs and networks from the so-called Cayley model.

     
  39. Frédéric Giroire, Stéphane Pérennes, and Issam Tahiri. Graphs with optimal forwarding indices: What is the best throughput you can get with a given number of edges?. Research Report RR-8752, INRIA Sophia Antipolis ; INRIA, June 2015. [WWW ] [PDF ]
    Keywords: graphs, forwarding index, routing, design problem, energy efficiency, extremal graphs.
    Abstract:
    The (edge) forwarding index of a graph is the minimum, over all possible routings of all the demands, of the maximum load of an edge. This metric is of a great interest since it captures the notion of global congestion in a precise way: the lesser the forwarding-index, the lesser the congestion. In this paper, we study the following design question: Given a number e of edges and a number n of vertices, what is the least congested graph that we can construct? and what forwarding-index can we achieve? Our problem has some distant similarities with the well-known (∆,D) problem, and we sometimes build upon results obtained on it. The goal of this paper is to study how to build graphs with low forwarding indices and to understand how the number of edges impacts the forwarding index. We answer here these questions for different families of graphs: general graphs, graphs with bounded degree, sparse graphs with a small number of edges by providing constructions, most of them asymptotically optimal. Hence, our results allow to understand how the forwarding-index drops when edges are added to a graph and also to determine what is the best (i.e least congested) structure with e edges. Doing so, we partially answer the practical problem that initially motivated our work: If an operator wants to power only e links of its network, in order to reduce the energy consumption (or wiring cost) of its networks, what should be those links and what performance can be expected?

     
  40. Frédéric Havet, A. Karolinna Maia de Oliveira, and Bojan Mohar. Finding a subdivision of a prescribed digraph of order 4. Research Report RR-8773, INRIA, September 2015. [WWW ] [PDF ]
    Abstract:
    The problem of when a given digraph contains a subdivision of a fixed digraph F is considered.Bang-Jensen et al. [2] laid out foundations for approaching this problem from the algorithmic pointof view. In this paper we give further support to several open conjectures and speculations about algorithmiccomplexity of finding F-subdivisions. In particular, up to 5 exceptions, we completely classify forwhich 4-vertex digraphs F, the F-subdivision problem is polynomial-time solvable and for which it is NPcomplete.While all NP-hardness proofs are made by reduction from some version of the 2-linkage problemin digraphs, some of the polynomial-time solvable cases involve relatively complicated algorithms.

     
  41. Seong-Gyun Jeong, Yuliya Tarabalka, Nicolas Nisse, and Josiane Zerubia. Inference of Curvilinear Structure based on Learning a Ranking Function and Graph Theory. Research Report RR-8789, Inria Sophia Antipolis, 2015. [WWW ] [PDF ]
    Abstract:
    To detect curvilinear structures in natural images, we propose a novel rankinglearning system and an abstract curvilinear shape inference algorithm based on graph theory. Weanalyze the curvilinear structures as a set of small line segments. In this work, the rankings ofthe line segments are exploited to systematize the topological feature of the curvilinear structures.Structured Support Vector Machine is employed to learn the ranking function that predicts thecorrespondence of the given line segments and the latent curvilinear structures. We first extractcurvilinear features using morphological profiles and steerable filtering responses. Also, we proposean orientation-aware feature descriptor and a feature grouping operator to improve the structuralintegrity during the learning process. To infer the curvilinear structure, we build a graph based onthe output rankings of the line segments. We progressively reconstruct the curvilinear structureby looking for paths between remote vertices in the graph. Experimental results show that theproposed algorithm faithfully detects the curvilinear structures within various datasets.

     
  42. Mamadou Moustapha Kanté, Fatima Zahra Moataz, Benjamin Momège, and Nicolas Nisse. Finding Paths in Grids with Forbidden Transitions. Research Report, Inria Sophia Antipolis ; Univeristé Nice Sophia Antipolis ; CNRS, February 2015. [WWW ] [PDF ]
    Keywords: asymmetric nodes, grid, planar graphs, forbidden transitions.
    Abstract:
    Une transition dans un graphe est une paire d'ar{\^e}tes incidente a un m{\^e}me sommet. Etant donn{\'e}s un graphe G = (V, E), deux sommets s, t $\in$ V et un ensemble associ{\'e} de transitions interdites F $\subseteq$ E × E, le probl{\`e}me de chemin {\'e}vitant des transitions interdites consiste {\`a} d{\'e}cider s’il existe un chemin {\'e}l{\'e}mentaire de s {\`a} t qui n’utilise aucune des transitions de F. C’est-{\`a}-dire qu’il est interdit d’emprunter cons{\'e}cutivement deux ar{\^e}tes qui soient une paire de F. Ce probl{\`e}me est motiv{\'e} par le routage dans les r{\'e}seaux routiers (o{\`u} une transition interdite repr{\'e}sente une interdiction de tourner) ainsi que dans les r{\'e}seaux optiques avec des noeuds asym{\'e}triques. Nous prouvons que le probl{\`e}me est NP-difficile dans les graphes planaires et plus particuli{\`e}rement dans les grilles. Nous montrons {\'e}galement que le probl{\`e}me peut {\^e}tre r{\'e}solu en temps polynomial dans la classe des graphes de largeur arborescente born{\'e}e.

     
  43. Nicolas Nisse, Alexandre Salch, and Valentin Weber. Recovery of disrupted airline operations using k-Maximum Matching in Graphs. Research Report RR-8679, Inria Sophia Antipolis ; INRIA, February 2015. [WWW ] [PDF ]
    Abstract:
    When an aircraft is approaching an airport, it gets a short time interval (called {\it slot}) that it can use to land. If the landing of the aircraft is delayed (because of bad weather, or if it arrives late, or if other aircrafts have to land first), it looses its slot and Air traffic controllers have to assign it a new slot. However, slots for landing are a scare resource of the airports and, to avoid that an aircraft waits too much time, Air traffic controllers have to regularly modify the assignment of the slots of the aircrafts. Unfortunately, for legal and economical reasons, Air traffic controllers can modify the slot-assignment only using two kind of operations: either assign to aircraft $A$ a slot that was free, or give to $A$ the slot of another aircraft $B$ and assign to $B$ a free slot. The problem is then the following.Let $k\geq 1$ be an odd integer and let $G$ be a graph and $M$ be a matching (set of pairwise disjoint edges) of $G$. What is the maximum size of a matching that can be obtained from $M$ by using only augmenting paths of length at most $k$? Moreover, how to compute such a maximum matching? This problem has already been studied in the context of wireless networks, mainly because it provides a simple approximation for the classical matching problem. We prove that this problem can be solved in polynomial-time when $k\leq 3$. Then, we show that, for any odd integer $k\geq 5$, the problem is NP-complete in planar bipartite graphs with maximum degree at most $3$.

     
  44. Guillaume Ducoffe, Mathias Lécuyer, Augustin Chaintreau, and Roxana Geambasu. Web Transparency for Complex Targeting: Algorithms, Limits, and Tradeoffs. SIGMETRICS '15 Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, June 2015.
    Note: Poster. [WWW ] [PDF ]
    Abstract:
    Big Data promises important societal progress but exacerbates the need for due process and accountability. Companies and institutions can now discriminate between users at an individual level using collected data or past behavior. Worse, today they can do so in near perfect opacity. The nascent field of web transparency aims to develop the tools and methods necessary to reveal how information is used, however today it lacks robust tools that let users and investigators identify targeting using multiple inputs. Here, we formalize for the first time the problem of detecting and identifying targeting on combinations of inputs and provide the first algorithm that is asymptotically exact. This algorithm is designed to serve as a theoretical foundational block to build future scalable and robust web transparency tools. It offers three key properties. First, our algorithm is service agnostic and applies to a variety of settings under a broad set of assumptions. Second, our algorithm's analysis delineates a theoretical detection limit that characterizes which forms of targeting can be distinguished from noise and which cannot. Third, our algorithm establishes fundamental tradeoffs that lead the way to new metrics for the science of web transparency. Understanding the tradeoff between effective targeting and targeting concealment lets us determine under which conditions predatory targeting can be made unprofitable by transparency tools.

     
2014
  1. Fedor Fomin, Pierre Fraigniaud, Nicolas Nisse, and Dimitrios M. M. Thilikos. Report on GRASTA 2014. 2014. [WWW ] [PDF ]
     
  2. Alvinice Kodjo. Design and optimization of wireless backhaul networks. Theses, Université Nice Sophia Antipolis, December 2014. [WWW ] [PDF ]
    Keywords: Infrastructure sharing, Energy saving, Design, Robust optimization, Microwave backhaul, Réseaux de collecte, Optimisation robuste, Dimensionnement, Consommation d'énergie, Partage d'infrastructure.
     
  3. Aurélien Lancin. Study of complex networks properties for the optimization of routing models. Theses, Université Nice Sophia Antipolis, December 2014. [WWW ] [PDF ]
    Keywords: Routing, Graph decomposition, Graph, Hyperbolicity, Algorithm, Parallel distributed simulation, Internet, Algorithme, Graphe, Hyperbolicité, Décomposition de graphe, Routage, BGP, Simulation, Simulation parallèle distribuée.
     
  4. Bi Li. Tree decompositions and routing problems. Theses, Université Nice Sophia Antipolis, November 2014. [WWW ] [PDF ]
    Keywords: Tree decomposition, Compact routing scheme, Prize collecting Steiner tree, Gathering, Décomposition arborescente, Schéma de routage compact.
     
  5. Nicolas Nisse. Algorithmic complexity: Between Structure and Knowledge How Pursuit-evasion Games help.. Habilitation à diriger des recherches, Université Nice Sophia Antipolis, May 2014. [WWW ] [PDF ]
    Keywords: Algorithm, Graph Theory, Pursuit-Evasion Games, Cops and Robber, Graph Searching, Graph decompositions, Graph Structural Properties, Mobile Agents Computing, Telecommunication Networks, Routing, Distributed Computing, Algorithmes, Th eorie des Graphes, Jeux de Poursuite- Evasion, Gendarmes et voleur, Encerclement dans les graphes, D ecompositions de graphes, Propri et es structurelles de graphes, Agents Mobiles, R eseaux de t el ecommunication, Routage, Calcul distribu é.
     
  6. Ana Karolinna Maia de Oliveira. Subdivisions of digraphs. Theses, Université Nice Sophia Antipolis, November 2014. [WWW ] [PDF ]
    Keywords: Digraph, Subdivision, Linkage, Oriented graphs, Digraphe, Graphes orientés.
     
  7. Truong Khoa Phan. Design and management of networks with low power consumption. Theses, Université Nice Sophia Antipolis, September 2014. [WWW ] [PDF ]
    Keywords: Software defined networks, Open Shortest Path First, Energy-aware routing, Redundancy elimination, Routage conscience-énergie, Élimination de redondance.
     
  8. Julio Araujo, Jean-Claude Bermond, and Guillaume Ducoffe. Eulerian and Hamiltonian dicycles in directed hypergraphs. Discrete Mathematics, Algorithms and Applications, 06:1450012, 2014. [WWW ] [PDF ]
    Keywords: Eulerian and Hamiltonian dicycles, 11xxx, de Bruijn dihyper-graphs Mathematics Subject Classification 2000: 11xxx, Directed hypergraphs.
     
  9. Julio Araujo, Nicolas Nisse, and Stéphane Pérennes. Weighted Coloring in Trees. Siam Journal on Discrete Mathematics, 28(4):2029 - 2041, 2014. [WWW ] [PDF ]
     
  10. Victor Campos, Claudia Linhares Sales, Ana Karolinna Maia, and Rudini Sampaio. Maximization Coloring Problems on graphs with few P4s. Discrete Applied Mathematics, 164(2):539-546, February 2014. [WWW ] [PDF ]
     
  11. Grit Classen, David Coudert, Arie Koster, and Napoleao Nepomuceno. Chance-Constrained Optimization of Reliable Fixed Broadband Wireless Networks. INFORMS Journal on Computing, 26(4):893-909, 2014. [WWW ] [PDF ]
    Keywords: network reliability, fixed wireless networks, capacitated network design, integer programming, chance-constrained programming.
     
  12. David Coudert and Guillaume Ducoffe. Recognition of C4-free and 1/2-hyperbolic graphs. Siam Journal on Discrete Mathematics, 28(3):1601-1617, September 2014. [WWW ] [PDF ]
    Keywords: rectangular matrix multiplication, Hyperbolicity, discrete metric space, graph algorithms, C4-free graphs, rectangular matrix multiplication..
     
  13. Fedor V. Fomin, Frédéric Giroire, Alain Jean-Marie, Dorian Mazauric, and Nicolas Nisse. To satisfy impatient Web surfers is hard. Journal of Theoretical Computer Science (TCS), 526:1-17, March 2014. [WWW ] [PDF ]
     
  14. Frédéric Havet and Andrew King. List circular backbone colouring. Discrete Mathematics and Theoretical Computer Science, Vol. 16 no. 1 (in progress)(1):89--104, March 2014.
    Note: Graph Theory. [WWW ] [PDF ]
    Keywords: Discrete Mathematics, Graph Theory.
     
  15. Frédéric Havet, Andrew D. King, Mathieu Liedloff, and Ioan Todinca. (Circular) backbone colouring: forest backbones in planar graphs. Discrete Applied Mathematics, 169:119-134, 2014. [WWW ] [PDF ]
     
  16. Frédéric Havet, Nagarajan Paramaguru, and Rathinaswamy Sampathkumar. Detection number of bipartite graphs and cubic graphs. Discrete Mathematics and Theoretical Computer Science, Vol. 16 no. 3 (in progress)(3):333-342, December 2014. [WWW ] [PDF ]
     
  17. Julio Araujo, Nathann Cohen, Susanna de Rezende, Frédéric Havet, and Phablo Moura. On the proper orientation number of bipartite graphs. In 9th International colloquium on graph theory and combinatorics, Grenoble, France, June 2014. [WWW ] [PDF ]
    Keywords: proper orientation, graph colouring, bipartite graph, hardness.
     
  18. Julio Araújo, Nicolas Nisse, and Stéphane Pérennes. Weighted Coloring in Trees. In 31st Symposium on Theoretical Aspects of Computer Science (STACS), Lyon, France, pages 75-86, March 2014. Dagstuhl Publishing. [WWW ] [PDF ]
     
  19. David Coudert, Brigitte Jaumard, and Fatima Zahra Moataz. Dynamic Routing and Spectrum Assignment with Non-Disruptive Defragmentation. In ALGOTEL 2014 -- 16èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Le Bois-Plage-en-Ré, France, pages 1-4, June 2014. [WWW ] [PDF ]
     
  20. David Coudert, Alvinice Kodjo, and Khoa Phan. Robust Optimization for Energy-aware Routing with Redundancy Elimination. In ALGOTEL 2014 -- 16èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Le-Bois-Plage-en-Ré, France, pages 1-4, June 2014. [WWW ] [PDF ]
     
  21. David Coudert, Dorian Mazauric, and Nicolas Nisse. Experimental Evaluation of a Branch and Bound Algorithm for computing Pathwidth. In 13th International Symposium on Experimental Algorithms, volume 8504 of Lecture Notes in Computer Science, Copenhagen, Denmark, pages 46-58, 2014. [WWW ] [PDF ]
     
  22. Gianlorenzo D'Angelo, Xavier Défago, and Nicolas Nisse. Understanding the Power of Stigmergy of Anonymous Agents in Discrete Environments. In Second International Symposium on Computing and Networking (CANDAR), Mt. Fuji, Shizuoka, Japan, December 2014. [WWW ] [PDF ]
     
  23. Gianlorenzo D'Angelo, Alfredo Navarra, and Nicolas Nisse. Gathering and Exclusive Searching on Rings under Minimal Assumptions. In Mainak Chatterjee, Jian-Nong Cao, Kishore Kothapalli, and Sergio Rajsbaum, editors, 15th International Conference on Distributed Computing and Networking (ICDCN), volume 8314, Coimbatore, India, pages 149-164, January 2014. Springer. [WWW ] [PDF ]
     
  24. Frédéric Giroire, Joanna Moulierac, and Truong Khoa Phan. Optimizing Rule Placement in Software-Defined Networks for Energy-aware Routing. In IEEE GLOBECOM, Austin Texas, United States, December 2014. IEEE. [WWW ] [PDF ]
    Keywords: networking, SDN, Energy Aware routing.
     
  25. Alvinice Kodjo, David Coudert, and Christelle Caillouet. Optimisation robuste pour le partage de réseaux d'accès micro-ondes entre opérateurs. In ROADEF - 15ème congrès annuel de la Société française de recherche opérationnelle et d'aide à la décision, Bordeaux, France, February 2014. Société française de recherche opérationnelle et d'aide à la décision. [WWW ]
    Keywords: Wireless backhaul network, robust optimization, infrastructure sharing.
     
  26. Mathias Lecuyer, Guillaume Ducoffe, Francis Lan, Andrei Papancea, Theofilos Petsios, Riley Spahn, Augustin Chaintreau, and Roxana Geambasu. XRay: Enhancing the Web's Transparency with Differential Correlation. In USENIX Security Symposium, San Diego, United States, August 2014.
    Note: Extended version of a paper presented at the 23rd USENIX Security Symposium (USENIX Security 14). [WWW ] [PDF ]
     
  27. Bi Li, Fatima Zahra Moataz, and Nicolas Nisse. Minimum Size Tree-Decompositions. In 9th International colloquium on graph theory and combinatorics (ICGT), Grenoble, France, 2014. [WWW ] [PDF ]
     
  28. Deepesh Agarwal, Christelle Caillouet, David Coudert, and Frédéric Cazals. Unveiling Contacts within Macro-molecular assemblies by solving Minimum Weight Connectivity Inference Problems. Research Report RR-8622, Inria, October 2014. [WWW ] [PDF ]
    Keywords: Molecular machines, Mixed integer linear program, Biophysics, Mass spectrometry, Protein assembly, Structural biology, Connectivity Inference Connected induced sub-graphs.
     
  29. Julio Araujo, Nathann Cohen, Susanna F. De Rezende, Frédéric Havet, and Phablo Moura. On the proper orientation number of bipartite graphs. Research Report RR-8492, INRIA, March 2014. [WWW ] [PDF ]
    Keywords: proper orientation, graph colouring, bipartite graph.
     
  30. Julio Araujo, Frédéric Havet, and Mathieu Schmitt. Steinberg-like theorems for backbone colouring. Research Report RR-8641, INRIA Sophia Antipolis ; INRIA, November 2014. [WWW ] [PDF ]
     
  31. Joergen Bang-Jensen, Frédéric Havet, and Anders Yeo. The complexity of finding arc-disjoint branching flows. Research Report RR-8640, INRIA Sophia Antipolis ; INRIA, November 2014. [WWW ] [PDF ]
    Keywords: disjoint branchings, branching flow, polynomial algorithm, NP-complete.
     
  32. Nathann Cohen, David Coudert, Guillaume Ducoffe, and Aurélien Lancin. Applying clique-decomposition for computing Gromov hyperbolicity. Research Report RR-8535, INRIA, June 2014. [WWW ] [PDF ]
    Keywords: Hyperbolicity, Algorithms, Graphs, Decomposition.
     
  33. David Coudert and Guillaume Ducoffe. On the recognition of $C\_4$-free and $1/2$-hyperbolic graphs. Research Report RR-8458, INRIA, January 2014. [WWW ] [PDF ]
     
  34. David Coudert, Guillaume Ducoffe, and Nicolas Nisse. Diameter of Minimal Separators in Graphs. Research Report RR-8639, Inria Sophia Antipolis ; I3S ; INRIA, November 2014. [WWW ] [PDF ]
     
  35. David Coudert, Alvinice Kodjo, and Khoa Phan. Robust Energy-aware Routing with Redundancy Elimination. Research Report RR-8457, INRIA, January 2014. [WWW ] [PDF ]
    Keywords: Robust Network Optimization, Green Networking, Energy-aware Routing, Redundancy Elimination.
     
  36. David Coudert, Dorian Mazauric, and Nicolas Nisse. Experimental Evaluation of a Branch and Bound Algorithm for computing Pathwidth. Research Report RR-8470, INRIA, February 2014. [WWW ] [PDF ]
    Keywords: Pathwidth, vertex-separation, branch-and-bound, Sage.
     
  37. Gianlorenzo D'Angelo, Xavier Défago, and Nicolas Nisse. Understanding the Power of Stigmergy of Anonymous Agents in Discrete Environments. Research Report RR-8614, Inria, 2014. [WWW ] [PDF ]
     
  38. Frédéric Giroire, Frédéric Havet, and Joanna Moulierac. Compressing Two-dimensional Routing Tables with Order. Research Report RR-8658, INRIA Sophia Antipolis ; INRIA, December 2014. [WWW ] [PDF ]
    Keywords: compact tables., FPT, approximation algorithm, routing, routing tables, software defined networks, complexity.
     
  39. Frédéric Giroire, Joanna Moulierac, and T. Khoa Phan. Optimizing Rule Placement in Software-Defined Networks for Energy-aware Routing. Research Report RR-8537, INRIA, May 2014. [WWW ] [PDF ]
     
  40. Frédéric Giroire, Stéphane Pérennes, and Issam Tahiri. Grid spanners with low forwarding index for energy efficient networks. Research Report RR-8643, INRIA Sophia Antipolis ; INRIA, December 2014. [WWW ] [PDF ]
     
  41. Frédéric Havet and Bernard Lidicky. Splitting a tournament into two subtournaments with given minimum outdegree. Research Report RR-8469, INRIA, February 2014. [WWW ] [PDF ]
     
  42. Bi Li, Fatima Zahra Moataz, Nicolas Nisse, and Karol Suchan. Size-Constrained Tree Decompositions. Research Report, INRIA Sophia-Antipolis, October 2014. [WWW ] [PDF ]
     
  43. Euripides Markou, Nicolas Nisse, and Stéphane Pérennes. Exclusive Graph Searching vs. Pathwidth. Research Report RR-8523, INRIA, 2014. [WWW ] [PDF ]
    Keywords: graph searching, pathwidth, computational complexity, monotone strategies, exclusivity property.
     
  44. Joanna Moulierac and Khoa Phan. Optimizing IGP Link Weights for Energy-efficiency in a Changing World. Research Report RR-8534, INRIA, May 2014. [WWW ] [PDF ]
    Keywords: Robust Network Optimization, Energy-aware Routing, Green Networking, Traffic Engineering.
     
2013
  1. Roberto Baldoni, N. Nisse, and Maarten van Steen, editors. Proceedings of the 17th International Conference on Principles of Distributed Systems (OPODIS), volume 8304 of Lecture Notes in Computer Science, December 2013. Springer. [WWW ]
     
  2. Yann Busnel, N. Nisse, and Franck Rousseau, editors. Actes des 15es Rencontres Francophones sur les aspects Algorithmiques des Télécommunications (AlgoTel), May 2013. Univ. Nantes. [WWW ]
     
  3. R. Modrzejewski. Distribution et stockage dans les réseaux. PhD thesis, Université Nice Sophia Antipolis, October 2013. [WWW ] [PDF ]
     
  4. R. Pardo Soares. Jeux de Poursuite-Evasion, Décompositions et Convexité dans les Graphes. PhD thesis, Université Nice Sophia Antipolis, November 2013. [WWW ] [PDF ]
     
  5. L. Addario-Berry, F. Havet, C. Linhares Sales, B. Reed, and S. Thomassé. Oriented trees in digraphs. Discrete Mathematics, 313(8):967-974, 2013. [WWW ]
     
  6. J. Araujo, V. Campos, F. Giroire, N. Nisse, L. Sampaio, and R Soares. On the hull number of some graph classes. Theoretical Computer Science, 475:1-12, January 2013. [WWW ] [PDF ]
     
  7. J. Araujo and C. Linhares Sales. A Hajós-like theorem for weighted coloring. Journal of the Brazilian Computer Society, 19(3):275-278, January 2013. [WWW ] [PDF ]
     
  8. J-C. Bermond, M. Cosnard, and S. Pérennes. Directed acyclic graphs with the unique dipath property. Theoretical Computer Science, 504:5-11, September 2013. [WWW ] [PDF ]
     
  9. J-C. Bermond, L. Gargano, S. Pérennes, A. A. Rescigno, and U. Vaccaro. Optimal Time Data Gathering in Wireless Networks with Multidirectional Antennas. Journal of Theoretical Computer Science (TCS), 509:122-139, October 2013. [WWW ] [PDF ]
     
  10. J-C. Bermond, R. Klasing, N. Morales, S. Pérennes, and P. Reyes. Gathering radio messages in the path. Discrete Mathematics, Algorithms and Applications, 5(1):1-28, March 2013. [WWW ] [PDF ]
     
  11. S. Bessy and F. Havet. Enumerating the edge-colourings and total colourings of a regular graph. Journal of Combinatorial Optimization, 25(4):523-535, 2013. [WWW ]
     
  12. V. Campos, F. Havet, R. Sampaio, and A. Silva. Backbone colouring: Tree backbones with small diameter in planar graphs. Theoretical Computer Science, 487:50-64, 2013. [WWW ]
     
  13. S. Caron, F. Giroire, D. Mazauric, J. Monteiro, and S. Pérennes. P2P Storage Systems: Study of Different Placement Policies. Peer-to-Peer Networking and Applications, March 2013. [WWW ] [PDF ]
     
  14. S. Cicerone, G. D'Angelo, G. Di Stefano, D. Frigioni, and V. Maurizio. Engineering a new algorithm for distributed shortest paths on dynamic networks. Algorithmica, 66(1):51-86, May 2013. [WWW ] [PDF ]
    Abstract:
    We study the problem of dynamically updatingall-pairs shortest paths in a distributed network while edge update operations occur to the network. We consider the practical case of a dynamic network in which an edge update can occur while one or more other edge updates are under processing. A node of the network might be affected by a subset of these changes, thus being involved in the concurrent executions related to such changes. In this paper, we provide a new algorithm for this problem, and experimentally compare its performance with respect to those of the most popular solutions in the literature: the classical distributed Bellman-Ford method, which is still used in real network and implemented in the RIP protocol, and DUAL, the Diffuse Update ALgorithm, which is part of CISCO's widely used EIGRP protocol. As input to the algorithms, we used both real-world and artificial instances of the problem. The experiments performed show that the space occupancy per node required by the new algorithm is smaller than that required by both Bellman-Ford and DUAL. In terms of messages, the new algorithm outperforms both Bellman-Ford and DUAL on the real-world topologies, while on artificial instances, the new algorithm sends a number of messages that is more than that of DUAL and much smaller than that of Bellman-Ford.

     
  15. W. Fang, X. Liang, S. Li, L. Chiaraviglio, and N. Xiong. VMPlanner: Optimizing Virtual Machine Placement and Traffic Flow Routing to Reduce Network Power Costs in Cloud Data Centers. Computer Networks, 57(1):179-196, January 2013. [WWW ] [PDF ]
    Abstract:
    In recent years, the power costs of cloud data centers have become a practical concern and have attracted significant attention from both industry and academia. Most of the early works on data center energy efficiency have focused on the biggest power consumers (i.e., computer servers and cooling systems), yet without taking the networking part into consideration. However, recent studies have revealed that the network elements consume 10-20\0f the total power in the data center, which poses a great challenge to effectively reducing network power cost without adversely affecting overall network performance. Based on the analysis on topology characteristics and traffic patterns of data centers, this paper presents a novel approach, called VMPlanner, for network power reduction in the virtualization-based data centers. The basic idea of VMPlanner is to optimize both virtual machine placement and traffic flow routing so as to turn off as many unneeded network elements as possible for power saving. We formulate the optimization problem, analyze its hardness, and solve it by designing VMPlanner as a stepwise optimization approach with three approximation algorithms. VMPlanner is implemented and evaluated in a simulated environment with traffic traces collected from a data center test-bed, and the experiment results illustrate the efficacy and efficiency of this approach.

     
  16. S. Guillemot, F. Havet, C. Paul, and A. Perez. On the (non-)existence of polynomial kernels for $P\_l$-free edge modification problems. Algorithmica, 65(4):900-926, 2013. [WWW ]
     
  17. F. Havet and L. Sampaio. On the Grundy and b-chromatic numbers of a graph. Algorithmica, 65(4):885-899, 2013. [WWW ]
     
  18. F. Havet and X. Zhu. The game Grundy number of graphs. Journal of Combinatorial Optimization, 25(4):752-765, 2013. [WWW ]
     
  19. A. Lancin and D. Papadimitriou. DRMSim: A Routing-Model Simulator for Large-Scale Networks. ERCIM News, 94:31-32, July 2013. [WWW ]
     
  20. D. Agarwal, J. Araujo, C. Caillouet, F. Cazals, D. Coudert, and S. Perennes. Connectivity Inference in Mass Spectrometry based Structure Determination. In H.L. Bodlaender and G.F. Italiano, editors, European Symposium on Algorithms, volume 8125 of Lecture Notes in Computer Science - LNCS, Sophia-Antipolis, France, France, pages 289-300, 2013. Springer. [WWW ]
     
  21. J. Araujo, F. Giroire, Y. Liu, R. Modrzejewski, and J. Moulierac. Energy Efficient Content Distribution. In IEEE International Conference on Communications (ICC), Budapest, Hungary, pages 4233-4238, June 2013. [WWW ] [PDF ]
     
  22. J. Araujo, G. Morel, L. Sampaio, R. Soares, and V. Weber. Hull number: P5-free graphs and reduction rules. In VII Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS), Playa del Carmen, Mexico, March 2013. [WWW ] [PDF ]
     
  23. J-C. Bermond, D. Coudert, G. D'Angelo, and F. Z. Moataz. Diverse Routing with Star SRLGs. In N. Nisse, Franck Rousseau, and Yann Busnel, editors, 15èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel), Pornic, France, pages 1-4, May 2013. [WWW ] [PDF ]
     
  24. J-C. Bermond, D. Coudert, G. D'Angelo, and F. Z. Moataz. SRLG-Diverse Routing with the Star Property. In Design of Reliable Communication Networks, DRCN, Budapest, Hungary, March 2013. [WWW ] [PDF ]
     
  25. L. Blin, J. Burman, and N. Nisse. Exclusive Graph Searching. In 21st European Symposium on Algorithms (ESA 2013), volume LNCS 8125 of Lecture Notes in Computer Science / ARCoSS, Sophia Antipolis, France, pages 181-192, 2013. Springer. [WWW ] [PDF ]
     
  26. C. Caillouet, D. Coudert, and A. Kodjo. Robust optimization in multi-operators microwave backhaul networks. In 4th Global Information Infrastructure and Networking Symposium, Trento, Italy, pages 1-6, 2013. IEEE. [WWW ] [PDF ]
     
  27. C. Caillouet and A.M.C.A. Koster. Robust Round Weighting with Traffic Uncertainty in Wireless Mesh Networks. In 26th European Conference on Operational Research (EURO XXVI), Rome, Italy, July 2013. [WWW ]
     
  28. N. Cohen, D. Coudert, and A. Lancin. Algorithme exact et approché pour le calcul de l'hyperbolicité d'un graphe. In N. Nisse, Franck Rousseau, and Yann Busnel, editors, 15èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel), Pornic, France, pages 1-4, May 2013.
    Note: Page 1-4. [WWW ] [PDF ]
     
  29. D. Coudert, A. Koster, K. Phan, and M. Tieves. Robust Redundancy Elimination for Energy-aware Routing. In The 2013 IEEE International Conference on Green Computing and Communications (GreenCom 2013), Beijing, China, August 2013. IEEE. [WWW ] [PDF ]
     
  30. G. D'Angelo, G. Di Stefano, A. Navarra, N. Nisse, and K. Suchan. A unified approach for different tasks on rings in robot-based computing systems. In 15th Workshop on Advances in Parallel and Distributed Computational Models (IPDPS Workshop), Boston, United States, pages 667-676, 2013. [WWW ] [PDF ]
     
  31. F. Giroire, S. Gupta Kumar, R. Modrzejewski, J. Monteiro, and S. Perennes. Repair Time in Distributed Storage Systems. In 6th International Conference on Data Management in Cloud, Grid and P2P Systems (Globe 2013), volume 8059, Prague, Czech Republic, pages 99-110, August 2013. Springer. [WWW ] [PDF ]
     
  32. F. Giroire, D. Mazauric, N. Nisse, S. Pérennes, and R. Soares. Connected Surveillance Game. In 20th Colloquium on Structural Information and Communication Complexity (SIROCCO), volume LNCS 8179 of Lecture Notes in Computer Science (LNCS), Ischia, Italy, pages pages 68-79, 2013. Springer. [WWW ] [PDF ]
     
  33. F. Giroire, R. Modrzejewski, N. Nisse, and S. Pérennes. Maintaining Balanced Trees For Structured Distributed Streaming Systems. In 20th Colloquium on Structural Information and Communication Complexity (SIROCCO), volume LNCS 8179, Ischia, Italy, pages pages 177-188, 2013. [WWW ] [PDF ]
     
  34. F. Giroire, S. Pérennes, and I. Tahiri. On the Hardness of Equal Shortest Path Routing. In International Network Optimization Conference, volume 41 of Electronic Notes in Discrete Mathematics, Tenerife, Spain, pages 439-446, 2013. Elsevier. [WWW ] [PDF ]
     
  35. F. Giroire, S. Pérennes, and I. Tahiri. Sur la complexité du routage OSPF. In N. Nisse, Franck Rousseau, and Yann Busnel, editors, 15èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel), Pornic, France, pages 1-4, 2013. [WWW ] [PDF ]
     
  36. A. Koster, K. Phan, and M. Tieves. Extended Cutset Inequalities for the Network Power Consumption Problem. In INOC - International Network Optimization Conference - 2013, volume 41, Tenerife, Spain, pages 69-76, May 2013. Electronic Notes in Discrete Mathematics, Springer. [WWW ] [PDF ]
     
  37. E. Le Rouzic, E. Bonetto, L. Chiaraviglio, F. Giroire, F. Idzikowski, F. Jimenez, C. Lange, J. Montalvo, F. Musumeci, I. Tahiri, A. Valenti, W. Van Heddeghem, Y. Ye, A. Bianco, and A. Pattavina. TREND towards more energy-efficient optical networks. In 17th International Conference on Optical Network Design and Modeling (ONDM), Brest, France, pages 211--216, 2013. [WWW ] [PDF ]
     
  38. R. Modrzejewski, L. Chiaraviglio, I. Tahiri, F. Giroire, E. Le Rouzic, E. Bonetto, F. Masumeci, R. Gonzalez, and C. Guerro. Energy Efficient Content Distribution in an ISP Network. In IEEE Global Communications Conference, Atlanta, United States, December 2013. [WWW ] [PDF ]
     
  39. N. Nisse. Fractional Combinatorial Two-Player Games. In 26th European Conference on Operational Research (EURO XXVI), Italy, 2013. [WWW ]
     
  40. N. Nisse and R. Soares. On the Monotonicity of Process Number. In 7th Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS), volume 44, Mexico, Mexico, pages 141-147, 2013. Elsevier. [WWW ] [PDF ]
     
  41. R. Pardo Soares. Fractional Combinatorial Games on Graphs. In N. Nisse, Franck Rousseau, and Yann Busnel, editors, 15èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel), Pornic, France, 2013. [WWW ] [PDF ]
     
  42. D. Agarwal, J. Araujo, C. Caillouet, F. Cazals, D. Coudert, and S. Pérennes. Connectivity Inference in Mass Spectrometry based Structure Determination. Research Report RR-8320, INRIA, June 2013. [WWW ] [PDF ]
     
  43. O. Amini, D. Coudert, and N. Nisse. Some Results on Non-deterministic Graph Searching in Trees. Research Report, 2013. [WWW ] [PDF ]
     
  44. J. Araujo, F. Giroire, Y. Liu, R. Modrzejewski, and J. Moulierac. Energy Efficient Content Distribution. Research Report RR-8091, INRIA, May 2013. [WWW ] [PDF ]
     
  45. J. Araujo, N. Nisse, and S. Pérennes. Weighted Coloring in Trees. Research Report RR-8249, INRIA, 2013. [WWW ] [PDF ]
     
  46. J-C. Bermond, B. Li, N. Nisse, H. Rivano, and M-L. Yu. Data Gathering and Personalized Broadcasting in Radio Grids with Interferences. Research Report RR-8218, INRIA, 2013. [WWW ] [PDF ]
     
  47. P. Bertomé, T. Bouvier, F. Mazoit, N. Nisse, and R. Pardo Soares. An Unified FPT Algorithm for Width of Partition Functions. Research Report RR-8372, INRIA, September 2013. [WWW ] [PDF ]
     
  48. L. Blin, J. Burman, and N. Nisse. Exclusive Graph Searching. Report, June 2013. [WWW ] [PDF ]
     
  49. D. Coudert, Luc Hogie, A. Lancin, D. Papadimitriou, S. Pérennes, and I. Tahiri. Feasibility study on distributed simulations of BGP. Research Report RR-8283, INRIA, April 2013. [WWW ] [PDF ]
     
  50. G. D'Angelo, A. Navarra, and N. Nisse. Robot Searching and Gathering on Rings under Minimal Assumptions. Research Report RR-8250, INRIA, 2013. [WWW ] [PDF ]
     
  51. F. Giroire, D. Mazauric, N. Nisse, S. Pérennes, and R. Pardo Soares. Connected Surveillance Game. Research Report RR-8297, INRIA, May 2013. [WWW ] [PDF ]
     
  52. F. Giroire, R. Modrzejewski, N. Nisse, and S. Pérennes. Maintaining Balanced Trees For Structured Distributed Streaming Systems. Research Report RR-8309, INRIA, May 2013. [WWW ] [PDF ]
     
  53. F. Giroire, N. Nisse, S. Pérennes, and R. Pardo Soares. Fractional Combinatorial Two-Player Games. Research Report RR-8371, INRIA, September 2013. [WWW ] [PDF ]
     
  54. F. Havet and A. K. Maia. On disjoint directed cycles with prescribed minimum lengths. Research Report RR-8286, INRIA, April 2013. [WWW ] [PDF ]
     
2012
  1. J. Araujo. Graph Coloring and Graph Convexity. PhD thesis, University of Nice-Sophia Antipolis and Federal University of Ceará, September 2012. [PDF ]
    Abstract:
    In this thesis, we study several problems of Graph Theory concerning Graph Coloring and Graph Convexity. Most of the results contained here are related to the computational complexity of these problems for particular graph classes. In the first and main part of this thesis, we deal with Graph Coloring which is one of the most studied areas of Graph Theory. We first consider three graph coloring problems called Greedy Coloring, Weighted Coloring and Weighted Improper Coloring. Then, we deal with a decision problem, called Good Edge-Labeling, whose definition was motivated by the Wavelength Assignment problem in optical networks. The second part of this thesis is devoted to a graph optimization parameter called (geodetic) hull number. The definition of this parameter is motivated by an extension to graphs of the notions of convex sets and convex hulls in the Euclidean space. Finally, we present in the appendix other works developed during this thesis, one about Eulerian and Hamiltonian directed hypergraphs and the other concerning distributed storage systems.

     
  2. L. Sampaio. Algorithmic aspects of graph colouring heuristics. PhD thesis, University of Nice-Sophia Antipolis, November 2012. [PDF ]
    Abstract:
    A proper colouring of a graph is a function that assigns a colour to each vertex with the restriction that adjacent vertices are assigned with distinct colours. Proper colourings are a natural model for many problems, like scheduling, frequency assignment and register allocation. The problem of finding a proper colouring of a graph with the minimum number of colours is a well-known NP-hard problem. In this thesis we study the Grundy number and the b-chromatic number of graphs, two parameters that evaluate some heuristics for finding proper colourings. We start by giving the state of the art of the results about these parameters. Then, we show that the problem of determining the Grundy number of bipartite or chordal graphs is NP-hard, but it is solvable in polynomial time for P5-free bipartite graphs. After, we show that the problem of determining the b-chromatic number of a chordal distance-hereditary graph is NP-hard, and we give polynomial-time algorithms for some subclasses of block graphs, complement of bipartite graphs and P4-sparse graphs. We also consider the fixed-parameter tractability of determining the Grundy number and the b-chromatic number, and in particular we show that deciding if the Grundy number (or the b-chromatic number) of a graph G is at least |V(G)| - k admits an FPT algorithm when k is the parameter. Finally, we consider the computational complexity of many problems related to comparing the b-chromatic number and the Grundy number with various other related parameters of a graph.

     
  3. B. M. T. Worou. Outils Algorithmiques pour la Détection des Communautés dans les Réseaux. PhD thesis, University of Nice-Sophia Antipolis, December 2012.
    Abstract:
    This thesis concerns the algorithmic aspects of the communities' detection in large graphs. The work can be used by a telecommunications operator whose graphs are associated to telephone calls and SMS or telecommunication networks. In this context, the detection of communities is used for the content recommendation, the analysis of customer data, the classification of Web pages, the detection of Web spamming, marketing activities and others. This thesis is organized around two major parts. In the first part, we introduce the field of detection of communities. Indeed this problem has been studied with different points of view during the last years. The main methods and applications are presented in this descriptive part. In the second part, we present our contribution to the problem. Our contribution consists of two main topics. First, we introduce a new quality function, the fractional arboricity which is more adapted to the problem of detecting communities in social networks. Then, we present a fast and performance guaranteed algorithm to approximate the optimal fractional arboricity and identifies the communities in question. Second, we study the detection of communities by optimizing the modularity, the most used quality function for communities' detection. We rewrite this function, and then, find new interpretations of the modularity and also links between the modularity and others cut functions. Finally, we propose two heuristics to approximate the optimization of the modularity. The first is an algorithm that approximates the modularity by using the Fiedler vector of the Laplacian matrix of the graph. The second algorithm is a fast heuristic based on the representation of physical interaction of nodes in a metric space. With this representation, we define an attraction/ repulsion mechanism between the vertices and then we obtain clusters in communities. Finally, we combine the optimization of the fractional arboricity and the optimization of the modularity into one communities' detection tool.

     
  4. F. Giroire, D. Mazauric, and J. Moulierac. Energy Efficient Routing by Switching-Off Network Interfaces, chapter 10 - Energy-Aware Systems and Networking for Sustainable Initiatives, pages 207-236. IGI Global, june 2012. [WWW ] [PDF ]
    Abstract:
    Several studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces, line cards, base chassis,... The goal thus is to find a routing that minimizes the (weighted) number of active network elements used when routing. In this paper, we consider a simplified architecture where a connection between two routers is represented as a link joining two network interfaces. When a connection is not used, both network interfaces can be turned off. Therefore, in order to reduce power consumption, the goal is to find the routing that minimizes the number of used links while satisfying all the demands. We first define formally the problem and we model it as an integer linear program. Then, we prove that this problem is not in APX, that is there is no polynomial-time constant-factor approximation algorithm. We propose a heuristic algorithm for this problem and we also prove some negative results about basic greedy and probabilistic algorithms. Thus we present a study on specific topologies, such as trees, grids and complete graphs, that provide bounds and results useful for real topologies. We then exhibit the gain in terms of number of network interfaces (leading to a global reduction of approximately 33 MWh for a medium-sized backbone network) for a set of existing network topologies: we see that for almost all topologies more than one third of the network interfaces can be spared for usual ranges of operation. Finally, we discuss the impact of energy efficient routing on the stretch factor and on fault tolerance.

     
  5. O. Amini, D. Peleg, S. Pérennes, I. Sau, and S. Saurabh. On the approximability of some degree-constrained subgraph problems. Discrete Applied Mathematics, 160(12):1661 - 1679, 2012. [WWW ] [PDF ]
    Abstract:
    In this article we provide hardness results and approximation algorithms for the following three natural degree-constrained subgraph problems, which take as input an undirected graph {$G = (V, E )$}. Let {$d \geq 2$} be a fixed integer. The Maximum {$d$}−degree-bounded Connected Subgraph ( MDBCS d ) problem takes as additional input a weight function {$\omega : E \right R^+$} , and asks for a subset {$E'\subseteq E$} such that the subgraph induced by {$E'$} is connected, has maximum degree at most d , and {$\sum_{e\in E'}\omeage(e)$} is maximized. The Minimum Subgraph of Minimum Degree {$\geq d$} ( MSMD d ) problem involves finding a smallest subgraph of G with minimum degree at least d . Finally, the Dual Degree-dense k -Subgraph ( DDD k S ) problem consists in finding a subgraph H of G such that {$| V ( H ) | \leq k$} and the minimum degree in H is maximized.

     
  6. J. Araujo, J-C. Bermond, F. Giroire, F. Havet, D. Mazauric, and R. Modrzejewski. Weighted improper colouring. Journal of Discrete Algorithms, 16:53-66, 2012.
    Note: Selected papers from the 22nd International Workshop on Combinatorial Algorithms (IWOCA 2011). [WWW ] [PDF ]
    Abstract:
    In this paper, we study a colouring problem motivated by a practical frequency assignment problem and, up to our best knowledge, new. In wireless networks, a node interferes with other nodes, the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles, etc. We model this with a weighted graph $(G,w)$ where the weight function $w$ on the edges of $G$ represents the noise (interference) between the two end-vertices. The total interference in a node is then the sum of all the noises of the nodes emitting on the same frequency. A weighted $t$-improper $k$-colouring of $(G,w)$ is a $k$-colouring of the nodes of $G$ (assignment of $k$ frequencies) such that the interference at each node does not exceed the threshold $t$. We consider here the Weighted Improper Colouring problem which consists in determining the weighted $t$-improper chromatic number defined as the minimum integer $k$ such that $(G,w)$ admits a weighted $t$-improper $k$-colouring. We also consider the dual problem, denoted the Threshold Improper Colouring problem, where, given a number $k$ of colours, we want to determine the minimum real $t$ such that $(G,w)$ admits a weighted $t$-improper $k$-colouring. We show that both problems are NP-hard and first present general upper bounds for both problems; in particular we show a generalisation of Lov\'asz's Theorem for the weighted $t$-improper chromatic number. Motivated by the original application, we then study a special interference model on various grids (square, triangular, hexagonal) where a node produces a noise of intensity 1 for its neighbours and a noise of intensity 1/2 for the nodes at distance two. We derive the weighted $t$-improper chromatic number for all values of $t$.

     
  7. J. Araujo, N. Cohen, F. Giroire, and F. Havet. Good edge-labelling of graphs. Discrete Applied Mathematics, 160(18):2501-2513, 2012. [WWW ] [PDF ]
    Abstract:
    {A {\it good edge-labelling} of a graph $G$ is a labelling of its edges such that for any two distinct vertices $u$, $v$, there is at most one $(u,v)$-path with non-decreasing labels. This notion was introduced in~\cite{BCP09} to solve wavelength assignment problems for specific categories of graphs. In this paper, we aim at characterizing the class of graphs that admit a good edge-labelling. First, we exhibit infinite families of graphs for which no such edge-labelling can be found. We then show that deciding if a graph admits a good edge-labelling is NP-complete. Finally, we give large classes of graphs admitting a good edge-labelling: $C_3$-free outerplanar graphs, planar graphs of girth at least 6, subcubic $\{C_3,K_{2,3}\}$-free graphs.} doi = {10.1016/j.dam.2011.07.021}

     
  8. J. Araujo and C. Linhares Sales. On the Grundy number of graphs with few P4's. Discrete Applied Mathematics, 160(18):2514-2522, 2012.
    Note: V Latin American Algorithms, Graphs, and Optimization Symposium -- Gramado, Brazil, 2009. [WWW ] [PDF ]
    Abstract:
    "The Grundy number of a graph $G$ is the largest number of colors used by any execution of the greedy algorithm to color $G$. The problem of determining the Grundy number of $G$ is polynomial if $G$ is a $P_4$-free graph and NP-hard if $G$ is a $P_5$-free graph. In this article, we define a new class of graphs, the fat-extended $P_4$-laden graphs, and we show a polynomial time algorithm to determine the Grundy number of any graph in this class. Our class intersects the class of $P_5$-free graphs and strictly contains the class of $P_4$-free graphs. More precisely, our result implies that the Grundy number can be computed in polynomial time for any graph of the following classes: $P_4$-reducible, extended $P_4$-reducible, $P_4$-sparse, extended $P_4$-sparse, $P_4$-extendible, $P_4$-lite, $P_4$-tidy, $P_4$-laden and extended $P_4$-laden, which are all strictly contained in the fat-extended $P_4$-laden class."

     
  9. J. Bang-Jensen, F. Havet, and N. Trotignon. Finding an induced subdivision of a digraph. Theoretical Computer Science, 443:10-24, 2012. [WWW ] [PDF ]
    Abstract:
    We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) $G$, does it contain an induced subdivision of a prescribed digraph $D$? The complexity of this problem depends on $D$ and on whether $H$ must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial instances as well as several NP-completeness proofs.

     
  10. L. Barrière, P. Flocchini, F. Fomin, P. Fraigniaud, N. Nisse, N. Santoro, and D. Thilikos. Connected Graph Searching. Information and Computation, 219:1-16, 2012. [WWW ] [PDF ]
    Abstract:
    In graph searching game the opponents are a set of searchers and a fugitive in a graph. The searchers try to capture the fugitive by applying some sequence moves that include placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture by moving along unguarded paths. The search number of a graph is the minimum number of searchers required to guarantee the capture of the fugitive. In this paper, we initiate the study of this game under the natural restriction of connectivity where we demand that in each step of the search the locations of the graph that are clean (i.e. non-accessible to the fugitive) remain connected. We give evidence that many of the standard mathematical tools used so far in the classic graph searching fail under the connectivity requirement. We also settle the question on ``the price of connectivity'' that is how many searchers more are required for searching a graph when the connectivity demand is imposed. We make estimations of the price of connectivity on general graphs and we provide tight bounds for the case of trees. In particular, for an $n$-vertex graph the ratio between the connected searching number and the non-connected one is $O(\log n)$ while for trees this ratio is always at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for all graphs. Our combinatorial results imply a complete characterization of connected graph searching on trees. It is based on a forbidden-graph characterization of the connected search number. We prove that the connected search game is monotone for trees, i.e. restricting search strategies to only those where the clean territories increase monotonically does not require more searchers. A consequence of our results is that the connected search number can be computed in polynomial time on trees, moreover, we show how to make this algorithm distributed. Finally, we reveal connections of this parameter to other invariants on trees such as the Horton-Stralher number.

     
  11. S. Baruah, V. Bonifaci, G. D'Angelo, H. Li, A. Marchetti-Spaccamela, N. Megow, and L. Stougie. Scheduling Real-time Mixed-criticality Jobs. IEEE Transactions on Computers, 61(8):1140-1152, 2012. [WWW ] [PDF ]
    Abstract:
    Many safety-critical embedded systems are subject to certification requirements; some systems may be required to meet multiple sets of certification requirements, from different certification authorities. Certification requirements in such "mixed-criticality" systems give rise to interesting scheduling problems, that cannot be satisfactorily addressed using techniques from conventional scheduling theory. In this paper, we study a formal model for representing such mixed-criticality workloads. We demonstrate first the intractability of determining whether a system specified in this model can be scheduled to meet all its certification requirements, even for systems subject to merely two sets of certification requirements. Then we quantify, via the metric of processor speedup factor, the effectiveness of two techniques, reservation-based scheduling and priority-based scheduling, that are widely used in scheduling such mixed-criticality systems, showing that the latter of the two is superior to the former. We also show that the speedup factors we obtain are tight for these two techniques.

     
  12. R. Bauer, G. D'Angelo, D. Delling, A. Schumm, and D. Wagner. The Shortcut Problem - Complexity and Algorithms. Journal of Graph Algorithms and Applications, 16(2):447-481, 2012. [WWW ] [PDF ]
    Abstract:
    We study a graph-augmentation problem arising from a technique applied in recent approaches for route planning. Many such methods enhance the graph by inserting shortcuts, i.e., additional edges (u,v) such that the length of (u,v) is the distance from u to v. Given a weighted, directed graph G and a number c in Z, the shortcut problem asks how to insert c shortcuts into G such that the expected number of edges that are contained in an edge-minimal shortest path from a random node s to a random node t is minimal. In this work, we study the algorithmic complexity of the problem and give approximation algorithms for a special graph class. Further, we state ILP-based exact approaches and show how to stochastically evaluate a given shortcut assignment on graphs that are too large to do so exactly.

     
  13. J-C. Bermond, D. Coudert, J. Moulierac, S. Pérennes, I. Sau, and F. Solano Donado. GMPLS Label Space Minimization through Hypergraph Layouts. Theoretical Computer Science (TCS), 444:3-16, July 2012. [WWW ] [PDF ]
    Abstract:
    {A}ll-{O}ptical {L}abel {S}witching ({AOLS}) is a new technology that performs packet forwarding without any optical-electrical-optical conversions. {I}n this report, we study the problem of routing a set of requests in {AOLS} networks using {GMPLS} technology, with the aim of minimizing the number of labels required to ensure the forwarding. {W}e first formalize the problem by associating to each routing strategy a logical hypergraph, called a hypergraph layout, whose hyperarcs are dipaths of the physical graph, called tunnels in {GMPLS} terminology. {W}e define a cost function for the hypergraph layout, depending on its total length plus its total hop count. {M}inimizing the cost of the design of an {AOLS} network can then be expressed as finding a minimum cost hypergraph layout. {W}e prove hardness results for the problem, namely for general directed networks we prove that it is {NP}-hard to find a {C} log n-approximation, where {C} is a positive constant and n is the number of nodes of the network. {F}or symmetric directed networks, we prove that the problem is {APX}-hard. {T}hese hardness results hold even if the traffic instance is a partial broadcast. {O}n the other hand, we provide approximation algorithms, in particular an {O}(log n)-approximation for symmetric directed networks. {F}inally, we focus on the case where the physical network is a directed path, providing a polynomial-time dynamic programming algorithm for a fixed number k of sources running in {O}(n^{k+2}) time.

     
  14. J-C. Bermond and J. Moulierac. Internet et la théorie des graphes. Revue TDC Textes et documents pour la Classe : la révolution Internet, 1042:32-33, 2012. [WWW ] [PDF ]
    Abstract:
    La th{\'e}orie des graphes constitue un domaine des math{\'e}matiques qui s'est d{\'e}velopp{\'e} au sein de disciplines diverses telles que la chimie (mod{\'e}lisation de structures), la biologie (g{\'e}nome), les sciences sociales (mod{\'e}lisation des relations) et le transport (r{\'e}seaux routiers, {\'e}lectriques, etc.). Le cycle eul{\'e}rien et le cycle hamiltonien R{\'e}seaux internet et graphes " petit-monde " Comment calculer un plus court chemin ?

     
  15. J-C. Bermond and J. Peters. Optimal Gathering in Radio Grids with Interference. Theoretical Computer Science, 457:10-26, October 2012. [WWW ] [PDF ]
    Abstract:
    We study the problem of gathering information from the nodes of a radio network into a central node. We model the network of possible transmissions by a graph and consider a binary model of interference in which two transmissions interfere if the distance in the graph from the sender of one transmission to the receiver of the other is $d_I$ or less. A {\em round} is a set of non-interfering transmissions. In this paper, we determine the exact number of rounds required to gather one piece of information from each node of a square two-dimensional grid into the central node. If $d_I = 2k-1$ is odd, then the number of rounds is $k(N-1)-c_k$ where $N$ is the number of nodes and $c_k$ is a constant that depends on $k$. If $d_I = 2k$ is even, then the number of rounds is $(k+\frac{1}{4})(N-1)-c'_k$ where $c'_k$ is a constant that depends on $k$. The even case uses a method based on linear programming duality to prove the lower bound, and sophisticated algorithms using the symmetry of the grid and non-shortest paths to establish the matching upper bound. We then generalize our results to hexagonal grids.

     
  16. S. Bhadra and A. Ferreira. Computing multicast trees in dynamic networks and the complexity of connected components in evolving graphs. J. Internet Services and Applications, 3(3):269-275, 2012. [WWW ] [PDF ]
    Abstract:
    New technologies and the deployment of mobile and nomadic services are driving the emergence of complex communications networks, that have a highly dynamic behavior. This naturally engenders new route-discovery problems under changing conditions over these networks. Unfortunately, the temporal variations in the network topology are hard to be effectively captured in a classical graph model. In this paper, we use and extend a recently proposed graph theoretic model, which helps capture the evolving characteristi- c of such networks, in order to compute multicast trees with minimum overall transmission time for a class of wireless mobile dynamic networks. We first show that computing different types of strongly connected components in this model is NP-Complete, and then propose an algorithm to build all rooted directed minimum spanning trees in already identified strongly connected components.

     
  17. V. Campos, A. Gyárfás, F. Havet, C. Linhares Sales, and F. Maffray. New bounds on the Grundy number of products of graphs. Journal of Graph Theory, 71(1):78-88, 2012. [WWW ] [PDF ]
    Abstract:
    The Grundy number of a graph $G$ is the largest $k$ such that $G$ has a greedy $k$-colouring, that is, a colouring with $k$ colours obtained by applying the greedy algorithm according to some ordering of the vertices of $G$. In this paper, we give new bounds on the Grundy number of the product of two graphs.

     
  18. Y. Chen, E. Le Merrer, Z. Li, Y. Liu, and G. Simon. OAZE: A Network-Friendly Distributed Zapping System for Peer-to-Peer IPTV. Computer Networks, 56(1):365-377, 2012. [WWW ] [PDF ]
    Abstract:
    IPTV systems attracting millions of users are now commonly deployed on peer-to-peer (P2P) infrastructures. Each channel is associated with a P2P overlay network for\ med by the users who receive, watch and redistribute this channel. However, zapping from one P2P overlay to another requires a significant amount of time, and therefore the P2P\ IPTV experience is not as good as for a multicast-based IPTV. In order to speed up the switching process and to reduce the overall cross-domain traffic generated by the IPTV s\ ystem, we propose a distributed algorithm called OAZE for Overlay Augmentation for Zapping Experience. The main idea is that every peer maintains connections to other peers in \ a subset of all channels to which it is likely to zap, and collaborates with the other peers in its channel for the remaining channels. We present in this paper the OAZE mechan\ ism. We focus in particular on the channel assignment problem, which consists in determining the optimal distribution of the responsibility to maintain contact peers in other c\ hannels in a given overlay. We propose an approximate algorithm having guaranteed performances in comparison to the optimal one, and an algorithm that is simpler and more pract\ ical. Simulations show that OAZE leads to substantial improvements on the connections between peers, resulting in less switching delay and lower network cost. This approach is \ overlay independent and is an appealing add-on for existing P2P IPTV systems.

     
  19. D. Coudert, F. Huc, and D. Mazauric. A Distributed Algorithm for Computing the Node Search Number in Trees. Algorithmica, 63(1-2):158-190, 2012. [WWW ] [PDF ]
    Abstract:
    We present a distributed algorithm to compute the node search number in trees. This algorithm extends the centralized algorithm proposed by Ellis \emph{et al.} [EST94]. It can be executed in an asynchronous environment, requires an overall computation time of $O(n\log{n})$, and $n$ messages of $\log_3{n}+4$ bits each. The main contribution of this work lies in the data structure proposed to design our algorithm, called \emph{hierarchical decomposition}. This simple and flexible data structure is used for four operations: updating the node search number after addition or deletion of any tree-edges in a distributed fashion; computing it in a tree whose edges are added sequentially and in any order; computing other graph invariants such as the process number and the edge search number, by changing only initialization rules; extending our algorithms for trees and forests of unknown size (using messages of up to $2\log_3{n}+5$ bits).

     
  20. G. D'Angelo, G. Di Stefano, and A. Navarra. Minimize the Maximum Duty in Multi-interface Networks. Algorithmica, 63(1-2):274-295, 2012. [WWW ] [PDF ]
    Abstract:
    We consider devices equipped with multiple wired or wireless interfaces. By switching of various interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider two basic networking problems in the field of multi-interface networks. The first one, known as the Coverage problem, requires to establish the connections defined by a network. The second one, known as Connectivity problem, requires to guarantee a connecting path between any pair of nodes of a network. Both are subject to the constraint of keeping as low as possible the maximum cost set of active interfaces at each single node. We study the problems of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges in the first case, or to ensure connectivity in the second case. We prove that the Coverage problem is NP-hard for any fixed $\Delta$$\ge$5 and k$\ge$16, with $\Delta$ being the maximum degree, and k being the number of different interfaces among the network. We also show that, unless P=NP, the problem cannot be approximated within a factor of $\eta$$\Delta$, for a certain constant $\eta$. We then provide a general approximation algorithm which guarantees a factor of O((1+b)$\Delta$), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented. Concerning the Connectivity problem, we prove that it is NP-hard for any fixed $\Delta$$\ge$3 and k$\ge$10. Also for this problem, the inapproximability result holds, that is, unless P=NP, the problem cannot be approximated within a factor of $\eta$$\Delta$, for a certain constant $\eta$. We then provide approximation and exact algorithms for the general problem and for special cases, respectively.

     
  21. L. Esperet, F. Kardos, and D. Král'. A superlinear bound on the number of perfect matchings in cubic bridgeless graphs. European Journal of Combinatorics, 33(5):767-798, 2012. [WWW ] [PDF ]
    Abstract:
    Lov{\'{a}}sz and Plummer conjectured in the 1970's that cubic bridgeless graphs have exponentially many perfect matchings. This conjecture has been verified for bipartite graphs by Voorhoeve in 1979, and for planar graphs by Chudnovsky and Seymour in 2008, but in general only linear bounds are known. In this paper, we provide the first superlinear bound in the general case.

     
  22. A. Ferreira and A. Jarry. Minimum-Energy Broadcast Routing in Dynamic Wireless Networks. Journal of Green Engineering, 2(2):115-123, 2012. [PDF ]
    Abstract:
    One of the new challenges facing research in wireless networks is the design of algorithms and protocols that are energy aware. A good example is the minimum-energy broadcast routing problem for a static network in the plane, which attracted a great deal of attention these past years. The problem is NP-hard and its approximation ratio complexity is a solution proved to be within a factor 6 of the optimal, based on finding a Minimum Spanning Tree of the static planar network. In this paper, we use for the first time the evolving graph combinatorial model as a tool to prove an NP-Completeness result, namely that computing a Minimum Spanning Tree of a planar network in the presence of mobility is actually NP-Complete. This result implies that the above approximation solution cannot be used in dynamic wireless networks. On the positive side, we give a polynomial-time algorithm to build a rooted spanning tree of an on/off network, that minimizes the maximum energy used.

     
  23. D. Gonçalves, F. Havet, A. Pinlou, and S. Thomassé. On spanning galaxies in digraphs. Discrete Applied Mathematics, 160(6):744-754, 2012. [WWW ] [PDF ]
    Abstract:
    In a directed graph, a {\it star} is an arborescence with at least one arc, in which the root dominates all the other vertices. A {\it galaxy} is a vertex-disjoint union of stars. In this paper, we consider the \textsc{Spanning Galaxy} problem of deciding whether a digraph $D$ has a spanning galaxy or not. We show that although this problem is NP-complete (even when restricted to acyclic digraphs), it becomes polynomial-time solvable when restricted to strong digraphs. In fact, we prove that restricted to this class, the \pb\ is equivalent to the problem of deciding if a strong digraph has a strong digraph with an even number of vertices. We then show a polynomial-time algorithm to solve this problem. We also consider some parameterized version of the \pb. Finally, we improve some results concerning the notion of directed star arboricity of a digraph $D$, which is the minimum number of galaxies needed to cover all the arcs of $D$. We show in particular that $dst(D)\leq \Delta(D)+1$ for every digraph $D$ and that $dst(D)\leq \Delta(D)$ for every acyclic digraph $D$.

     
  24. F. Havet, C. Linhares Sales, and L. Sampaio. b-coloring of tight graphs. Discrete Applied Mathematics, 160(18):2709-2715, 2012. [WWW ]
     
  25. F. Havet, B. Reed, and J.-S. Sereni. Griggs and Yeh's conjecture and $L(p,1)$-labellings. SIAM Journal on Discrete Mathematics, 26(1):145-168, 2012. [WWW ] [PDF ]
    Abstract:
    An $L(p,1)$-labeling of a graph is a function $f$ from the vertex set to the positive integers such that $|f(x)-f(y)|\geqslant p$ if dist$(x,y)=1$ and $|f(x)-f(y)|\geqslant 1$ if dist$(x,y)=2$, where dist$(x,y)$ is the distance between the two vertices $x$ and $y$ in the graph. The span of an $L(p,1)$-labeling $f$ is the difference between the largest and the smallest labels used by $f$. In 1992, Griggs and Yeh conjectured that every graph with maximum degree $\Delta\geqslant 2$ has an $L(2,1)$-labeling with span at most $\Delta^2$. We settle this conjecture for $\Delta$ sufficiently large. More generally, we show that for any positive integer $p$ there exists a constant $\Delta_p$ such that every graph with maximum degree $\Delta\geqslant \Delta_p$ has an $L(p,1)$-labeling with span at most $\Delta^2$. This yields that for each positive integer $p$, there is an integer $C_p$ such that every graph with maximum degree $\Delta$ has an $L(p,1)$-labeling with span at most $\Delta^2+C_p$.

     
  26. N. Nisse, I. Rapaport, and K. Suchan. Distributed computing of efficient routing schemes in generalized chordal graphs. Theoretical Computer Science, 444(27):17-27, 2012. [WWW ] [PDF ]
    Abstract:
    Efficient algorithms for computing routing tables should take advantage of the particular properties arising in large scale networks. There are in fact at least two properties that any routing scheme must consider: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Therefore, we propose a routing scheme that computes short routes in the class of k-chordal graphs, i.e., graphs with no chordless cycles of length more than k. We study the tradeoff between the length of routes and the time complexity for computing them. In the class of k-chordal graphs, our routing scheme achieves an additive stretch of at most k-1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k-1. In order to compute the routing tables of any n-node graph with diameter D we propose a distributed algorithm which uses O(log n)-bit messages and takes O(D) time. We then propose a slightly modified version of the algorithm for computing routing tables in time O(min{Delta.D, n}), where Delta is the the maximum degree of the graph. Using these tables, our routing scheme achieves a better additive stretch of 1 in chordal graphs (notice that chordal graphs are 3-chordal graphs). The routing scheme uses addresses of size log n bits and local memory of size 2(d-1) log n bits in a node of degree d.

     
  27. M. Ajmone-Marsan, S. Buzzi, L. Chiaraviglio, M. Meo, C. Guerrero, F. Idzikowski, Y. Ye, and J. Lopez Vizcaino. TREND: Toward Real Energy-efficient Network Design. In SustainIT 2012 - The Second IFIP Conference on Sustainable Internet and ICT for Sustainability, Pisa, Italy, pages 1-6, October 2012. [PDF ]
    Abstract:
    This paper briefly describes the objectives of the TREND (Toward Real Energy-efficient Network Design) Network of Excellence of the European Commission 7th Framework Programme, and outlines some of the main results obtained so far within the project, looking at wireless access networks, core networks, and content distribution issues.

     
  28. S. Baruah, V. Bonifaci, G. D'Angelo, H. Li, A. Marchetti-Spaccamela, S. Van Der Ster, and L. Stougie. The preemptive uniprocessor scheduling of mixed-criticality implicit-deadline sporadic task systems. In 24th Euromicro Conference on Real-Time Systems (ECRTS12), Pisa, Italy, pages 145-154, July 2012. IEEE. [WWW ] [PDF ]
    Abstract:
    Systems in many safety-critical application domains are subject to certification requirements. For any given system, however, it may be the case that only a subset of its functionality is safety-critical and hence subject to certification; the rest of the functionality is non safety critical and does not need to be certified, or is certified to a lower level of assurance. An algorithm called EDF-VD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixed-criticality task systems. Analyses of EDF-VD significantly superior to previously-known ones are presented, based on metrics such as processor speedup factor (EDF-VD is proved to be optimal with respect to this metric) and utilization bounds.

     
  29. F. Becker, A. Kosowski, N. Nisse, I. Rapaport, and K. Suchan. Interconnection network with a shared whiteboard: Impact of (a)synchronicity on computing power. In 24th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 11-17, 2012. ACM. [WWW ] [PDF ]
    Abstract:
    In this work we study the computational power of graph-based models of distributed computing in which each node additionally has access to a global whiteboard. A node can read the contents of the whiteboard and, when activated, can write one message of $O(\log n)$ bits on it. A message is only based on the local knowledge of the node and the current content of the whiteboard. When the protocol terminates, each node computes the output based on the final contents of the whiteboard in order to answer some question on the network's topology. We propose a framework to formally define several scenarios modelling how nodes access the whiteboard, in a synchronous way or not. This extends the work of Becker {\it et al.} [IPDPS 2011] where nodes were imposed to create their messages only based on their local knowledge (i.e., with the whiteboard empty). We prove that the four models studied have increasing power of computation: any problem that can be solved in the weakest one can be solved in the the second, and so on. Moreover, we exhibit problems that {\it separate} models, i.e., that can be solved in one model but not in a weaker one. These problems are related to Maximal Independent Set and detection of cycles. Finally we investigate problems related to connectivity as the construction of spanning- or BFS-tree in our different models.

     
  30. J-C. Bermond, D. Coudert, G. D'Angelo, and F. Z. Moataz. Diverse Routing in networks with star SRLGs. In ACM International Conference on emerging Networking EXperiments and Technologies (CoNEXT) Student Workshop, Nice, France, pages 1-2, December 2012. [WWW ] [PDF ]
    Abstract:
    The notion of \emph{Shared Risk Link Group}, SRLG has been introduced to capture multiple correlated failures in a network. A SRLG is a set of links that fail simultaneously if a given event (risk) occurs. In such multiple failures scenario, the problem of Diverse Routing consists in finding two SRLG-disjoint paths between a pair of nodes. We consider such problem for localized failures, when all the links of a SRLG verify the star property i.e. when they are incident to the same node. We prove that in this case the problem is in general NP-complete and determine some polynomial cases.

     
  31. L. Blin, J. Burman, and N. Nisse. Brief Announcement: Distributed Exclusive and Perpetual Tree Searching. In 26th International Symposium on Distributed Computing (DISC), volume 7611, pages 403-404, 2012. Springer, LNCS. [WWW ] [PDF ]
    Abstract:
    We tackle a practical version of the well known {\it graph searching} problem, where a team of robots aims at capturing an intruder in a graph. The robots and the intruder move along the edges of the graph. The intruder is invisible, arbitrary fast, and omniscient. It is caught whenever it stands on a node occupied by a robot, and cannot escape to a neighboring node. We study graph searching in the CORDA model of mobile computing: robots are asynchronous, and they perform cycles of {\it Look-Compute-Move} actions. Moreover, motivated by physical constraints, we consider the \emph{exclusive} property, stating that no two or more robots can occupy the same node at the same time. In addition, we assume that the network and the robots are anonymous. Finally, robots are \emph{oblivious}, i.e., each robot performs its move actions based only on its current ''vision'' of the positions of the other robots. Our objective is to characterize, for a graph $G$, the set of integers $k$ such that graph searching can be achieved by a team of $k$ robots starting from \emph{any} $k$ distinct nodes in $G$. Our main result consists in a full characterization of this set, for any asymmetric tree. Towards providing a characterization for all trees, including trees with non-trivial automorphisms, we have also provides a set of positive and negative results, including a full characterization for any line. All our positive results are based on the design of algorithms enabling \emph{perpetual} graph searching to be achieved with the desired number of robots.

     
  32. L. Blin, J. Burman, and N. Nisse. Nettoyage perpétuel de réseaux. In 14es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), pages 31-34, 2012. [WWW ] [PDF ]
    Abstract:
    Dans le cadre du {\it nettoyage de graphes contaminés} ({\it graph searching}), des agents mobiles se d\'eplacent successivement le long des ar\^etes du graphe afin de les {\it nettoyer}. Le but g\'en\'eral est le nettoyage en utilisant le moins d'agents possible. Nous placons notre étude dans le mod\`ele de calcul distribu\'e {\it CORDA minimaliste}. Ce mod\`ele est muni d'hypoth\`eses tr\`es faibles : les n\oe{}uds du r\'eseau et les agents sont anonymes, n'ont pas de m\'emoire du pass\'e ni sens commun de l'orientation et agissent par \emph{cycles} {\it Voir-Calculer-Agir} de mani\`ere \emph{asynchrone}. Un int\'er\^et de ce mod\`ele vient du fait que si le nettoyage peut \^etre fait \`a partir de positions arbitraires des agents (par exemple, apr\`es pannes ou recontamination), l'absence de m\'emoire implique un nettoyage perp\'etuel et donc fournit une premi\`ere approche de nettoyage de graphe {\it tol\'erant aux pannes}. Les contraintes dues au mod\`ele {\it CORDA minimaliste} nous am\`enent \`a d\'efinir une nouvelle variante de nettoyage de graphes - le {\it nettoyage sans collision}, autrement dit, plusieurs agents ne peuvent occuper simultan\'ement un m\^eme sommet. Nous montrons que, dans un contexte \emph{centralis\'e}, cette variante ne satisfait pas certaines propri\'et\'es classiques de nettoyage comme par exemple la monotonie. Nous montrons qu'interdire les ``collisions'' peut augmenter le nombre d'agents n\'ecessaires d'un facteur au plus $\Delta$ le degr\'e maximum du graphe et nous illustrons cette borne. De plus, nous caract\'erisons compl\`etement le nettoyage sans collision dans les arbres. Dans le contexte \emph{distribu\'e}, la question qui se pose est la suivante. Existe-t-il un algorithme qui, \'etant donn\'e un ensemble d'agents mobiles arbitrairement r\'epartis sur des sommets distincts d'un r\'eseau, permet aux agents de nettoyer perp\'etuellement le graphe? Dans le cas des chemins, nous montrons que la r\'eponse est n\'egative si le nombre d'agents est pair dans un chemin d'ordre impair, ou si il y a au plus deux agents dans un chemin d'ordre au moins $3$. Nous proposons un algorithme qui nettoie les chemins dans tous les cas restants, ainsi qu'un algorithme pour nettoyer les arbres lorsqu'un nombre suffisant d'agents est disponible initialement.

     
  33. L. Chiaraviglio and A. Cianfrani. On the Effectiveness of Sleep Modes in Backbone Networks with Limited Configurations. In 20th International Conference on Software, Telecommunications and Computer Networks (SoftCOM 2012), Split, Croatia, pages 1-6, September 2012. [PDF ]
    Abstract:
    We study the problem of putting in sleep mode devices of a backbone network, while limiting the number of times each device changes its power state (full power mode or sleep mode). Our aim is to limit the number of network configurations, i.e., the change of the current set of network devices at full power. We develop a model, based on random graph theory, to compute the energy saving given a traffic variation, QoS constraints, and the number of allowed network configurations. Results show that the energy savings with few configurations (two or three per day) are close to the maximum one, in which a new configuration is applied for each traffic matrix. Thus, we can conclude that a practical implementation of sleep mode strategies for network operators is to define, on the basis of typical traffic trend, few configurations to be activated in specific time instants.

     
  34. D. Coudert, L. Hogie, A. Lancin, D. Papadimitriou, S. Pérennes, and I. Tahiri. Feasibility study on distributed simulations of BGP. In PADS - 26th ACM/IEEE/SCS Workshop on Principles of Advanced and Distributed Simulation - 2012, Zhangjiajie, Chine, April 2012. IEEE. [WWW ] [PDF ]
    Abstract:
    The Autonomous System (AS) topology of the Internet (up to 61k ASs) is growing at a rate of about 10\(nil)er year. The Border Gateway Protocol (BGP) starts to show its limits in terms of the number of routing table entries it can dynamically process and control. Due to the increasing routing information processing and storage, the same trend is observed for routing model simulators such as DRMSim specialized in large-scale simulations of routing models. Therefore, DRMSim needs enhancements to support the current size of the Internet topology and its evolution (up to 100k ASs). To this end, this paper proposes a feasibility study of the extension of DRMSim so as to support the Distributed Parallel Discrete Event paradigm. We first detail the possible distribution models and their associated communication overhead. Then, we analyze this overhead by executing BGP on a partitioned topology according to different scenarios. Finally, we conclude on the feasibility of such a simulator by computing the expected additional time required by a distributed simulation of BGP compared to its sequential simulation.

     
  35. G. D'Angelo, M. D'Emidio, D. Frigioni, and V. Maurizio. Engineering a new loop-free shortest paths routing algorithm. In 11th International Symposium on Experimental Algorithms (SEA2012), volume 7276 of Lecture Notes in Computer Science, Bordeaux, France, pages 123-134, June 2012. Springer. [WWW ] [PDF ]
    Abstract:
    We present LFR (Loop Free Routing), a new loop-free distance vector routing algorithm, which is able to update the shortest paths of a distributed network with n nodes in fully dynamic scenarios. If Phi is the total number of nodes affected by a set of updates to the network, and phi is the maximum number of destinations for which a node is affected, then LFR requires O(Phi*Delta) messages and O(n + phi*Delta) space per node, where Delta is the maximum degree of the nodes of the network. We experimentally compare LFR with DUAL, one of the most popular loop-free distance vector algorithms, which is part of CISCO's EIGRP protocol and requires O(Phi*Delta) messages and $\Theta$(n*Delta) space per node. The experiments are based on both real-world and artificial instances and show that LFR is always the best choice in terms of memory require- ments, while in terms of messages LFR outperforms DUAL on real-world instances, whereas DUAL is the best choice on artificial instances.

     
  36. G. D'Angelo, M. D'Emidio, D. Frigioni, and D. Romano. Enhancing the computation of distributed shortest paths on real dynamic networks. In 1st Mediterranean Conference on Algorithms, volume 7659 of Lecture Notes in Computer Science, Ein-Gedi, Israel, pages 148-158, December 2012. Springer. [WWW ] [PDF ]
    Abstract:
    The problem of finding and updating shortest paths in distributed networks is considered crucial in today's practical applications. In the recent past, there has been a renewed interest in devising new efficient distance-vector algorithms as an attractive alternative to link-state solutions for large-scale Ethernet networks, in which scalability and reliability are key issues or the nodes can have limited storage capabilities. In this paper we present Distributed Computation Pruning (DCP), a new technique, which can be combined with every distance-vector routing algorithm based on shortest paths, allowing to reduce the total number of messages sent by that algorithm and its space occupancy per node. To check its effectiveness, we combined DCP with DUAL (Diffuse Update ALgorithm), one of the most popular distance-vector algorithm in the literature, which is part of CISCO's widely used EIGRP protocol, and with the recently introduced LFR (Loop Free Routing) which has been shown to have good performances on real networks. We give experimental evidence that these combinations lead to a significant gain both in terms of number of messages sent and memory requirements per node.

     
  37. G. D'Angelo, M. D'Emidio, D. Frigioni, and C. Vitale. Fully Dynamic Maintenance of Arc-Flags in Road Networks. In 11th International Symposium on Experimental Algorithms (SEA2012), volume 7276 of Lecture Notes in Computer Science, Bordeaux, France, pages 135-147, June 2012. Springer. [WWW ] [PDF ]
    Abstract:
    The problem of finding best routes in road networks can be solved by applying Dijkstra's shortest paths algorithm. Unfortunately, road networks deriving from real-world applications are huge yielding unsustainable times to compute shortest paths. For this reason, great research efforts have been done to accelerate Dijkstra's algorithm on road networks. These efforts have led to the development of a number of speed-up techniques, as for example Arc-Flags, whose aim is to compute additional data in a preprocessing phase in order to accelerate the shortest paths queries in an on-line phase. The main drawback of most of these techniques is that they do not work well in dynamic scenarios. In this paper we propose a new algorithm to update the Arc-Flags of a graph subject to edge weight decrease operations. To check the practical performances of the new algorithm we experimentally analyze it, along with a previously known algorithm for edge weight increase operations, on real-world road networks subject to fully dynamic sequences of operations. Our experiments show a significant speed-up in the updating phase of the Arc-Flags, at the cost of a small space and time overhead in the preprocessing phase.

     
  38. G. D'Angelo, G. Di Stefano, R. Klasing, and A. Navarra. Gathering of Robots on Anonymous Grids without multiplicity detection. In 19th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2012), volume 7355 of Lecture Notes in Computer Science, Reykjavìk, Iceland, pages 327-338, June 2012. Springer. [WWW ] [PDF ]
    Abstract:
    The paper studies the gathering problem on grid networks. A team of robots placed at different nodes of a grid, have to meet at some node and remain there. Robots operate in Look-Compute-Move cycles; in one cycle, a robot perceives the current configuration in terms of occupied nodes (Look), decides whether to move towards one of its neighbors (Compute), and in the positive case makes the computed move instantaneously (Move). Cycles are performed asynchronously for each robot. The problem has been deeply studied for the case of ring networks. However, the known techniques used on rings cannot be directly extended to grids. Moreover, on rings, another assumption concerning the so-called multiplicity detection capability was required in order to accomplish the gathering task. That is, a robot is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. In this paper, we provide a full characterization about gatherable configurations for grids. In particular, we show that in this case, the multiplicity detection is not required. Very interestingly, sometimes the problem appears trivial, as it is for the case of grids with both odd sides, while sometimes the involved techniques require new insights with respect to the well-studied ring case. Moreover, our results reveal the importance of a structure like the grid that allows to overcome the multiplicity detection with respect to the ring case.

     
  39. G. D'Angelo, G. Di Stefano, and A. Navarra. How to gather asynchronous oblivious robots on anonymous rings. In 26th International Symposium on Distributed Computing (DISC 2012), volume 7611 of Lecture Notes in Computer Science, Salvador, Brazil, pages 330-344, October 2012. Springer. [WWW ] [PDF ]
    Abstract:
    A set of robots arbitrarily placed on different nodes of an anonymous ring have to meet at one common node and remain in there. This problem is known in the literature as the gathering. Anonymous and oblivious robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are asynchronous among robots. Moreover, each robot is empowered by the so called multiplicity detection capability, that is, it is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem, and is able to detect all the ungatherable configurations. It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration, even those left open by previous works.

     
  40. O. Dalle and E. Mancini. Integrated tools for the simulation analysis of peer-to-peer backup systems. In Proceedings of the 5th International ICST Conference on Simulation Tools and Techniques, SIMUTOOLS '12, pages 178-183, March 2012. ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering). [WWW ] [PDF ]
    Abstract:
    In order to evaluate the performance and estimate the resource usage of peer-to-peer backup systems, it is important to analyze the time they spend in storing, retrieving and keeping the redundancy of the stored files. The analysis of such systems is difficult due to the random behavior of the peers and the variations of network conditions. Simulations provide a unique means for reproducing such varying conditions in a controlled way. In this paper we describe a general meta-model for peer-to-peer backup systems and a tool-chain, based on SimGrid, to help in their analysis. We validated the meta-model and tool-chain through the analysis of a common scenario, and verified that they can be used, for example, for retrieving the relations between the storage size, the saved data fragment sizes and the induced network workload.

     
  41. F. V. Fomin, F. Giroire, A. Jean-Marie, D. Mazauric, and N. Nisse. Satisfaire un internaute impatient est difficile. In 14es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), pages 79-82, 2012.
    Note: Best paper. [WWW ] [PDF ]
    Abstract:
    Consid\'erons un internaute qui va d'une page Web \`a une autre en suivant les liens qu'il rencontre. Pour \'eviter que l'internaute ne (s'im)patiente, il est important d'essayer de t\'el\'echarger les documents avant que l'internaute ne les atteigne. Cependant, le co\^ut d'un tel pr\'e-t\'el\'echargement ne doit pas exc\'eder le gain en temps qu'il g\'en\`ere. Ainsi, il faut minimiser la bande passante utilis\'ee pour le pr\'e-t\'el\'echargement tout en s'assurant que l'internaute impatient n'attende jamais. Nous mod\'elisons ce probl\`eme sous forme d'un jeu de type {\it Cops and Robber} dans les graphes. En particulier, \'etant donn\'es un graphe $G$ qui repr\'esente le graphe du Web et une page Web de d\'epart $v_0 \in V(G)$, nous d\'efinissons l'{\it indice de contr\^ole} de $G$, $ic(G,v_0) \in \mathbb{N}$, qui mod\'elise la vitesse minimum de t\'el\'echargement suffisante pour que l'internaute partant de $v_0$ n'attende jamais quoi qu'il fasse. Nous consid\'erons le probl\`eme de d\'ecider si $ic(G,v_0) \leq k$ et d\'emontrons plusieurs r\'esultats de complexit\'e. En particulier, d\'ecider si $ic(G,v_0) \leq 2$ est NP-difficile si $G$ est cordal, et d\'ecider si $ic(G,v_0) \leq 4$ est PSPACE-complet si $G$ est un graphe orient\'e acyclique. Nous donnons un algorithme exponentiel exact qui calcule $ic(G,v_0)$ en temps $O^*(2^n)$ dans un graphe de $n$ sommets quelconque. Puis, nous montrons que le probl\`eme est polynomial dans le cas des arbres et des graphes d'intervalles. Enfin, nous donnons une caract\'erisation combinatoire de l'indice de contr\^ole. Pour tout graphe $G$ et $v_0 \in V(G)$, $ic(G,v_0) \geq \max_{S} \lceil \frac{|N[S]|-1}{|S|} \rceil$ avec $v_0 \in S \subseteq V$, $S$ induit un sous-graphe connexe et $N[S]$ l'ensemble des sommets de $S$ ou voisins d'un sommet de $S$. Il y a de plus \'egalit\'e dans le cas des arbres.

     
  42. F. V. Fomin, F. Giroire, A. Jean-Marie, D. Mazauric, and N. Nisse. To Satisfy Impatient Web surfers is Hard. In 6th International Conference on FUN with Algorithms (FUN), volume 7288, pages 166-176, 2012. Springer, LNCS. [WWW ] [PDF ]
    Abstract:
    Prefetching is a basic mechanism to avoid to waste time when accessing data. However, a tradeoff must be established between the amount of network's resources wasted by the prefetching and the gain of time. For instance, in the Web, browsers may download documents in advance while an Internaut is surfing on the Web. Since the web surfer follows the hyperlinks in an unpredictable way, the choice of the web pages to be prefetched must be computed online. The question is then to determine the minimum amount of resources used by prefetching and that ensures that all documents accessed by the web surfer have previously been loaded in the cache. We model this problem as a game similar to Cops and Robber Games in graphs. A fugitive starts on a marked vertex of a (di)graph G. Turn by turn, an observer marks at most k >= 1 vertices and then the fugitive can move along one edge/arcs of G. The observer wins if he prevents the fugitive to reach an unmarked vertex. The fugitive wins otherwise, i.e., if she enters an unmarked vertex. The surveillance number of a graph is the least k >=1 allowing the observer to win whatever the fugitive does. We also consider the connected variant of this game, i.e., when a vertex can be marked only if it is adjacent to an already marked vertex. All our results hold for both variants, connected or not. We show that deciding whether the surveillance number of a chordal graph equals 2 is NP-hard. Deciding if the surveillance number of a DAG equals 4 is PSPACE-complete. Moreover, computing the surveillance number is NP-hard in split graphs. On the other hand, we provide polynomial time algorithms to compute surveillance number of trees and interval graphs. Moreover, in the case of trees, we establish a combinatorial characterization, related to isoperimetry, of the surveillance number.

     
  43. F. Giroire, J. Moulierac, T.K. Phan, and F. Roudaut. Minimization of Network Power Consumption with Redundancy Elimination. In IFIP Networking, Prague, Czech Republic, pages 247-258, May 2012. Springer. [WWW ] [PDF ]
    Abstract:
    Recently, energy-aware routing has gained increasing popularity in the networking research community. The idea is that traffic demands are aggregated over a subset of the network links, allowing other links to be turned off to save energy. In this paper, we propose GreenRE - a new energy-aware routing model with the support of the new technique of data redundancy elimination (RE). This technique, enabled within the routers, can identify and remove repeated content from network transfers. Hence, capacity of network links are virtually increased and more traffic demands can be aggregated. Based on our real experiments on Orange Labs platform, we show that performing RE consumes some energy. Thus, while preserving connectivity and QoS, it is important to identify at which routers to enable RE and which links to turn off so that the power consumption of the network is minimized. We model the problem as an Integer Linear Program and propose a greedy heuristic algorithm. Simulations on several network topologies show that GreenRE can gain further 300f energy savings in comparison with the traditional energy-aware routing model.

     
  44. A. Goldman, P. Floriano, and A. Ferreira. A tool for obtaining information on DTN traces. In Proceedings of the 4th Extreme Conference on Communication, Zurique, CH, 2012. [PDF ]
    Abstract:
    The applications for dynamic networks are growing every day, and thus, so is the number of studies on them. An important part of such studies is the generation of results through simulation and comparison with other works. We implemented a tool to generate information on a given network trace, obtained by building its corresponding evolving graph. This information is useful to help researchers choose the most suitable trace for their work, to interpret the results correctly and to compare data from their work to the optimal results in the network. In this work, we present the implementation of the DTNTES tool which provides the aforementioned services and use the system to evaluate the DieselNet trace.

     
  45. F. Idzikowski, R. Duque, F. Jimenez, E. Le Rouzic, L. Chiaraviglio, and M. Ajmone-Marsan. Energy Saving in Optical Operator Networks: the Challenges, the TREND Vision, and Some Results. In ECOC 2012 - European Conference and Exhibition on Optical Communication, Amsterdam, Netherlands, pages 1-3, September 2012. [PDF ]
    Abstract:
    We discuss how to save energy in IP-over-WDM networks, presenting the vision of TREND, the FP7 NoE, and the saving that can be obtained with an adaptive routing solution that puts network interfaces of various granularities to sleep in periods of low traffic. Results refer to two operator networks, considering power and traffic forecasts for 2020.

     
  46. A. Kosowski, B. Li, N. Nisse, and K. Suchan. k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth. In 14es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), pages 83-86, 2012. [WWW ] [PDF ]
    Abstract:
    {\it Cops and robber games} concern a team of cops that must capture a robber moving in a graph. We consider the class of $k$-chordal graphs, i.e., graphs with no induced cycle of length greater than $k$, $k\geq 3$. We prove that $k-1$ cops are always sufficient to capture a robber in $k$-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including $k$-chordal graphs. We present a quadratic algorithm that, given a graph $G$ and $k\geq 3$, either returns an induced cycle larger than $k$ in $G$, or computes a {\it tree-decomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k-1$ vertices. This allows us to prove that any $k$-chordal graph with maximum degree $\Delta$ has treewidth at most $(k-1)(\Delta-1)+2$, improving the $O(\Delta (\Delta-1)^{k-3})$ bound of Bodlaender and Thilikos (1997). Moreover, any graph admitting such a tree-decomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$. As an application, for any $n$-node graph admitting such a tree-decomposition, we propose a {\it compact routing scheme} using routing tables, addresses and headers of size $O(\log n)$ bits and achieving an additive stretch of $O(k\log \Delta)$. As far as we know, this is the first routing scheme with $O(\log n)$-routing tables and small additive stretch for $k$-chordal graphs.

     
  47. A. Kosowski, B. Li, N. Nisse, and K. Suchan. k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth. In 39th International Colloquium on Automata, Languages and Programming (ICALP, track C), volume 7392, pages 610-622, 2012. Springer, LNCS. [WWW ] [PDF ]
    Abstract:
    {\it Cops and robber games} concern a team of cops that must capture a robber moving in a graph. We consider the class of $k$-chordal graphs, i.e., graphs with no induced cycle of length greater than $k$, $k\geq 3$. We prove that $k-1$ cops are always sufficient to capture a robber in $k$-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including $k$-chordal graphs. We present a quadratic algorithm that, given a graph $G$ and $k\geq 3$, either returns an induced cycle larger than $k$ in $G$, or computes a {\it tree-decomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k-1$ vertices. This allows us to prove that any $k$-chordal graph with maximum degree $\Delta$ has treewidth at most $(k-1)(\Delta-1)+2$, improving the $O(\Delta (\Delta-1)^{k-3})$ bound of Bodlaender and Thilikos (1997). Moreover, any graph admitting such a tree-decomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$. As an application, for any $n$-node graph admitting such a tree-decomposition, we propose a {\it compact routing scheme} using routing tables, addresses and headers of size $O(\log n)$ bits and achieving an additive stretch of $O(k\log \Delta)$. As far as we know, this is the first routing scheme with $O(\log n)$-routing tables and small additive stretch for $k$-chordal graphs.

     
  48. J. Moulierac, T.K. Phan, N. Thoai, and N.C. Tran. Xcast6 Treemap Islands - Revisiting Multicast Model. In ACM CoNEXT Student Workshop, Nice, France, December 2012. ACM. [WWW ] [PDF ]
    Abstract:
    Due to the complexity and poor scalability, IP Multicast has not been used on the Internet. Recently, Xcast6 - a complementary protocol of IP Multicast has been proposed. However, the key limitation of Xcast6 is that it only supports small multicast sessions. To overcome this, we propose Xcast6 Treemap islands (X6Ti) - a hybrid model of Overlay Multicast and Xcast6. In summary, X6Ti has many advantages: support large multicast groups, simple and easy to deploy on the Internet, no router configuration, no restriction on the number of groups, no multicast routing protocol and no group management protocol. Based on simulation, we compare X6Ti with IP Multicast and NICE protocols to show the benefits of our new model.

     
  49. D.D. Nguyen, T.K. Phan, N. Thoai, and T.T. Tran. MaxNet and TCP Reno/RED on Mice Traffic. In Modeling, Simulation and Optimization of Complex Processes, pages 247-255, 2012. Springer Berlin Heidelberg. [WWW ] [PDF ]
    Abstract:
    Congestion control is a distributed algorithm to share network bandwidth among competing users on the Internet. In the common case, quick response time for mice traffic (HTTP traffic) is desired when mixed with elephant traffic (FTP traffic). The current approach using loss-based with Additive Increase, Multiplicative Decrease (AIMD) is too greedy and eventually, most of the network bandwidth would be consumed by elephant traffic. As a result, it causes longer response time for mice traffic because there is no room left at the routers. MaxNet is a new TCP congestion control architecture using an explicit signal to control transmission rate at the source node. In this paper, we show that MaxNet can control well the queue length at routers and therefore the response time to HTTP traffic is several times faster than with TCP Reno/RED.

     
  50. J. Araujo, F. Giroire, Y. Liu, R. Modrzejewski, and J. Moulierac. Energy Efficient Content Distribution. Technical report RR-8091, INRIA, October 2012. [WWW ] [PDF ]
    Abstract:
    To optimize energy efficiency in network, operators try to switch off as many network devices as possible. Recently, there is a trend to introduce content caches as an inherent capacity of network equipment, with the objective of improving the efficiency of content distribution and reducing network congestion. In this work, we study the impact of using in-network caches and CDN cooperation on an energy-efficient routing. We formulate this problem as Energy Efficient Content Distribution. The objective is to find a feasible routing, so that the total energy con- sumption of the network is minimized subject to satisfying all the demands and link capacity. We exhibit the range of parameters (size of caches, popularity of content, demand intensity, etc.) for which caches are useful. Experiment results show that by placing a cache on each backbone router to store the most popular content, along with well choosing the best content provider server for each demand to a CDN, we can save a total up to 23\0f power in the backbone, while 16\ªan be gained solely thanks to caches.

     
  51. J. Araujo, G. Morel, L. Sampaio, R. Soares, and V. Weber. Hull number: $P_5$-free graphs and reduction rules. Technical report RR-8045, INRIA, August 2012. [WWW ] [PDF ]
    Abstract:
    In this paper, we study the (geodesic) hull number of graphs. For any two vertices $u,v\in V$ of a connected undirected graph $G=(V,E)$, the closed interval $I[u,v]$ of $u$ and $v$ is the set of vertices that belong to some shortest $(u,v)$-path. For any $S \subseteq V$, let $I[S]= \bigcup\_{u,v\in S} I[u,v]$. A subset $S\subseteq V$ is (geodesically) convex if $I[S] = S$. Given a subset $S\subseteq V$, the convex hull $I\_h[S]$ of $S$ is the smallest convex set that contains $S$. We say that $S$ is a hull set of $G$ if $I\_h[S] = V$. The size of a minimum hull set of $G$ is the hull number of $G$, denoted by $hn(G)$. First, we show a polynomial-time algorithm to compute the hull number of any $P\_5$-free triangle-free graph. Then, we present four reduction rules based on vertices with the same neighborhood. We use these reduction rules to propose a fixed parameter tractable algorithm to compute the hull number of any graph $G$, where the parameter can be the size of a vertex cover of $G$ or, more generally, its neighborhood diversity, and we also use these reductions to characterize the hull number of the lexicographic product of any two graphs.

     
  52. J. Bang-Jensen, F. Havet, and A. K. Maia. Finding a subdivision of a digraph. Technical report RR-8024, INRIA, July 2012. [WWW ] [PDF ]
    Abstract:
    We consider the following problem for oriented graphs and digraphs: Given a directed graph D, does it contain a subdivision of a prescribed digraph F? We give a number of examples of polynomial instances, several NP-completeness proofs as well as a number of conjectures and open problems.

     
  53. J-C. Bermond, D. Coudert, G. D'Angelo, and F. Z. Moataz. Diverse Routing with the star property. Technical report RR-8071, INRIA, September 2012. [WWW ] [PDF ]
    Abstract:
    The notion of Shared Risk Link Groups (SRLG) has been introduced to capture survivability issues where a set of links of a network fail simultaneously. In this context, the \emph{diverse routing} problem is to find a set of SRLG-disjoint paths between a given pair of end nodes of the network. This problem has been proved $NP$-complete in general\~\cite{Hu03} and some polynomial instances have been characterized\~\cite{CDP+07}. In this paper, we investigate the diverse routing problem in networks satisfying the \emph{star property}\~\cite{LW05}. This property states that an edge may be subject to several SRLGs but all edges subject to a given SRLG are incident to a common node. We first provide counter-examples to the polynomial time algorithm proposed in\~\cite{LW05} for computing pairs of SRLG-disjoint paths in networks with the star property, and then prove that this problem is in fact $NP$-hard in the strong sense. More generally, we prove that the diverse routing problem in networks with the star property is $NP$-hard in the strong sense, hard to approximate, and $W[1]$-hard when the parameter is the number of SRLG-disjoint paths. Last, we devise polynomial time algorithms for practically relevant subcases, in particular when the number of SRLG is constant, the maximum degree of the vertices is strictly smaller than 5, and when the network is a directed acyclic graph.

     
  54. L. Blin, J. Burman, and N. Nisse. Perpetual Graph Searching. Technical report RR-7897, INRIA, February 2012. [WWW ] [PDF ]
    Abstract:
    In {\it graph searching}, a team of mobile agents aims at clearing the edges of a contaminated graph. To clear an edge, an agent has to slide along it, however, an edge can be {\it recontaminated} if there is a path without agents from a contaminated edge to a clear edge. To goal of graph searching is to clear the graph, i.e., all edges are clear simultaneously, using the fewest number of agents. We study this problem in the {\it minimal CORDA} model of distributed computation. This model has very weak hypothesis: network nodes and agents are anonymous, have no memory of the past, and agents have no common sense of orientation. Moreover, all agents execute the same algorithm in the {\it Look-Compute-Move} manner and in an asynchronous environment. One interest of this model is that, if the clearing can be done by the agents starting from arbitrary positions (e.g., after faults or recontamination), the lack of memory implies that the clearing is done perpetually and then provides a first approach of fault-tolerant graph searching. Constraints due to the minimal CORDA model lead us to define a new variant of graph searching, called {\it graph searching without collisions}, where more than one agent cannot occupy the same node. We show that, in a centralized setting, this variant does not have the same behavior as classical graph searching. For instance, it not monotonous nor close by subgraph. We show that, in a graph with maximum degree $\Delta$, the smallest number of agents required to clear a graph without collisions is at most $\Delta$ times the number of searchers required when collisions are allowed. Moreover, this bound is tight up to a constant ratio. Then, we fully characterize graph searching without collisions in trees. In a distributed setting, i.e., in the minimal CORDA model, the question we ask is the following. Given a graph $G$, does there exist an algorithm that clears $G$, whatever be the initial positions of the agents on distinct vertices. In the case of a path network, we show that it is not possible is the number of agents is even in a path of odd order, or if there are at most two agents in a path with at least three vertices. We present an algorithm that clears all paths in all remaining cases. Finally, we propose an algorithm that clears any tree using a sufficient number of agents.

     
  55. V. Campos, F. Havet, R. Sampaio, and A. Silva. Backbone colouring: tree backbones with small diameter in planar graphs. Technical report RR-8151, INRIA, November 2012. [WWW ] [PDF ]
    Abstract:
    Given a graph $G$ and a spanning subgraph $T$ of $G$, a {\it backbone $k$-colouring} for $(G,T)$ is a mapping $c:V(G)\to\{1,\ldots,k\}$ such that $|c(u)-c(v)|\geq 2$ for every edge $uv\in E(T)$ and $|c(u)-c(v)|\geq 1$ for every edge $uv\in E(G)\setminus E(T)$. The {\it backbone chromatic number} $BBC(G,T)$ is the smallest integer $k$ such that there exists a backbone $k$-colouring of $(G,T)$. In 2007, Broersma et al. \cite{BFG+07} conjectured that $BBC(G,T)\leq 6$ for every planar graph $G$ and every spanning tree $T$ of $G$. In this paper, we prove this conjecture when $T$ has diameter at most four.

     
  56. N. Cohen, D. Coudert, and A. Lancin. Exact and approximate algorithms for computing the hyperbolicity of large-scale graphs. Technical report RR-8074, INRIA, September 2012. [WWW ] [PDF ]
    Abstract:
    Let $G$ be a connected graph, and let $\dd(a,b)$ denotes the shortest path distance between vertices $a$ and $b$ of $G$. The graph $G$ is $\delta$-hyperbolic if for any vertices $a, b, c, d$ of $G$, the two largest of the three sums $S\_1=\dd(a,b)+\dd(c,d)$, $S\_2 = \dd(a,c)+\dd(b,d)$, and $S\_3 = \dd(a,d)+\dd(b,c)$ differ by at most $2\delta$. This can be determined in time $O(n^4)$ which could be prohibitive for large graphs. In this document, we propose an exact algorithm for determining the hyperbolicity of a graph that is scalable for large graphs. The time complexity of this algorithm is a function of the size of the largest bi-connected component of the graph, of the shortest path distance distribution in this componenant and of the value of the hyperbolicity. In the worst case, the time complexity remains in $O(n^4)$, but it is much faster in practice. We also propose both a multiplicative factor and an additive constant approximation algorithms. We then analyze further the time complexity of our exact algorithm for several class of graphs, and present some computational results on large-scale graphs.

     
  57. G. D'Angelo, G. Di Stefano, and A. Navarra. How to gather asynchronous oblivious robots on anonymous rings. Technical report RR-7963, INRIA, 2012. [WWW ] [PDF ]
    Abstract:
    A set of robots arbitrarily placed on the nodes of an anonymous graph have to meet at one common node and remain in there. This problem is known in the literature as the \emph{gathering}. Robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are performed asynchronously for each robot. Moreover, each robot is empowered by the so called \emph{multiplicity detection} capability, that is, a robot is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem, and is able to detect all the non-gatherable configurations. It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration.

     
  58. G. D'Angelo, G. Di Stefano, A. Navarra, N. Nisse, and K. Suchan. A unified approach for different tasks on rings in robot-based computing systems. Technical report RR-8013, INRIA, 2012. [WWW ] [PDF ]
    Abstract:
    A set of autonomous robots have to collaborate in order to accomplish a common task in a ring-topology where neither nodes nor edges are labeled. We present a unified approach to solve three important problems in the field: the \emph{exclusive perpetual exploration}, the \emph{exclusive perpetual graph searching} and the \emph{gathering} problems. In the first problem, each robot aims at visiting each node infinitely often; in perpetual graph searching, the team of robots aims at clearing all edges of the network infinitely often; and in the gathering problem, all robots must eventually occupy the same node. We investigate these tasks in the famous {\it CORDA} distributed computing model where the robots cannot communicate but can perceive the positions of other robots. More precisely, each robot is equipped with visibility sensors and motion actuators, and it operates in {\it Look-Compute-Move} asynchronous cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it eventually moves to this neighbor (Move). Moreover, robots are endowed with very weak capabilities. Namely, they are {\it anonymous}, {\it oblivious}, {\it uniform} (execute the same algorithm) and have {\it no common sense of orientation}. For the first two problems, the {\it exclusivity constraint} must also be satisfied, i.e., a node can be occupied by at most one robot. Finally, the robots have the {\it local multiplicity detection capability} which is required to solve the gathering problem. In this setting, we devise algorithms that, starting from any exclusive rigid (i.e. aperiodic and asymmetric) configuration, solve the three above mentioned problems in anonymous ring-topologies. Our main algorithms consist of two phases. The first phase is common to all problems and allows $k>2$ robots to achieve a particular configuration in an $n$-node ring, $k9)$ and $(k=5,n=10)$.

     
  59. G. Ducoffe. Eulerian and Hamiltonian Directed Hypergraphs. Technical report RR-7893, INRIA, 2012. [WWW ] [PDF ]
    Abstract:
    Let $H=(\mathcal{V},\mathcal{E})$ be a directed hypergraph, sometimes called a dihypergraph. Each vertex $v\in{\mathcal{V}}$ is incident to some hyperarcs in $\mathcal{E}$. Conversely, each hyperarc $E\in{\mathcal{E}}$ is incident to some vertices in $\mathcal{V}$. $H$ is Eulerian if there is a circuit $C$ such that each hyperarc $E\in{\mathcal{E}}$ appears exactly once in $C$. Similarly, $H$ is Hamiltonian if there is a circuit $C^{'}$ such that every vertex $v\in{\mathcal{V}}$ appears exactly once in $C^{'}$. We show that both of the problems are NP-complete. Some necessary conditions for a dihypergraph to be Eulerian are presented. We exhibit some families of hypergraphs for which those are sufficient conditions. We also generalize a part of the properties of the Eulerian digraphs to the uniform and regular directed hypergraphs. Stronger generalizations of \textit{Eulerianicity} to dihypergraphs are also studied. Finally, we show that the de Bruijn and Kautz dihypergraphs are Eulerian and Hamiltonian in most cases. We also study some properties of their bipartite representation digraph.

     
  60. F. Havet and A. D. King. List circular backbone colouring. Technical report RR-8159, INRIA, November 2012. [WWW ] [PDF ]
    Abstract:
    A natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge. In the $q$-backbone colouring problem, these minimum distances are either $q$ or $1$, depending on whether or not the edge is in the {\em backbone}. In this paper we consider the list version of this problem, with particular focus on colours in $\Z\_p$ -- this problem is closely related to the problem of circular choosability. We first prove that the {\em list circular $q$-backbone chromatic number} of a graph is bounded by a function of the list chromatic number. We then consider the more general problem in which each edge is assigned an individual distance between its endpoints, and provide bounds using the Combinatorial Nullstellensatz. Through this result and through structural approaches, we achieve good bounds when both the graph and the backbone belong to restricted families of graphs.

     
  61. F. Havet, A. D. King, M. Liedloff, and I. Todinca. (Circular) backbone colouring: tree backbones in planar graphs. Technical report RR-8152, INRIA, November 2012. [WWW ] [PDF ]
    Abstract:
    Consider an undirected graph G and a subgraph H of G, on the same vertex set. The q-backbone chromatic number BBCq(G,H) is the minimum k such that G can be properly coloured with colours from {1, ..., k}, and moreover for each edge of H, the colours of its ends differ by at least q. In this paper we focus on the case when G is planar and H is a forest. We give a series of NP-hardness results as well as upper bounds for BBCq(G,H), depending on the type of the forest (matching, galaxy, spanning tree). Eventually, we discuss a circular version of the problem.

     
  62. F. Havet, A. K. Maia, and M-L. Yu. Complexity of greedy edge-colouring. Technical report RR-8171, INRIA, December 2012. [WWW ] [PDF ]
    Abstract:
    The Grundy index of a graph G = (V,E) is the greatest number of colours that the greedy edge-colouring algorithm can use on G. We prove that the problem of determining the Grundy index of a graph G = (V,E) is NP-hard for general graphs. We also show that this problem is polynomial-time solvable for caterpillars. More specifically, we prove that the Grundy index of a caterpillar is $\Delta(G)$ or $\Delta(G)+1$ and present a polynomial-time algorithm to determine it exactly.

     
  63. F. Havet, N. Paramaguru, and R. Sampathkumar. Detection number of bipartite graphs and cubic graphs. Technical report RR-8115, INRIA, October 2012. [WWW ] [PDF ]
    Abstract:
    For a connected graph $G$ of order $|V(G)|\,\geq\,3$ and a $k$-labelling $c\,:\,E(G)\,\rightarrow\,\{1,2,\ldots,k\}$ of the edges of $G,$ the {\it code} of a vertex $v$ of $G$ is the ordered $k\!$-tuple $(\ell\_1,\ell\_2,\ldots,\ell\_k),$ where $\ell\_i$ is the number of edges incident with $v$ that are labelled $i.$ The $k$-labelling $c$ is {\it detectable} if every two adjacent vertices of $G$ have distinct codes. The minimum positive integer $k$ for which $G$ has a detectable $k$-labelling is the {\it detection number} of $G.$ In this paper, we show that it is NP-complete to decide if the detection number of a cubic graph is $2.$ We also show that the detection number of every bipartite graph of minimum degree at least $3$ is at most $2.$ Finally, we give some sufficient condition for a cubic graph to have detection number $3.$

     
  64. A. Kosowski, B. Li, N. Nisse, and K. Suchan. k-Chordal Graphs: from Cops and Robber to Compact Routing via Treewidth. Technical report RR-7888, INRIA, February 2012. [WWW ] [PDF ]
    Abstract:
    {\it Cops and robber games} concern a team of cops that must capture a robber moving in a graph. We consider the class of $k$-chordal graphs, i.e., graphs with no induced cycle of length greater than $k$, $k\geq 3$. We prove that $k-1$ cops are always sufficient to capture a robber in $k$-chordal graphs. This leads us to our main result, a new structural decomposition for a graph class including $k$-chordal graphs. We present a quadratic algorithm that, given a graph $G$ and $k\geq 3$, either returns an induced cycle larger than $k$ in $G$, or computes a {\it tree-decomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k-1$ vertices. This allows us to prove that any $k$-chordal graph with maximum degree $\Delta$ has treewidth at most $(k-1)(\Delta-1)+2$, improving the $O(\Delta (\Delta-1)^{k-3})$ bound of Bodlaender and Thilikos (1997). Moreover, any graph admitting such a tree-decomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$. As an application, for any $n$-node graph admitting such a tree-decomposition, we propose a {\it compact routing scheme} using routing tables, addresses and headers of size $O(\log n)$ bits and achieving an additive stretch of $O(k\log \Delta)$. As far as we know, this is the first routing scheme with $O(\log n)$-routing tables and small additive stretch for $k$-chordal graphs.

     
  65. N. Nisse and R. Soares. On The Monotonicity of Process Number. Technical report RR-7003, INRIA, October 2012. [WWW ] [PDF ]
    Abstract:
    Graph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with tree- and path-decomposition of graphs. In order to define decompositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider such a game that has been defined and studied in the context of routing reconfiguration problems in WDM networks. Namely, in the processing game, the fugitive is invisible, arbitrary fast, it moves in the opposite direction of the arcs of a digraph, but only as long as it has access to a strongly connected component free of searchers. We prove that the processing game is monotone which leads to its equivalence with a new digraph decomposition.

     
2011
  1. N. Cohen. Some results in graph theory and its applications. PhD thesis, Ecole doctorale STIC, Université de Nice-Sophia Antipolis, October 2011. [WWW ]
    Abstract:
    This thesis consists in successive glimpses of different problems in discrete mathematics related to graph theory. Its mains focus is on graph colouring, i.e. on assignments of integer values to the vertices (or edges) of a graph satisfying a set of local constraints, most of the time the exclusion of specific patterns in the coloured graph. For several different types of colouring (vertex and edge choosability, acyclic or linear colouring, ...) a state of the art is provided, along with results ensuring the existence of such colourings on planar graphs or subclasses of them -- with the aim of minimising the number of colours used for a given Maximum Degree, or Maximum Average Degree. This thesis also deals with decompositions of graphs into induced subgraphs, and asserts that similarly to what Wilson's theorem implies for non-induced graph decomposition, there exists for any graph $H$ an infinite sequence of dense graph whose edge set can be partitioned in induced copies of $H$. The proof methodology involves hypergraphs, for which a decomposition result is presented, i.e. that the complete 3-uniform hypergraph can be partitioned into $\lceil \frac {n(n-1)} 6\rceil$ $\alpha$-acyclic hypergraphs as conjectured. In a third part are gathered algorithmic questions. Those are problems of optimisation or existence motivated by telecommunications in networks, studied with the classical framework of computational complexity, or the search of subgraphs through parametrised complexity. In a fourth part it, considers counting problems belonging to the study of chemical graphs, and finally details some Integer LinearPrograms used in the Mathematics software Sage.

     
  2. J-C Maureira Bravo. Internet on Rails. THESE, Ecole doctorale STIC, Université de Nice Sophia-Antipolis, January 2011. [WWW ] [PDF ]
    Keywords: Train communications, WiFi, horizontal handover, layer 2 routes update, infrastructure network, combined chordal topologies, simulations..
    Abstract:
    This thesis proposes a new method for providing network connectivity to vehicles over a predefined trajectory (trains, metros, urban buses, etc.). The communication between the vehicle and the infrastructure network is based only on WiFi technology. The contributions of this work are two-fold: 1) the horizontal handover (between WiFi access points) and 2) the design and analysis of an infrastructure network (backbone network plus WiFi access network) deployed along the trajectory of the vehicle. In the first contribution, we propose a handover scheme, called Spiderman Handover, which describes the horizontal handover for an in-motion network (on-board the vehicle) considering a procedure to update the routing information of a bridged infrastructure network (OSI layer 2). We evaluate our proposal by means of simulation and we validate our results by experimental measurements. In the second contribution, we study theoretically the parameters of several chordal like topologies in order to build a backbone network for a linear access network. By comparing these parameters, we propose a backbone network composed by a combination of two chordal topologies. This backbone network provides a good balance between their deployment cost, number of hops to the gateway of the network and a reasonable resilience. Finally, we evaluate the integration of this infrastructure network and the handover scheme by means of simulations. Results showed that the proposed handover scheme works properly on the proposed infrastructure network, allowing the provision of a continuous network connectivity to passengers on-board trains, metros or urban buses.

     
  3. D. Mazauric. Optimisation discrète dans les réseaux de télécommunication: reconfiguration du routage, routage efficace en énergie, ordonnancement de liens et placement de données. PhD thesis, Ecole doctorale STIC, Université de Nice Sophia-Antipolis, November 2011. [WWW ] [PDF ]
    Abstract:
    Nous nous intéressons dans cette thèse à différents types de réseaux (optiques, sans-fil, pair-à -pair) ayant chacun leurs spécificités mais partageant des problématiques communes : assurer la meilleure qualité de services possible, garantir la stabilité du système, minimiser les ressources et donc le coût de fonctionnement. Tout d'abord, nous étudions le problème de la reconfiguration du routage dans les réseaux optiques consistant à rerouter les requêtes de connexion en minimisant les perturbations pour les utilisateurs. Puis, nous nous intéressons au problème de la détermination de routages efficaces en énergie dans les réseaux coeur. Pour ce faire, nous étudions le problème de trouver des routages minimisant le nombre d'équipements utilisés. Ensuite, nous nous intéressons aux algorithmes d'ordonnancement des liens dans les réseaux sans-fil en présence d'interférence. Enfin, nous considérons le problème de stockage de données dans les réseaux pair-à -pair. Nous étudions l'impact de différentes politiques de placement sur la durée de vie des données et nous déterminons un choix de placement optimal. Pour résoudre ces problèmes, nous utilisons les outils théoriques des mathématiques discrètes (graphes, configurations, optimisation combinatoire), d'algorithmique (complexité, algorithmique distribuée) et de probabilités.

     
  4. J. Ribault. Reuse and Scalability in Modeling and Simulation Software Engineering. THESE, Ecole doctorale STIC, Université de Nice Sophia-Antipolis, January 2011. [WWW ] [PDF ]
    Keywords: simulation, évènements discrets, aspects, séparation des préoccupations, instrumentation, modélisation, composant, simulation distribuée, réutilisation.
    Abstract:
    L'{\'e}tude d'un syst{\`e}me {\`a} l'aide de simulations informatiques {\`a} {\'e}v{\'e}nements discrets implique plusieurs activit{\'e}s: sp{\'e}ci cation du mod{\`e}le conceptuel, description de l'architecture logicielle du mod{\`e}le, d{\'e}veloppement des logiciels, sc{\'e}narisation de la simulation, instrumentation, plani cation d'exp{\'e}rimentation, con guration des ressources de calcul, ex{\'e}cution, post-traitement et analyse, validation et de v{\'e}ri cation (V\&V). De nombreux {\'e}l{\'e}ments logiciels sont requis pour remplir toutes ces activit{\'e}s. Toutefois, il est fr{\'e}quent de cr{\'e}er un nouveau simulateur {\`a} partir de rien quand on commence une {\'e}tude {\`a} l'aide de simulation. Dans ce cas il est n{\'e}cessaire de d{\'e}velopper de multiples outils prenant en charge les activit{\'e}s de la simulation. Cette th{\`e}se aborde le d{\'e} de la cr{\'e}ation de nouveaux simulateurs tout en r{\'e}utilisant des mod{\`e}les et des outils provenant d'autres simulateurs. En e et, la r{\'e}utilisation de logiciel augmente la abilit{\'e}, est moins sujette aux erreurs, permet une meilleure utilisation des expertises compl{\'e}mentaires, am{\'e}liore la conformit{\'e} aux normes, et acc{\'e}l{\`e}re le d{\'e}veloppement. La r{\'e}utilisation de logiciels peut {\^e}tre appliqu{\'e}e {\`a} toutes les activit{\'e}s de la simulation. Plusieurs probl{\`e}mes doivent {\^e}tre r{\'e}solus pour tirer pleinement pro t de la r{\'e}utilisation. Dans cette th{\`e}se, nous abordons trois questions principales: Tout d'abord, nous {\'e}tudions les solutions pratiques de r{\'e}utilisation permettant de combiner un ensemble choisi d'{\'e}l{\'e}ments logiciels utiles pour la mod{\'e}lisation et la simulation, en incluant aussi bien les mod{\`e}les, les moteurs de simulation, les algorithmes et les outils; Deuxi{\`e}mement, nous nous concentrons sur les questions li{\'e}es {\`a} l'instrumentation; Troisi{\`e}mement, nous {\'e}tudions le probl{\`e}me de l'int{\'e}gration d'{\'e}l{\'e}ments logiciels provenant d'autres simulateurs dans un nouveau simulateur. Pour atteindre ces objectifs, nous {\'e}tudions des techniques avanc{\'e}es de du g{\'e}nie logiciel, tels que le g{\'e}nie logiciel {\`a} base de composants (CBSE) et la programmation orient{\'e}e aspect, sur lesquels nous construisons une solution originale pour la mod{\'e}lisation et la simulation {\`a} l'aide de multiples couches r{\'e}utilisables. Nous avons d{\'e}velopp{\'e} un prototype d'architecture logicielle qui prouve la faisabilit{\'e} de cette solution.

     
  5. J-C. Bermond, F. Ergincan, and M. Syska. Quisquater Festschrift, volume 6805 of Lecture Notes in Computer Science, chapter Line Directed Hypergraphs, pages 25-34. Springer-Verlag, Berlin Heidelberg, 2011. [PDF ]
    Abstract:
    In this article we generalize the concept of line digraphs to line dihypergraphs. We give some general properties in particular concerning connectivity parameters of dihypergraphs and their line dihypergraphs, like the fact that the arc connectivity of a line dihypergraph is greater than or equal to that of the original dihypergraph. Then we show that the De Bruijn and Kautz dihypergraphs (which are among the best known bus networks) are iterated line digraphs. Finally we give short proofs that they are highly connected.

     
  6. G. A. Wainer, K. Al-Zoubi, O. Dalle, R.C. Hill, S. Mittal, J. L. R. Martin, H. Sarjoughian, L. Touraille, M. K. Traoré, and B. P. Zeigler. Discrete-Event Modeling and Simulation: Theory and Applications, chapter 18 - Standardizing DEVS Simulation Middleware, pages 459-494. Taylor and Francis, 2011. [WWW ]
     
  7. G . Wainer, K. Al-Zoubi, O. Dalle, R. C. Hill, S. Mittal, J. L. R. Martin, H. Sarjoughian, L. Touraille, M. K. Traoré, and B. P. Zeigler. Discrete-Event Modeling and Simulation: Theory and Applications, chapter 17 - Standardizing DEVS model representation, pages 427-458. Taylor and Francis, 2011. [WWW ]
     
  8. V. Andova, N. Cohen, and R. Skrekovski. Graph Classes (Dis)satisfying the Zagreb Indices Inequality. MATCH Commun. Math. Comput. Chem., 65(3):647-658, 2011. [PDF ]
    Abstract:
    Recently Hansen and Vuki\^cevi\'c proved that the inequality $M_1/n \leq M_2/m$, where $M_1$ and $M_2$ are the first and second Zagreb indices, holds for chemical graphs, and Vuki\^cevi\'c and Graovac proved that this also holds for trees. In both works is given a distinct counterexample for which this inequality is false in general. Here, we present some classes of graphs with prescribed degrees, that satisfy $M_1/n \leq M_2/m$: Namely every graph $G$ whose degrees of vertices are in the interval $[c; c + \sqrt c]$ for some integer $c$ satisies this inequality. In addition, we prove that for any $\Delta \geq 5$, there is an infinite family of graphs of maximum degree $\Delta$ such that the inequality is false. Moreover, an alternative and slightly shorter proof for trees is presented, as well as for unicyclic graphs.

     
  9. M. Basavaraju, L. S. Chandran, N. Cohen, F. Havet, and T. Müller. Acyclic edge-coloring of planar graphs. SIAM Journal of Discrete Mathematics, 25(2):463--478, 2011. [PDF ]
    Abstract:
    A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an {\it acyclic edge-coloring}. The {\it acyclic chromatic index} of a graph $G$, denoted $\chi'_a(G)$ is the minimum $k$ such that $G$ admits an {\it acyclic edge-coloring} with $k$ colors. We conjecture that if $G$ is planar and $\Delta(G)$ is large enough then $\chi'_a(G)=\Delta(G)$. We settle this conjecture for planar graphs with girth at least $5$. We also show that $\chi'_a(G)\leq \Delta(G) + 12$ for all planar $G$, which improves a previous result by Fiedorowicz et al.

     
  10. J. Beauquier, J. Burman, and S. Kutten. A self-stabilizing Transformer for Population Protocols with Covering. Theoretical Computer Science, 412(33):4247-4259, 2011. [WWW ]
    Abstract:
    Developing \emph{self-stabilizing} solutions is considered to be more challenging and complicated than developing classical solutions, where a proper initialization of the variables can be assumed. Hence, to ease the task of the developers, some automatic techniques have been proposed to design self-stabilizing algorithms. In this paper, we propose an \emph{automatic transformer} for algorithms in an extended \emph{population protocol model}. Population protocols is a model that was introduced recently for networks with a large number of resource-limited mobile agents. We use a variant of this model. First, we assume agents having characteristics (e.g., moving speed, communication radius) affecting their intercommunication ``speed'', which is reflected by their \emph{cover times}. Second, we assume the existence of a special agent with an unbounded memory, the \emph{base station}. The automatic transformer takes as an input an algorithm solving a \emph{static problem} (and meeting some additional rather natural requirements) and outputs a self-stabilizing algorithm for the same problem. The transformer is built using a \emph{re-execution approach} (the technique consisting of executing an algorithm repeatedly in order to obtain its self-stabilizing version). We show that in the model we use, a transformer based on such an approach is impossible without the assumption of an unbounded memory agent.

     
  11. J-C. Bermond, Y. M. Chee, N. Cohen, and X. Zhang. The $\alpha$-Arboricity of Complete Uniform Hypergraphs. SIAM Journal on Discrete Mathematics, 25(2):600-610, 2011. [PDF ]
    Abstract:
    The $\alpha$-arboricity of the complete 3-uniform hypergraph is determined completely.$\alpha$-Acyclicity is an important notion in database theory. The $\alpha$-arboricity of a hypergraph H is the minimum number of $\alpha$-acyclic hypergraphs that partition the edge set of H.

     
  12. J-C. Bermond, X. Muñoz, and I. Sau. Traffic Grooming in Bidirectional WDM Ring Networks. Networks, 58(1):20-35, 2011. [WWW ] [PDF ]
    Abstract:
    We study the minimization of ADMs (Add-Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all-to-all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor $C$ and $N$, the size of the ring. We first study exhaustively the cases $C=1$, $C = 2$, and $C=3$, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case $C>3$, focusing specifically on the case $C = k(k+1)/2$ for some $k \geq 1$. We give optimal decompositions for several congruence classes of $N$ using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings.

     
  13. V. Bilo, M. Flammini, G. Monaco, and L. Moscardelli. On the performances of Nash equilibria in isolation games. Journal of Combinatorial Optimization, 22:378-391, 2011.
    Note: Special Issue: Selected Papers from the 15th International Computing and Combinatorics Conference. [WWW ]
    Abstract:
    We study the performances of Nash equilibria in isolation games, a class of competitive location games recently introduced in Zhao et al. (Proc. of the 19th International Symposium on Algorithms and Computation (ISAAC), pp. 148–159, 2008 ). For all the cases in which the existence of Nash equilibria has been shown, we give tight or asymptotically tight bounds on the prices of anarchy and stability under the two classical social functions mostly investigated in the scientific literature, namely, the minimum utility per player and the sum of the players’ utilities. Moreover, we prove that the convergence to Nash equilibria is not guaranteed in some of the not yet analyzed cases.

     
  14. B. Bresar, F. Kardos, J. Katrenic, and G. Semanisin. Minimum $k$-path vertex cover. Discrete Applied Mathematics, 159(12):1189-1195, 2011. [PDF ]
    Abstract:
    A subset $S$ of vertices of a graph $G$ is called a {\em $k$-path vertex cover} if every path of order $k$ in $G$ contains at least one vertex from $S$. Denote by $\psi_k(G)$ the minimum cardinality of a $k$-path vertex cover in $G$. It is shown that the problem of determining $\psi_k(G)$ is NP-hard for each $k\geq2$, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of $\psi_k(G)$ and provide several estimations and exact values of $\psi_k(G)$. We also prove that $\psi_3(G)\le (2n+m)/6$, for every graph $G$ with $n$ vertices and $m$ edges.

     
  15. C. Caillouet, S. Pérennes, and H. Rivano. Framework for Optimizing the Capacity of Wireless Mesh Networks. Computer Communications, 34(13):1645-1659, 2011. [WWW ]
    Keywords: Wireless mesh networks, capacity, routing, scheduling, linear programming, column and cut generation..
    Abstract:
    In this paper, we address the problem of computing the transport capacity of Wireless Mesh Networks (WMNs) dedicated to Internet access. Routing and transmission scheduling have a major impact on the capacity provided to the clients. A cross-layer optimization of these problems allows the routing to take into account contentions due to radio interference. We present a generic Mixed Integer Linear Programing description of the congurations of a given WMN, addressing gateway placement, routing, and scheduling optimizations. We then develop new optimization models that can take into account a large variety of radio interference models, and QoS requirements on the routing. We also provide efficient resolution methods that deal with realistic size instances. It allows to work around the combinatoric of simultaneously achievable transmissions and point out a critical region in the network bounding the network achievable capacity. Based upon strong duality arguments, it is then possible to restrict the computation to a bounded area. It allows for computing solutions very efficiently on large networks.

     
  16. J. Chalopin, V. Chepoi, N. Nisse, and Y. Vaxès. Cop and robber games when the robber can hide and ride. SIAM Journal of Discrete Maths., 25(1):333-359, 2011. [WWW ] [PDF ]
    Abstract:
    In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G=(V,E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as graphs admitting a dismantling scheme. In this paper, we characterize in a similar way the cop-win graphs in the game in which the cop and the robber move at different speeds s' and s, s'<= s. We also investigate several dismantling schemes necessary or sufficient for the cop-win graphs in the game in which the robber is visible only every k moves for a fixed integer k>1. We characterize the graphs which are cop-win for any value of k.

     
  17. N. Cohen, D. Coudert, D. Mazauric, N. Nepomuceno, and N. Nisse. Tradeoffs in process strategy games with application in the WDM reconfiguration problem. Theoretical Computer Science (TCS), 412(35):4675-4687, August 2011. [WWW ] [PDF ]
    Abstract:
    We consider a variant of the graph searching games that models the routing reconfiguration problem in WDM networks. In the digraph processing game, a team of agents aims at {\it processing}, or clearing, the vertices of a digraph~$D$. We are interested in two different measures: 1) the total number of agents used, and 2) the total number of vertices occupied by an agent during the processing of $D$. These measures respectively correspond to the maximum number of simultaneous connections interrupted and to the total number of interruptions during a routing reconfiguration in a WDM network. Previous works have studied the problem of independently minimizing each of these parameters. In particular, the corresponding minimization problems are APX-hard, and the first one is known not to be in APX. In this paper, we give several complexity results and study tradeoffs between these conflicting objectives. In particular, we show that minimizing one of these parameters while the other is constrained is NP-complete. Then, we prove that there exist some digraphs for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even for a basic class of digraphs. On the other hand, we exhibit classes of graphs for which good tradeoffs can be achieved. We finally detail the relationship between this game and the routing reconfiguration problem. In particular, we prove that any instance of the processing game, i.e. any digraph, corresponds to an instance of the routing reconfiguration problem.

     
  18. N. Cohen and F. Havet. Linear and 2-Frugal Choosability of Graphs of Small Maximum Average Degree. Graphs and Combinatorics, 27(6):831-849, 2011. [WWW ] [PDF ]
    Abstract:
    A proper vertex colouring of a graph $G$ is {\it 2-frugal} (resp. {\it linear}) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths). A graph $G$ is {\it 2-frugally} (resp. {\it linearly}) {\it $L$-colourable} if for a given list assignment $L:V(G)\mapsto 2^{\mathbb N}$, there exists a 2-frugal (resp. linear) colouring $c$ of $G$ such that $c(v)\in L(v)$ for all $v\in V(G)$. If $G$ is 2-frugally (resp. linearly) $L$-list colourable for any list assignment such that $|L(v)|\ge k$ for all $v\inV(G)$, then $G$ is {\it 2-frugally} (resp. {\it linearly}) {\it $k$-choosable}. In this paper, we improve some bounds on the 2-frugal choosability and linear choosability of graphs with small maximum average degree.

     
  19. D. Coudert, F. Giroire, and I. Sau. Circuits in graphs through a prescribed set of ordered vertices. Journal of Interconnection Networks (JOIN), 11(3-4):121-141, 2011. [WWW ] [PDF ]
    Abstract:
    A \emph{circuit} in a simple undirected graph $G=(V,E)$ is a sequence of vertices $\{v_1,v_2,\ldots,v_{k+1}\}$ such that $v_1=v_{k+1}$ and $\{v_i,v_{i+1}\} \in E$ for $i=1,\ldots,k$. A circuit $C$ is said to be \emph{edge-simple} if no edge of $G$ is used twice in $C$. In this article we study the following problem: which is the largest integer $k$ such that, given any subset of $k$ ordered vertices of a graph $G$, there exists an edge-simple circuit visiting the $k$ vertices in the prescribed order? We first study the case when $G$ has maximum degree at most 3, establishing the value of $k$ for several subcases, such as when $G$ is planar or 3-vertex-connected. Our main result is that $k=10$ in infinite square grids. To prove this, we introduce a methodology based on the notion of core graph, in order to reduce the number of possible vertex configurations, and then we test each one of the resulting configurations with an Integer Linear Program (ILP) solver.

     
  20. D. Coudert and J-S. Sereni. Characterization of graphs and digraphs with small process number. Discrete Applied Mathematics (DAM), 159(11):1094-1109, July 2011. [WWW ] [PDF ]
    Abstract:
    We introduce the process number of a digraph as a tool to study rerouting issues in \wdm networks. This parameter is closely related to the vertex separation (or pathwidth). We consider the recognition and the characterization of (di)graphs with small process number. In particular, we give a linear time algorithm to recognize (and process) graphs with process number at most $2$, along with a characterization in terms of forbidden minors, and a structural description. As for digraphs with process number $2$, we exhibit a characterization that allows one to recognize (and process) them in polynomial time.

     
  21. J. Czap, S. Jendrol', and F. Kardos. On the strong parity chromatic number. Discussiones Mathematicae Graph Theory, 31:587-600, 2011. [PDF ]
    Abstract:
    A vertex colouring of a 2-connected plane graph $G$ is a strong parity vertex colouring if for every face $f$ and each colour $c$, the number of vertices incident with $f$ coloured by $c$ is either zero or odd. Czap et al. [Discrete Math. 311 (2011) 512–520] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs

     
  22. J. Czap, S. Jendrol', and F. Kardos. Facial parity edge colouring. Ars Mathematica Contemporanea, 4(2):255-269, 2011. [PDF ]
    Abstract:
    A \emph{facial parity edge colouring} of a connected bridgeless plane graph is such an edge colouring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same colour, in addition, for each face $\alpha$ and each colour $c$, either no edge or an odd number of edges incident with $\alpha$ is coloured with $c$. From Vizing's theorem it follows that every $3$-connected plane graph has a such colouring with at most $\Delta^* +1$ colours, where $\Delta^* $ is the size of the largest face. In this paper we prove that any connected bridgeless plane graph has a facial parity edge colouring with at most $92$ colours.

     
  23. J. Czap, S. Jendrol', F. Kardos, and J. Miskuf. Looseness of Plane Graphs. Graphs and Combinatorics, 27(1):73-85, 2011. [PDF ]
    Abstract:
    A face of a vertex coloured plane graph is called {\em loose} if the number of colours used on its vertices is at least three. The {\em looseness} of a plane graph $G$ is the minimum $k$ such that any surjective $k$-colouring involves a loose face. In this paper we prove that the looseness of a connected plane graph $G$ equals the maximum number of vertex disjoint cycles in a dual graph $G^*$ increased by 2. We also show upper and lower bounds on the looseness of graphs based on the number of vertices, the edge connectivity, and the girth of the dual graph. These bounds improve the result of Negami for the looseness of plane triangulations. We also present infinite classes of graphs where the equalities are attained.

     
  24. G. D'Angelo, Gabriele Di Stefano, Alfredo Navarra, and Cristina Pinotti. Recoverable Robust Timetables: An Algorithmic Approach on Trees. IEEE Transactions on Computers, 60(3):433 - 446, March 2011. [WWW ] [PDF ]
    Abstract:
    In the context of scheduling and timetabling, we study a challenging combinatorial problem which is very interesting for both practical and theoretical points of view. The motivation behind it is to cope with scheduled activities which might be subject to unavoidable disruptions, such as delays, occurring during the operational phase. The idea is to preventively plan some extra time for the scheduled activities in order to be "prepared" if a delay occurs, and absorb it without the necessity of rescheduling all the activities from scratch. This realizes the concept of designing robust timetables. During the planning phase, one should also consider recovery features that might be applied at runtime if disruptions occur. This leads to the concept of recoverable robust timetables. In this new concept, it is assumed that recovery capabilities are given as input along with the possible disruptions that must be considered. The main objective is the minimization of the overall needed time. The quality of a robust timetable is measured by the price of robustness, i.e., the ratio between the cost of the robust timetable and that of a nonrobust optimal timetable. We show that finding an optimal solution for this problem is NP-hard even though the topology of the network, which models dependencies among activities, is restricted to trees. However, we manage to design a paeudopolynomial time algorithm based on dynamic programming and apply it on both random networks and real case scenarios provided by Italian railways. We evaluate the effect of robustness on the scheduling of the activities and provide the price of robustness with respect to different scenarios. We experimentally show the practical effectiveness and efficiency of the proposed algorithm.

     
  25. O. Dalle. Should Simulation Products Use Software Engineering Techniques or Should They Reuse Products of Software Engineering? -- Part 1. Modeling & Simulation Magazine, 11(3), 07 2011.
    Note: Online publication. [WWW ] [PDF ]
    Abstract:
    This two-part article addresses the issues concerning the building of new simulation software by either reusing existing general purpose software products and frameworks or by writing the simulation software from scratch. As a means of discussing the use of existing software, this first part escribes a selected list of such existing software: the Eclipse IDE as graphical user front-end, Maven for the management and building of projects, Bonita for supporting simulation workflows, Ruby on Rails and its Hobo extension to provide online persistence, and the Fractal Component Model for supporting the popular Component-Based Modeling \& Simulation approach. The second part, to be published in the next issue of the \emph{M\&S Magazine}, will further explore some interesting features found in the selected software solutions, and discuss their benefits when applied to simulation.

     
  26. O. Dalle. Should Simulation Products Use Software Engineering Techniques or Should They Reuse Products of Software Engineering? -- Part 2. Modeling & Simulation Magazine, 11(4), 10 2011.
    Note: Online publication. [WWW ]
    Abstract:
    This two-part article addresses the issues concerning the building of new simulation software by either reusing existing general purpose software products and frameworks or by writing the simulation software from scratch. As a means of discussing the use of existing software, this first part escribes a selected list of such existing software: the Eclipse IDE as graphical user front-end, Maven for the management and building of projects, Bonita for supporting simulation workflows, Ruby on Rails and its Hobo extension to provide online persistence, and the Fractal Component Model for supporting the popular Component-Based Modeling \& Simulation approach. The second part, to be published in the next issue of the \emph{M\&S Magazine}, will further explore some interesting features found in the selected software solutions, and discuss their benefits when applied to simulation.

     
  27. R. Erman, F. Havet, B. Lidicky, and O. Pangrác. 5-colouring graphs with 4 crossings. SIAM Journal on Discrete Mathematics, 25(1):401-422, 2011. [PDF ]
    Abstract:
    We disprove a conjecture of Oporowski and Zhao stating that every graph with crossing number at most 5 and clique number at most 5 is 5-colourable. However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5-colourable. We also show some colourability results on graphs that can be made planar by removing few edges. In particular, we show that if there exists three edges whose removal leaves the graph planar then it is $5$-colourable.

     
  28. L. Esperet, F. Kardos, A. D. King, D. Král', and S. Norine. Exponentially many perfect matchings in cubic graphs. Advances in Mathematics, 227(4):1646-1664, 2011. [PDF ]
    Abstract:
    We show that every cubic bridgeless graph $G$ has at least $2^{|V(G)|/3656}$ perfect matchings. This confirms an old conjecture of Lov{\'{a}}sz and Plummer.

     
  29. P. Giabbanelli and J. G. Peters. Complex networks and epidemics. Technique et Science Informatiques, 20(2):181-212, 2011.
    Abstract:
    The study of spreading processes, such as infectious diseases or computer worms, is well-motivated by its financial impact and humanitarian aspects. A vast amount of research has emerged through the theory of complex networks, that sheds light on the properties found in a wide range of "real-world" networks. We review these properties in the context of spreads, with an emphasis on the settings underlying some of the major claims in the literature such as whether or not a scale-free network is particularly prone to spreading phenomena. Stochastic models have been well studied in the literature, and thus we focus on deterministic models, highlighting the connections between the two approaches. Finally, we classify immunization strategies into four categories, which allows comparisons on common features from a computer science perspective. Several topics for future work are suggested. For example, it remains open whether immunization strategies, such as those based on degree, benefit from complex network properties.

     
  30. F. Havet, S. Jendrol', R. Soták, and E. Skrabul'áková. Facial non-repetitive edge-colouring of plane graphs. Journal of Graph Theory, 66(1):38--48, 2011. [WWW ] [PDF ]
    Abstract:
    A sequence $r_1,r_2,\dots,r_{2n}$ such that $r_i=r_{n+i}$ for all $1\leq i \leq n$, is called a {\em repetition}. A sequence $S$ is called {\em non-repetitive} if no {\it block} (i.e. subsequence of consecutive terms of $S$) is a repetition. Let $G$ be a graph whose edges are coloured. A trail is called {\em non-repetitive} if the sequence of colours of its edges is non-repetitive. If $G$ is a plane graph, a {\em facial non-repetitive edge-colouring} of $G$ is an edge-colouring such that any {\it facial trail} (i.e. trail of consecutive edges on the boundary walk of a face) is non-repetitive. We denote $\pi'_f(G)$ the minimum number of colours of a facial non-repetitive edge-colouring of $G$. In this paper, we show that $\pi'_f(G)\leq 8$ for any plane graph $G$. We also get better upper bounds for $\pi'_f(G)$ in the cases when $G$ is a tree, a plane triangulation, a simple $3$-connected plane graph, a hamiltonian plane graph, an outerplanar graph or a Halin graph. The bound $4$ for trees is tight.

     
  31. F. Havet, M. Klazar, J. Kratochvìl, D. Kratsch, and M. Liedloff. Exact algorithms for L(2,1)-labelling. Algorithmica, 59(2):169--194, 2011. [PDF ]
    Abstract:
    The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph $G=(V,E)$ into an interval of integers $\{0, \dots ,k\}$ is an $L(2,1)$-labeling of $G$ of span $k$ if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed $k\ge 4$, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive $O((k+1)^n)$ algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of $k=4$ -- here the running time of our algorithm is $O(1.3006^n)$. % $O(1.3161^n)$. Furthermore we show that dynamic programming can be used to establish 0x1.508aap-869n $O(c^n)$ algorithm to compute an optimal $L(2,1)$-labeling, for a constant $c< 4$. an $O(3.8730^n)$ algorithm to compute an optimal $L(2,1)$-labeling.

     
  32. F. Kardos, J. Katrenic, and I. Schiermeyer. On computing the minimum 3-path vertex cover and dissociation number of graphs. Theoretical Computer Science, 412(50):7009-7017, 2011. [PDF ]
    Abstract:
    The dissociation number of a graph $G$ is the number of vertices in a maximum size induced subgraph of $G$ with vertex degree at most 1. A $k$-path vertex cover of a graph $G$ is a subset $S$ of vertices of $G$ such that every path of order $k$ in $G$ contains at least one vertex from $S$. The minimum $3$-path vertex cover is a dual problem to the dissociation number. For this problem we present an exact algorithm with a running time of $\mathcal{O}^*(1.5171^n)$ on a graph with $n$ vertices. We also provide a polynomial time randomized approximation algorithm with an expected approximation ratio of $\frac{23}{11}$ for the minimum $3$-path vertex cover.

     
  33. F. Kardos, D. Král', and J. Volec. Fractional colorings of cubic graphs with large girth. SIAM Journal on Discrete Mathematics, 25(3):1454-1476, 2011. [PDF ]
    Abstract:
    We show that every (sub)cubic $n$-vertex graph with sufficiently large girth has fractional chromatic number at most $2.2978$ which implies that it contains an independent set of size at least $0.4352n$. Our bound on the independence number is valid to random cubic graphs as well as it improves existing lower bounds on the maximum cut in cubic graphs with large girth.

     
  34. J. Araujo, J-C. Bermond, F. Giroire, F. Havet, D. Mazauric, and R. Modrzejewski. Weighted Improper Colouring. In C. S. Iliopoulos and W. F. Smyth, editors, Combinatorial Algorithms, volume 7056 of Lecture Notes in Computer Science, Victoria, Canada, pages 1-18, June 2011. Springer Berlin Heidelberg. [WWW ] [PDF ]
    Abstract:
    In this paper, we study a colouring problem motivated by a practical frequency assignment problem and up to our best knowledge new. In wireless networks, a node interferes with the other nodes the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles, etc. We model this with a weighted graph $G$ where the weights on the edges represent the noise (interference) between the two end-nodes. The total interference in a node is then the sum of all the noises of the nodes emitting on the same frequency. A weighted $t$-improper $k$-colouring of $G$ is a $k$-colouring of the nodes of $G$ (assignment of $k$ frequencies) such that the interference at each node does not exceed some threshold $t$. The Weighted Improper Colouring problem, that we consider here consists in determining the weighted $t$-improper chromatic number defined as the minimum integer $k$ such that $G$ admits a weighted $t$-improper $k$-colouring. We also consider the dual problem, denoted the Threshold Improper Colouring problem, where given a number $k$ of colours (frequencies) we want to determine the minimum real $t$ such that $G$ admits a weighted $t$-improper $k$-colouring. We show that both problems are NP-hard and first present general upper bounds; in particular we show a generalisation of Lov\'asz's Theorem for the weighted $t$-improper chromatic number. We then show how to transform an instance of the Threshold Improper Colouring problem into another equivalent one where the weights are either 1 or $M$, for a sufficient big value $M$. Motivated by the original application, we study a special interference model on various grids (square, triangular, hexagonal) where a node produces a noise of intensity 1 for its neighbours and a noise of intensity 1/2 for the nodes that are at distance 2. Consequently, the problem consists of determining the weighted $t$-improper chromatic number when $G$ is the square of a grid and the weights of the edges are 1, if their end nodes are adjacent in the grid, and 1/2 otherwise. Finally, we model the problem using linear integer programming, propose and test heuristic and exact Branch-and-Bound algorithms on random cell-like graphs, namely the Poisson-Voronoi tessellations.

     
  35. J. Araujo, V. Campos, F. Giroire, L. Sampaio, and R. Soares. On the hull number of some graph classes. In Proceedings of European Conference on Combinatorics, Graph Theory and Applications (EuroComb'11), volume 38 of Electronic Notes in Discrete Mathematics, Budapest, Hungary, pages 49-55, September 2011. [WWW ] [PDF ]
    Abstract:
    Given a graph G = (V, E), the closed interval of a pair of vertices u, v \in V , denoted by I[u, v], is the set of vertices that belongs to some shortest (u, v)-path. For a given S \subseteq V , let I[S] = u,v \in S I[u, v]. We say that S \subseteq V is a convex set if I[S] = S. The convex hull Ih [S] of a subset S \subseteq V is the smallest convex set that contains S. We say that S is a hull set if Ih [S] = V . The cardinality of a minimum hull set of G is the hull number of G, denoted by hn(G). We show that deciding if hn(G) \leq k is an NP-complete problem, even if G is bipartite. We also prove that hn(G) can be computed in polynomial time for cactus and P4 -sparse graphs.

     
  36. J. Araujo, F. Giroire, and J. Monteiro. Hybrid Approaches for Distributed Storage Systems. In Proceedings of Fourth International Conference on Data Management in Grid and P2P Systems (Globe'11), Toulouse, France, September 2011. [WWW ] [PDF ]
    Abstract:
    Distributed or peer-to-peer storage solutions rely on the in- troduction of redundant data to be fault-tolerant and to achieve high reliability. One way to introduce redundancy is by simple replication. This strategy allows an easy and fast access to data, and a good band- width efficiency to repair the missing redundancy when a peer leaves or fails in high churn systems. However, it is known that erasure codes, like Reed-Solomon, are an effi- cient solution in terms of storage space to obtain high durability when compared to replication. Recently, the Regenerating Codes were proposed as an improvement of erasure codes to better use the available bandwidth when reconstructing the missing information. In this work, we compare these codes with two hybrid approaches. The first was already proposed and mixes erasure codes and replication. The second one is a new proposal that we call Double Coding. We compare these approaches with the traditional Reed-Solomon code and also Re- generating Codes from the point of view of availability, durability and storage space. This comparison uses Markov Chain Models that take into account the reconstruction time of the systems.

     
  37. J. Bang-Jensen, F. Havet, and N. Trotignon. Finding an induced subdivision of a digraph. In VI Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2011), volume 37, Bariloche, Argentina, pages 09-14, 04 2011.
    Abstract:
    We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) $G$, does it contain an induced subdivision of a prescribed digraph $D$? The complexity of this problem depends on $D$ and on whether $H$ must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial instances as well as several NP-completeness proofs.

     
  38. S. K. Baruah, V. Bonifaci, G. D'Angelo, A. Marchetti-Spaccamela, S. Van Der Ster, and L. Stougie. Mixed-Criticality Scheduling of Sporadic Task Systems. In Camil Demetrescu and Magnús M. Halldórsson, editors, 19th Annual European Symposium on Algorithms (ESA 2011), volume 6942 of Lecture Notes in Computer Science, Saarbruecken, Germany, pages 555-566, August 2011. Springer. [WWW ] [PDF ]
    Abstract:
    We consider the scheduling of mixed-criticality task systems, that is, systems where each task to be scheduled has multiple levels of worst-case execution time estimates. We design a scheduling algorithm, EDF-VD, whose effectiveness we analyze using the processor speedup metric: we show that any 2-level task system that is schedulable on a unit-speed processor is correctly scheduled by EDF-VD using speed $\phi$; here $\phi$ 2 criticality levels.We finally consider 2-level instances on m identical machines. We prove speedup bounds for scheduling an independent collection of jobs and for the partitioned scheduling of a 2-level task system.

     
  39. J. Beauquier, P. Blanchard, J. Burman, and S. Delaet. Computing Time Complexity of Population Protocols with Cover Times - the ZebraNet Example. In 13th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2011, Lecture Notes in Computer Science, pages 47-61, 2011. Springer. [WWW ]
    Abstract:
    Population protocols are a communication model for large sensor networks with resource-limited mobile agents. The agents move asynchronously and communicate via pair-wise interactions. The original fairness assumption of this model involves a high level of asynchrony and prevents an evaluation of the convergence time of a protocol (via deterministic means). The introduction of some "partial synchrony" in the model, under the form of cover times, is an extension that allows evaluating the time complexities. In this paper, we take advantage of this extension and study a data collection protocol used in the ZebraNet project for the wild-life tracking of zebras in a reserve in central Kenya. In ZebraNet, sensors are attached to zebras and the sensed data is collected regularly by a mobile base station crossing the area. The data collection protocol of ZebraNet has been analyzed through simulations, but to our knowledge, this is the rst time, that a purely analytical study is presented. Our first result is that, in the original protocol, some data may never be delivered to the base station. We then propose two slightly modify ed and correct protocols and we compute their worst case time complexities. Still, in both cases, the result is far from the optimal.

     
  40. J. Beauquier, J. Burman, and V. Malykh. ZebraNet Analysé dans le Modéle des Protocoles de Population. In Ducourthial et Bertrand et Felber et Pascal, editor, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel, France, 2011. [WWW ]
    Abstract:
    Nous \'etudions le protocole de collecte de donn\'ees du projet ZebraNet, dans le modčle des protocoles de population. Dans ce projet des capteurs sont attach\'es \'a une population de z\'ebres, en Afrique Centrale, et fournissent des donn\'ees aux biologistes qui \'etudient leurs structures migratoires et comportementales. Nous montrons qu'un protocole voisin de celui utilis\'e dans ce projet ne se termine pas. Cela entra\^ine que le protocole originel ne se termine pas non plus. Aussi proposons nous une modification qui fournit la terminaison. Nous prouvons la correction de ce protocole modifi\'e et nous analysons sa complexit\'e en temps au pire, dans le mod\'ele des protocoles de population avec temps de couverture. La comparaison de cette complexit\'e avec celle du protocole optimal est tr\'es d\'efavorable. Le protocole de collecte de donn\'ees de ZebraNet a fait l'objet de simulations, mais c'est la premi\'ere fois, \'a notre connaissance, qu'est r\'ealis\'ee une \'etude purement analytique.

     
  41. J. Beauquier and J. Burman. Self-stabilizing Mutual Exclusion and Group Mutual Exclusion for Population Protocols with Covering. In 15th International Conference On Principles Of Distributed Systems, OPODIS 2011, Lecture Notes in Computer Science, 2011. Springer. [WWW ]
    Abstract:
    This paper presents and proves correct two self-stabilizing deterministic algorithms solving the mutual exclusion and the group mutual exclusion problems in the model of population protocols with covering. In this variant of the population protocol model, a local fairness is used and bounded state anonymous mobile agents interact in pairs according to constraints expressed in terms of their cover times. The cover time is an indicator of the "time" for an agent to communicate with all the other agents. This indicator is expressed in the number of the pairwise communications (events) and is unknown to agents. In the model, we also assume the existence of a particular agent, the base station. In contrast with the other agents, it has a memory size proportional to the number of the agents. We prove that without this kind of assumption, the mutual exclusion problem has no solution. The algorithms in the paper use a phase clock tool. This is a synchronization tool that was recently proposed in the model we use. For our needs, we extend the functionality of this tool to support also phases with unbounded (but finite) duration. This extension seems to be useful also in the future works.

     
  42. F. Becker, M. Matamala, N. Nisse, I. Rapaport, K. Suchan, and I. Todinca. Reconstruire un graphe en une ronde. In Ducourthial, Bertrand et Felber, and Pascal, editors, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel, France, 2011. [WWW ]
    Abstract:
    {Nous étudions quelles propriétés d'un réseau peuvent être calculées à partir d'une petite quantité d'informations locales fournie par ses noeuds. Notre modèle est une restriction de CONGEST, un modèle distribué classique. Il est proche du modèle de complexité de communication avec messages simultanés de Babai et al. Chacun des n noeuds --qui ne connaissent que leur identifiant, ceux de leurs voisins et la taille du graphe-- envoie un message de taille O(log(n)) bits à une entité centrale, le superviseur. Celui-ci doit alors déterminer une certaine propriété du réseau. Nous montrons que des questions telles que: ''Est-ce que le graphe contient un triangle? un carré ? Quel est son diamètre?" ne peuvent pas être résolues dans ce modèle. En revanche, pour de nombreuses classes de graphes : celles de dégénérescence bornée (incluant les graphes planaires, ceux de largeur arborescente bornée... ), les sommets peuvent succinctement donner une description complète du graphe au superviseur. Nous laissons ouverte la question de décider la connexité.}, x-editorial-board={yes}, x-proceedings={yes}, x-international-audience={no}, x-pays= {CL}, sorte = "conf-nat",

     
  43. F. Becker, M. Matamala, N. Nisse, I. Rapaport, K. Suchan, and I. Todinca. Adding a referee to an interconnection network: What can(not) be computed in one round. In 25th IEEE International Parallel & Distributed Processing Symposium (IPDPS), pages 508-514, 2011. IEEE. [WWW ] [PDF ]
    Abstract:
    {In this paper we ask which properties of a distributed network can be computed from a little amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model and it is close to the simultaneous messages (communication complexity) model defined by Babai, Kimmel and Lokam. More precisely, each of these n nodes -which only knows its own ID and the IDs of its neighbors- is allowed to send a message of O(log n) bits to some central entity, called the referee. Is it possible for the referee to decide some basic structural properties of the network topology G? We show that simple questions like, "does G contain a square?", "does G contain a triangle?" or "Is the diameter of G at most 3? cannot be solved in general. On the other hand, the referee can decode the messages in order to have full knowledge of G when G belongs to many graph classes such as planar graphs, bounded treewidth graphs and, more generally, bounded degeneracy graphs. We leave open questions related to the connectivity of arbitrary graphs. }, x-editorial-board={yes}, x-proceedings={yes}, x-international-audience={yes}, x-pays = {CL}, sorte = "conf-int",

     
  44. S. Belhareth, D. Coudert, D. Mazauric, N. Nisse, and I. Tahiri. Reconfiguration avec contraintes physiques dans les réseaux WDM. In Ducourthial et Bertrand et Felber et Pascal, editor, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel, France, 2011. [WWW ] [PDF ]
    Abstract:
    Dans un réseau WDM, utiliser une nouvelle longueur d'onde dans une fibre demande à recalibrer les autres longueurs d'ondes. Cela génère un coût (e.g., énergétique) qui dépend non linéairement du nombre de longueurs d'ondes utilisant la fibre. Lorsqu'un ensemble de requêtes doivent changer de chemins optiques dans le réseau (lors d'une opération de maintenance sur un lien du réseau), l'ordre dans lequel les requêtes sont déplacées influe sur le coût total de l'opération. Nous initions l'étude du problème d'optimisation correspondant. Nous prouvons que déterminer l'ordre de déplacements optimal est NP-complet pour un réseau de 2 nœuds. Nous donnons des bornes générales et identifions des classes d'instances faciles. Enfin, nous proposons et évaluons par simulations des heuristiques pour ce problème.

     
  45. J-C. Bermond, L. Gargano, S. Pérennes, A.A. Rescigno, and U. Vaccaro. Optimal Time Data Gathering in Wireless Networks with Omni-Directional Antennas. In SIROCCO 2011, volume 6796 of Lecture Notes in Computer Science, Gdansk, Poland, pages 306-317, June 2011. Springer-Verlag. [PDF ]
    Abstract:
    We study algorithmic and complexity issues originating from the problem of data gathering in wireless networks. We give an algorithm to construct minimum makespan transmission schedules for data gathering when the communication graph $G$ is a tree network, the interference range is \emph{any} integer $m\geq 2$, and no buffering is allowed at intermediate nodes. In the interesting case in which all nodes in the network have to deliver an arbitrary non-zero number of packets, we provide a closed formula for the makespan of the optimal gathering schedule. Additionally, we consider the problem of determining the computational complexity of data gathering in general graphs and show that the problem is weakly NP-complete. On the positive side, we design a simple $(1+2/m)$ factor approximation algorithm for general networks.

     
  46. C. Caillouet and A. Koster. Routage et Ordonnancement Robustes dans les Réseaux Radio Maillés. In Ducourthial, Bertrand et Felber, and Pascal, editors, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel, France, 2011. [WWW ]
     
  47. C. Caillouet, X. Li, and T. Razafindralambo. A Multi-objective Approach for Data Collection in Wireless Sensor Networks. In 10th International Conference on Ad Hoc Networks and Wireless (AdHocNow), Padderborn, Germany, July 2011. [WWW ]
     
  48. C. Caillouet and T. Razafindralambo. Compromis énergie-délai pour la collecte de données dans les réseaux de capteurs. In Ducourthial, Bertrand et Felber, and Pascal, editors, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel, France, 2011. [WWW ]
     
  49. V. Campos, C. Linhares Sales, A. K. Maia, N. Martins, and R. Sampaio. Restricted coloring problems on graphs with few $P_4$'s. In VI Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS'11), volume 37 of Electronic Notes in Discrete Mathematics, pages 57-62, 2011. [WWW ] [PDF ]
    Abstract:
    In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number and the harmonious chromatic number of $P_4$ -tidy graphs and $(q , q − 4)$-graphs, for every fixed q. These classes include cographs, $P_4$ -sparse and $P_4$ -lite graphs. We also obtain a polynomial time algorithm to determine the Grundy number of $(q , q − 4)$-graphs. All these coloring problems are known to be NP-hard for general graphs.

     
  50. G. Classen, D. Coudert, A. Koster, and N. Nepomuceno. Bandwidth assignment for reliable fixed broadband wireless networks. In 12th IEEE International Symposium on a World of Wireless Mobile and Multimedia Networks (WoWMoM), Lucca, Italy, pages 1-6, June 2011. IEEE. [PDF ]
    Abstract:
    In this paper, we investigate on conceiving reliable fixed broadband wireless networks under outage probability constraints. We introduce a joint optimization of data routing and bandwidth assignment that minimizes the total renewal fees of licenses, while handling all the traffic requirements simultaneously. This problem differs from classical capacity planning in the sense that the capacity of microwave radio links are prone to variations due to external factors (e.g., weather). Therefore, we must consider probabilistic constraints to deal with random parameters (viz., modulation schemes) and guarantee a desirable reliability level of the solution. We propose a (joint) chance-constrained programming approach to tackle this problem. This approach remains one of the main challenges of modern stochastic programming and it is still considered as very difficult and widely intractable. We then derive integer linear programming (ILP) counterparts for these chance-constrained programs and propose cutset-based valid inequalities to enhance the performance of ILP solvers. Preliminary computational results illustrate the price of reliability and present a comparative study on the performance of the different formulations.

     
  51. G. Classen, D. Coudert, A. Koster, and N. Nepomuceno. A Chance-Constrained Model & Cutting Planes for Fixed Broadband Wireless Networks. In International Network Optimization Conference (INOC), volume 6701 of Lecture Notes in Computer Science, Hamburg, Germany, pages 37-42, June 2011. [PDF ]
    Abstract:
    In this paper, we propose a chance-constrained mathematical program for fixed broadband wireless networks under unreliable channel conditions. The model is reformulated as integer linear program and valid inequalities are derived for the corresponding polytope. Computational results show that by an exact separation approach the optimality gap is closed by~$42$\,\0n average.

     
  52. D. Coudert, N. Nepomuceno, and I. Tahiri. Energy saving in fixed wireless broadband networks. In International Network Optimization Conference (INOC), volume 6701 of Lecture Notes in Computer Science, Hamburg, Germany, pages 484-489, June 2011. [PDF ]
    Abstract:
    In this paper, we present a mathematical formulation for saving energy in fixed broadband wireless networks by selectively turning off idle communication devices in low-demand scenarios. This problem relies on a fixed-charge capacitated network design (FCCND), which is very hard to optimize. We then propose heuristic algorithms to produce feasible solutions in a short time.

     
  53. D. Coudert, N. Nepomuceno, and I. Tahiri. Optimisation de la consommation énergétique dans les réseaux sans fil fixes. In Pascal Ducourthial, Bertrand et Felber, editor, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel France, 2011. [WWW ] [PDF ]
    Abstract:
    {N}ous {\'e}tudions le probl{\`e}me d'optimisation {\'e}nerg{\'e}tique dans les r{\'e}seaux sans fil fixes dans le cas d'une faible demande de trafic par rapport {\`a} la capacit{\'e} du r{\'e}seau. {N}ous proposons un programme lin{\'e}aire pour r{\'e}soudre le probl{\`e}me, puis nous pr{\'e}sentons une heuristique permettant de trouver rapidement une bonne solution.

     
  54. G. D'Angelo, Mattia D'Emidio, Daniele Frigioni, and Vinicio Maurizio. A Speed-Up Technique for Distributed Shortest Paths Computation. In Beniamino Murgante, Osvaldo Gervasi, Andrés Iglesias, David Taniar, and Bernady O. Apduhan, editors, 11th International Conference on Computational Science and Its Applications (ICCSA 2011), volume 6783 of Lecture Notes in Computer Science, Santander, Spain, pages 578-593, June 2011. Springer. [WWW ] [PDF ]
    Abstract:
    We propose a simple and practical speed-up technique, which can be combined with every distance vector routing algorithm based on shortest paths, allowing to reduce the total number of messages sent by that algorithm. We combine the new technique with two algorithms known in the literature: DUAL, which is part of CISCO's widely used EIGRP protocol, and the recent DUST, which has been shown to be very effective on networks with power law node degree distribution. We give experimental evidence that these combinations lead to an important gain in terms of the number of messages sent by DUAL and DUST at the price of a little increase in terms of space occupancy per node.

     
  55. G. D'Angelo, Gabriele Di Stefano, and Alfredo Navarra. Min-Max Coverage in Multi-interface Networks. In Ivana Cerná, Tibor Gyimóthy, Juraj Hromkovic, Keith Jefferey, Rastislav Královic, Marko Vukolic, and Stefan Wolf, editors, 37th Conference on Current Trends in Theory and Practice of Computer Science, volume 6543 of Lecture Notes in Computer Science, Novy Smokovec, Slovakia, pages 190-201, January 2011. Springer. [WWW ] [PDF ]
    Abstract:
    We consider devices equipped with multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider the problem of establishing the connections defined by a network G = (V,E) while keeping as low as possible the maximum cost set of active interfaces at the single nodes. Nodes V represent the devices, edges E represent the connections that must be established. We study the problem of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges. We prove that the problem is NP-hard for any fixed $\Delta$ $\ge$ 5 and k $\ge$ 16, with $\Delta$ being the maximum degree, and k being the number of different interfaces among the network. We also show that the problem cannot be approximated within $\Omega$(ln $\Delta$). We then provide a general approximation algorithm which guarantees a factor of O((1 + b)ln ($\Delta$)), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented.

     
  56. G. D'Angelo, Gabriele Di Stefano, and Alfredo Navarra. Bandwidth Constrained Multi-interface Networks. In Ivana Cerná, Tibor Gyimóthy, Juraj Hromkovic, Keith Jefferey, Rastislav Královic, Marko Vukolic, and Stefan Wolf, editors, 37th Conference on Current Trends in Theory and Practice of Computer Science, volume 6543 of Lecture Notes in Computer Science, Novy Smokovec, Slovakia, pages 202-213, January 2011. Springer. [WWW ] [PDF ]
    Abstract:
    In heterogeneous networks, devices can communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost, and provides a communication bandwidth. In this paper, we consider the problem of activating the cheapest set of interfaces among a network G = (V,E) in order to guarantee a minimum bandwidth B of communication between two specified nodes. Nodes V represent the devices, edges E represent the connections that can be established. In practical cases, a bounded number k of different interfaces among all the devices can be considered. Despite this assumption, the problem turns out to be NP-hard even for small values of k and $\Delta$, where $\Delta$ is the maximum degree of the network. In particular, the problem is NP-hard for any fixed k $\ge$ 2 and $\Delta$ $\ge$ 3, while it is polynomially solvable when k = 1, or $\Delta$ $\le$ 2 and k = O(1). Moreover, we show that the problem is not approximable within $\eta$logB or $\Omega$(loglog|V|) for any fixed k $\ge$ 3, $\Delta$ $\ge$ 3, and for a certain constant $\eta$, unless P=NP. We then provide an approximation algorithm with ratio guarantee of b max , where b max is the maximum communication bandwidth allowed among all the available interfaces. Finally, we focus on particular cases by providing complexity results and polynomial algorithms for $\Delta$ $\le$ 2.

     
  57. G. D'Angelo, Gabriele Di Stefano, and Alfredo Navarra. Gathering of Six Robots on Anonymous Symmetric Rings. In Adrian Kosowski and Masafumi Yamashita, editors, Structural Information and Communication Complexity, volume 6796 of Lecture Notes in Computer Science, Gdansk, Poland, pages 174-185, July 2011. Springer. [WWW ] [PDF ]
    Abstract:
    The paper deals with a recent model of robot-based computing which makes use of identical, memoryless mobile robots placed on nodes of anonymous graphs. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. In particular, we consider the case of only six robots placed on the nodes of an anonymous ring in such a way they constitute a symmetric placement with respect to one single axis of symmetry, and we ask whether there exists a strategy that allows the robots to gather at one single node. This is in fact the first case left open after a series of papers [1,2,3,4] dealing with the gathering of oblivious robots on anonymous rings. As long as the gathering is feasible, we provide a new distributed approach that guarantees a positive answer to the posed question. Despite the very special case considered, the provided strategy turns out to be very interesting as it neither completely falls into symmetry-breaking nor into symmetry-preserving techniques.

     
  58. G. D'Angelo, Gabriele Di Stefano, and Alfredo Navarra. Maximum Flow and Minimum-Cost Flow in Multi-Interface Networks. In 5th International Conference on Ubiquitous Information Management and Communication, Seoul, Korea, Republic Of, pages 19, February 2011. ACM. [WWW ] [PDF ]
    Abstract:
    In heterogeneous networks, devices can communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost, and provides a communication bandwidth. In this paper, we consider two fundamental optimization problems. In the first one, we aim to activate a set of interfaces in the network G = (V, E) in order to guarantee the maximal bandwidth between two given nodes. Nodes V represent the devices, edges E represent the connections that can be established according to the availability of the interfaces in the devices. In the second problem, we look for activating the cheapest set of interfaces among a network in order to guarantee a minimum bandwidth B of communication between two specified nodes. We show that the first problem is polynomially solvable while the second one is NP-Hard. However, we experimentally analyzed an algorithm for the second problem, showing that in practical cases it guarantees a low approximation ratio which allows us to use it in real-world networks.

     
  59. G. D'Angelo, Daniele Frigioni, and Camillo Vitale. Dynamic Arc-Flags in Road Networks. In Panos M. Pardalos and Steffen Rebennack, editors, 10th International Symposium, SEA 2011, volume 6630 of Lecture Notes in Computer Science, Kolimpari, Chania, Crete, Greece, pages 88-99, April 2011. Springer. [WWW ] [PDF ]
    Abstract:
    In this work we introduce a new data structure, named Road-Signs, which allows us to efficiently update the Arc-Flags of a graph in a dynamic scenario. Road-Signs can be used to compute Arc-Flags, can be efficiently updated and do not require large space consumption for many real-world graphs like, e.g., graphs arising from road networks. In detail, we define an algorithm to preprocess Road-Signs and an algorithm to update them each time that a weight increase operation occurs on an edge of the network. We also experimentally analyze the proposed algorithms in real-world road networks showing that they yields a significant speed-up in the updating phase of Arc-Flags, at the cost of a very small space and time overhead in the preprocessing phase.

     
  60. O. Dalle and E. Mancini. Traces Generation To Simulate Large-Scale Distributed Applications. In S. Jain, R. R. Creasey, J. Himmelspach, K. P. White, and M. Fu, editors, Winter Simulation Conference, Phoenix, AZ, États-Unis, pages 10p., December 2011. [WWW ] [PDF ]
    Abstract:
    In order to study the performance of scheduling algorithms, simulators of parallel and distributed applications need accurate models of the application's behavior during execution. For this purpose, traces of low-level events collected during the actual execution of real applications are needed. Collecting such traces is a difficult task due to the timing, to the interference of instrumentation code, and to the storage and transfer of the collected data. To address this problem we propose a comprehensive software architecture, which instruments the application's executables, gather hierarchically the traces, and post-process them in order to feed simulation models. We designed it to be scalable, modular and extensible.

     
  61. O. Dalle and J. Ribault. Some Desired Features for the DEVS Architecture Description Language. In Proceedings of the Symposium On Theory of Modeling and Simulation -- DEVS Integrative M&S Symposium (TMS/DEVS 2011), volume Book 4 -- Symposium on Theory of Modeling & Simulation - DEVS Integrative M&S Symposium (TMS/DEVS), Boston, MA, États-Unis, pages 258-263, 04 2011. [WWW ] [PDF ]
    Abstract:
    ADL are particularly well suited for component-based model frameworks that support hierarchical composition, such as DEVS with coupled models. In this paper we present some features found in the ADL of another hierarchical component model, namely the Fractal Component Model (FCM). To our best knowledge, these features are not yet available in most of the current DEVS implementations. Using a few examples coming from our experience, we demonstrate the usefulness of these features for Modeling & Simulation and their potential relevance for inclusion in a future DEVS implementation standard.

     
  62. S. Felix and J. Galtier. Shortest Paths and Probabilities on Time-Dependent Graphs - Applications to Transport Networks. In Proceedings of the 11th International Conference on ITS Telecommunications, Saint Petersburg, Russia, pages 56--62, August 2011. [WWW ]
    Abstract:
    In this paper, we focus on time-dependent graphs which seem to be a good way to model transport networks. In the first part, we remind some notations and techniques related to time-dependent graphs. In the second one, we introduce new algorithms to take into account the notion of probability related to paths in order to guarantee travelling times with a certain accuracy. We also discuss different probabilistic models and show the links between them.

     
  63. F. Giroire, D. Mazauric, and J. Moulierac. Routage efficace en énergie. In Ducourthial et Bertrand et Felber et Pascal, editor, 13es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Cap Estérel, France, 2011. [WWW ]
    Abstract:
    De récentes études montrent que la charge de trafic des routeurs n'a qu'une faible influence sur leur consommation énergétique. Par conséquent, la consommation dans les réseaux est fortement liée au nombre d'équipements du réseau activés (interfaces, chassis, etc). Dans un objectif de minimisation de l'énergie dans les réseaux, il est intéressant de minimiser le nombre (pondéré) d'équipements utilisés lors du routage. Dans cet article, nous considérons une architecture simplifiée où un lien entre deux routeurs relie deux interfaces. Quand un lien n'est pas activé, les deux interfaces correspondantes peuvent être éteintes. Par conséquent, afin de réduire la consommation d'énergie, l'objectif est de trouver un routage qui minimise le nombre de liens utilisés et satisfait toutes les demandes. Nous montrons des résultats d'inapproximabilité de ce problème, même si l'on considère des instances particulières. Nous prouvons des bornes en général et pour des topologies particulières telles que la grille, l'arbre ou le graphe complet. Nous proposons ensuite une heuristique dont nous évaluons les performances à l'aide de simulations sur des topologies réelles. Nous étudions ensuite l'impact de ces solutions efficaces en énergie sur la tolérance aux pannes et sur la longueur moyenne des routes.

     
  64. Y. Liu and G. Simon. Peer-Assisted Time-shifted Streaming Systems: Design and Promises. In IEEE International Conference on Communications (ICC'2011), Kyoto, Japan, 06 2011. IEEE. [PDF ]
    Abstract:
    Time-shifted streaming (or catch-up TV) allows viewers to watch their TV programs within an expanded time window. In this paper, we emphasize the challenging characteristics of time-shifted TV systems that prevent known delivery systems to be used. We model time-shifted TV as multiple-interval graph, then we present a Peer-Assisted Catch-Up Streaming system, namely PACUS, where a set of end users' computers assists the server for the content delivery. We show in particular how the PACUS tracker server can be efficiently implemented for catch-up TV. We demonstrate the benefits of PACUS by simulations. We especially highlight that PACUS reduces the traffic at the server side with the advantages of lightweight and self-adaptive unstructured peer-to-peer systems.

     
  65. F. Maffray and G. Morel. Algorithmes linéaires pour les graphes sans $P_5$ 3-colorables. In 12e congrès annuel de la ROADEF, 2011.
     
  66. P. Aboulker, F. Havet, and N. Trotignon. On wheel-free graphs. Research Report RR-7651, INRIA, June 2011. [WWW ] [PDF ]
    Abstract:
    A wheel is a graph formed by a chordless cycle and a vertex that has at least three neighbors in the cycle. We prove that every 3-connected graph that does not contain a wheel as a subgraph is in fact minimally 3-connected. We prove that every graph that does not contain a wheel as a subgraph is 3-colorable.

     
  67. L. Addario-Berry, F. Havet, C. Linhares Sales, B. Reed, and S. Thomassé. Oriented trees in digraphs. Research Report 7502, INRIA, 01 2011. [WWW ] [PDF ]
    Abstract:
    Let $f(k)$ be the smallest integer such that every $f(k)$-chromatic digraph contains every oriented tree of order $k$. Burr proved that $f(k)\leq (k-1)^2$ and conjectured $f(k)=2n-2$. In this paper, we give some sufficient conditions for an $n$-chromatic digraphs to contains some oriented tree. In particular, we show that every acyclic $n$-chromatic digraph contains every oriented tree of order $n$. We also show that $f(k)\leq k^2/2-k/2+1$. Finally, we consider the existence of antidirected trees in digraphs. We prove that every antidirected tree of order $k$ is contained in every $(5k-9)$-chromatic digraph. We conjecture that if $|E(D)| > (k-2) |V(D)|$, then the digraph $D$ contains every antidirected tree of order $k$. This generalizes Burr's conjecture for antidirected trees and the celebrated Erd\H{o}s-S\'os Conjecture. We give some evidences for our conjecture to be true.

     
  68. J. Araujo, J-C. Bermond, F. Giroire, F. Havet, D. Mazauric, and R. Modrzejewski. Weighted Improper Colouring. Research Report RR-7590, INRIA, 04 2011. [WWW ] [PDF ]
    Keywords: graph colouring, improper colouring, grids, integer programming, algorithms.
    Abstract:
    {I}n this paper, we study a new colouring problem up to our best knowledge inspired by the imperative of practical networks. {I}n real-life wireless networks, nodes interfere with one another with various intensities depending on numerous parameters: distance between them, the geographical topography, obstacles, etc. {W}e model this with a noise matrix. {T}he interference perceived by a node then is the sum of all the noise of the nodes emitting on the same frequency. {T}he problem is then to determine the minimum number of colours (or frequencies) needed to colour the whole graph so that the interference does not exceed a given threshold. {W}e provide several general results, such as bounds on this number of colours (e.g. a {B}rook's like theorem). {W}e then study the practical case of square of infinite grids which corresponds to operators' network and a noise decreasing with the distance. {W}e provide the chromatic number of the square, triangular and hexagonal grids for all possible admissible interference levels. {F}inally, we model the problem using linear programming, propose and test a heuristic and an exact branch\&bound algorithms on random cell-like graphs, namely the {P}oisson {V}oronoi tessellations.

     
  69. J. Araujo, V. Campos, F. Giroire, N. Nisse, L. Sampaio, and R. Soares. On the hull number of some graph classes. Technical report RR-7567, INRIA, September 2011. [WWW ] [PDF ]
    Abstract:
    In this paper, we study the geodetic convexity of graphs focusing on the problem of the complexity to compute inclusion-minimum hull set of a graph in several graph classes. For any two vertices $u,v\in V$ of a connected graph $G=(V,E)$, the {\em closed interval} $I[u,v]$ of $u$ and $v$ is the the set of vertices that belong to some shortest $(u,v)$-path. For any $S \subseteq V$, let $I[S]= \bigcup\_{u,v\in S} I[u,v]$. A subset $S\subseteq V$ is {\em geodesically convex} if $I[S] = S$. In other words, a subset $S$ is convex if, for any $u,v \in S$ and for any shortest $(u,v)$-path $P$, $V(P) \subseteq S$. Given a subset $S\subseteq V$, the {\em convex hull} $I\_h[S]$ of $S$ is the smallest convex set that contains $S$. We say that $S$ is a {\em hull set} of $G$ if $I\_h[S] = V$. The size of a minimum hull set of $G$ is the {\em hull number} of $G$, denoted by $hn(G)$. The {\sc Hull Number} problem is to decide whether $hn(G)\leq k$, for a given graph $G$ and an integer $k$. Dourado {\it et al.} showed that this problem is NP-complete in general graphs. In this paper, we answer an open question of Dourado et al.\~\cite{Douradoetal09} by showing that the {\sc Hull Number} problem is NP-hard even when restricted to the class of bipartite graphs. Then, we design polynomial time algorithms to solve the {\sc Hull Number} problem in several graph classes. First, we deal with the class of complements of bipartite graphs. Then, we generalize some results in\~\cite{ACGSS11} to the class of $(q,q-4)$-graphs and to the class of cacti. Finally, we prove tight upper bounds on the hull numbers. In particular, we show that the hull number of an $n$-node graph $G$ without simplicial vertices is at most $1+\lceil \frac{3(n-1)}{5}\rceil$ in general, at most $1+\lceil \frac{n-1}{2}\rceil$ if $G$ is regular or has no triangle, and at most $1+\lceil \frac{n-1}{3}\rceil$ if $G$ has girth at least $6$.

     
  70. F. Becker, A. Kosowski, N. Nisse, I. Rapaport, and K. Suchan. Interconnection network with a shared whiteboard: Impact of (a)synchronicity on computing power. Technical report RR-7746, INRIA, 2011. [WWW ] [PDF ]
    Abstract:
    In this work we study the computational power of graph-based models of distributed computing in which each node additionally has access to a global whiteboard. A node can read the contents of the whiteboard and, when activated, can write one message of $O(\log n)$ bits on it. A message is only based on the local knowledge of the node and the current content of the whiteboard. When the protocol terminates, each node computes the output based on the final contents of the whiteboard in order to answer some question on the network's topology. We propose a framework to formally define several scenarios modelling how nodes access the whiteboard, in a synchronous way or not. This extends the work of Becker {\it et al.} [IPDPS 2011] where nodes were imposed to create their messages only based on their local knowledge (i.e., with the whiteboard empty). We prove that the four models studied have increasing power of computation: any problem that can be solved in the weakest one can be solved in the the second, and so on. Moreover, we exhibit problems that {\it separate} models, i.e., that can be solved in one model but not in a weaker one. These problems are related to Maximal Independent Set and detection of cycles. Finally we investigate problems related to connectivity as the construction of spanning- or BFS-tree in our different models.

     
  71. S. Belhareth, D. Coudert, D. Mazauric, N. Nisse, and I. Tahiri. Reconfiguration with physical constraints in WDM networks. Research Report RR-7850, INRIA, 2011. [WWW ] [PDF ]
    Keywords: Reconfiguration, WDM, NP-complete, Physical Layer Impaiments..
    Abstract:
    In a WDM network, setting up a new wavelength in a fiber requires recalibrating the other wavelengths passing through this fiber. This induces a cost (e.g., time, energy, degradation of QoS) that depends nonlinearly on the number of wavelengths using the fiber. When a set of connection requests must change their optical paths in the network (e.g., during a maintenance operation on a link in the network), the order in which requests are switched affects the total cost of the operation. That is, the reconfiguration of the routing in a WDM network has some cost due to physical layer impairments. We initiate the study of the corresponding optimization problem by modeling the cost of switching a request as a non-linear function depending on the load of the links used by the new lightpath. We prove that determining the optimal rerouting order is NP-complete for a $2$-nodes network. We then give general lower and upper bounds on the minimum cost and we identify classes of instances where the problem can be solved in polynomial time. Finally, we design heuristics for this problem and we analyze and compare them by simulations.

     
  72. J-C. Bermond, A. Jean-Marie, D. Mazauric, and M-L. Yu. Well Balanced Designs for Data Placement. Research Report 7725, INRIA, 09 2011. [WWW ]
    Abstract:
    The problem we consider in this article is motivated by data placement in particular data replication in video on demand systems. We are given a set $V$ of $n$ servers and $b$ files (data, documents). Each file is replicated on exactly $k$ servers. A placement consists in finding a family of $b$ subsets of $V$ (representing the files) called blocks each of size $k$. Each server has some probability to fail and we want to find a placement which minimizes the variance of the number of available files. It was conjectured that there always exists an optimal placement (with variance better than that of any other placement for any value of the probability of failure). We show that the conjecture is true, if there exists a well balanced design, that is a family of blocks, such that each j-element subset of $V$ , $1 \leq j \leq k$, belongs to the same or almost the same number of blocks (difference at most one). The existence of well balanced designs is a difficult problem as it contains as subproblem the existence of Steiner systems. We completely solve the case $k=2$ and give bounds and constructions for $k = 3$ and some values of $n$ and $b$.

     
  73. S. Bessy and F. Havet. Enumerating the edge-colourings and total colourings of a regular graph. Research Report RR-7652, INRIA, June 2011. [WWW ] [PDF ]
    Abstract:
    In this paper, we are interested in computing the number of edge colourings and total colourings of a graph. We prove that the maximum number of $k$-edge-colourings of a $k$-regular graph on $n$ vertices is $k\cdot(k-1!)^{n/2}$. Our proof is constructible and leads to a branching algorithm enumerating all the $k$-edge-colourings of a $k$-regular graph using a time $O^*((k-1!)^{n/2})$ and polynomial space. In particular, we obtain a algorithm on time $O^*(2^{n/2})=O^*(1.4143^n)$ and polynomial space to enumerate all the $3$-edge colourings of a cubic graph, improving the running time of $O^*(1.5423^n)$ of the algorithm due to Golovach et al.\~\cite{GKC10}. We also show that the number of $4$-total-colourings of a connected cubic graph is at most $3.2^{3n/2}$. Again, our proof yields a branching algorithm to enumerate all the $4$-total-colourings of a connected cubic graph.

     
  74. V. Campos and F. Havet. 5-choosability of graphs with 2 crossings. Research Report RR-7618, INRIA, 05 2011. [WWW ] [PDF ]
    Abstract:
    {W}e show that every graph with two crossings is 5-choosable. {W}e also prove that every graph which can be made planar by removing one edge is 5-choosable.

     
  75. J. G. Chang, F. Havet, M. Montassier, and A. Raspaud. Steinberg's Conjecture and near-colorings. Rapport de recherche RR-7669, INRIA, 7 2011. [WWW ] [PDF ]
    Abstract:
    Let ${\cal F}$ be the family of planar graphs without cycles of length 4 and 5. Steinberg's Conjecture (1976) that says every graph of ${\cal F}$ is 3-colorable remains widely open. Motiv\'ees par une relaxation propos\'ee par Erd\H{o}s (1991), plusieurs \'etudes ont montr\'e la conjecture pour des sous-classes de ${\cal F}$. Par exemple, Borodin {\it et al.}~ont prouv\'e que tout graphe planaire sans cycles de longueur 4 \`a 7 est 3-colorable. Dans ce rapport, nous relaxons le probl\`eme non pas sur la classe de graphes mais sur le type de coloration en consid\'erant des {\em quasi-colorations}. Un graphe $G=(V,E)$ est dit $(i,j,k)$-colorable si son ensemble de sommet peut \^etre partitionner en trois ensembles $V_1,V_2,V_3$ tels que les graphes $G[V_1],G[V_2],G[V_3]$ induits par ces ensembles soit de degr\'e maximum au plus $i,j,k$ respectivement. Avec cette terminologie, la Conjecture de Steinberg dit que tout graphe de ${\cal F}$ est $(0,0,0)$-colorable. Un r\'esultat de Xu (2008) implique que tout graphe de ${\cal F}$ est $(1,1,1)$-colorable. Nous montrons ici que tout graphe de ${\cal F}$ est $(2,1,0)$-colorable et $(4,0,0)$-colorable.

     
  76. F. Fomin, F. Giroire, A. Jean-Marie, D. Mazauric, and N. Nisse. To Satisfy Impatient Web surfers is Hard. Technical report RR-7740, INRIA, September 2011. [WWW ] [PDF ]
    Abstract:
    Prefetching is a basic mechanism to avoid to waste time when accessing data. However, a tradeoff must be established between the amount of network's resources wasted by the prefetching and the gain of time. For instance, in the Web, browsers may download documents in advance while an Internaut is surfing on the Web. Since the web surfer follows the hyperlinks in an unpredictable way, the choice of the web pages to be prefetched must be computed online. The question is then to determine the minimum amount of resources used by prefetching and that ensures that all documents accessed by the web surfer have previously been loaded in the cache. We model this problem as a game similar to Cops and Robber Games in graphs. A fugitive starts on a marked vertex of a (di)graph G. Turn by turn, an observer marks at most k >= 1 vertices and then the fugitive can move along one edge/arcs of G. The observer wins if he prevents the fugitive to reach an unmarked vertex. The fugitive wins otherwise, i.e., if she enters an unmarked vertex. The surveillance number of a graph is the least k >=1 allowing the observer to win whatever the fugitive does. We also consider the connected variant of this game, i.e., when a vertex can be marked only if it is adjacent to an already marked vertex. All our results hold for both variants, connected or not. We show that deciding whether the surveillance number of a chordal graph equals 2 is NP-hard. Deciding if the surveillance number of a DAG equals 4 is PSPACE-complete. Moreover, computing the surveillance number is NP-hard in split graphs. On the other hand, we provide polynomial time algorithms to compute surveillance number of trees and interval graphs. Moreover, in the case of trees, we establish a combinatorial characterization, related to isoperimetry, of the surveillance number.

     
  77. F. Giroire, S. K. Gupta, R. Modrzejewski, J. Monteiro, and S. Pérennes. Analysis of the Repair Time in Distributed Storage Systems. Research Report RR-7538, INRIA, 02 2011. [WWW ] [PDF ]
    Keywords: P2P storage systems, data lifetime, queuing model, regenerating codes per- formance evaluation.
    Abstract:
    {D}istributed or peer-to-peer storage systems introduce redundancy to preserve the data in case of peer failures or departures. {T}o ensure long-term fault tolerance, the storage system must have a self-repair service that continuously reconstructs lost fragments of redundancy. {T}he speed of this reconstruction process is crucial for the data survival. {T}his speed is mainly determined by available bandwidth, a critical resource of such systems. {W}e propose a new analytical framework that takes into account the correlation of concurrent repairs when estimating the repair time and the probability of data loss. {M}ainly, we intro- duce queuing models in which reconstructions are served by peers at a rate that depends on the available bandwidth. {T}he models and schemes proposed are validated by mathematical analysis, extensive set of simulations, and experimentation using the {G}rid'5000 test-bed platform.

     
  78. F. Havet and X. Zhu. The game Grundy number of graphs. Rapport de recherche RR-7646, INRIA, June 2011. [WWW ] [PDF ]
    Keywords: colouring game, game Grundy number, trees, partial 2-trees.
    Abstract:
    Given a graph G = (V;E), two players, Alice and Bob, alternate their turns in choosing uncoloured vertices to be coloured. Whenever an uncoloured vertex is chosen, it is coloured by the least positive integer not used by any of its coloured neighbours. Alice's goal is to minimize the total number of colours used in the game, and Bob's goal is to maximize it. The game Grundy number of G is the number of colours used in the game when both players use optimal strategies. It is proved in this paper that the maximum game Grundy number of forests is 3, and the game Grundy number of any partial 2-tree is at most 7.

     
  79. F. Maffray and G. Morel. On 3-colorable $P_5$-free graphs. Technical report 191, Les Cahiers Leibniz, Laboratoire G-SCOP, 2011. [PDF ]
     
  80. J. Moulierac, T. K. Phan, N. Thoai, and C. Tran. Xcast6 Treemap Islands - A Mixed Model of Application and Network Layer Multicast. Rapport de recherche RR-7784, INRIA, December 2011. [WWW ] [PDF ]
    Keywords: IP multicast, Application Layer Multicast, Xcast, media streaming, linear program, algorithms.
    Abstract:
    IP multicast is a protocol that deals with group communications with the aim of reducing traffic redundancy in the network. However, due to difficulty in deployment and poor scalability with a large number of multicast groups, IP multicast is still not widely deployed and used on the Internet. Recently, Xcast6 and Xcast6 Treemap, the two network layer multicast protocols, have been proposed with complementary scaling properties to IP multicast: they support a very large number of active multicast sessions. However, the key limitation of these protocols is that they only support small multicast group. In this paper, we propose Xcast6 Treemap island - a hybrid model of Application Layer Multicast (ALM) and Xcast6 that can work for large multicast group. Our model has several key advantages: ease of deployment, efficiency in bandwidth savings, no control message between end-host and router, zero multicast forwarding state at router and no need for a multicast address allocation protocol. In addition, this model is a potential service from which an ISP can get new revenue. Finally, in simulation section, we have made a comparison with IP multicast and NICE protocol to show the feasibility of our new model.

     
2010
  1. D. Coudert and D. Simplot-Ryl, editors. Ad Hoc & Sensor Wireless Networks, an International Journal -- Special issue on Ad hoc, Mobile and Wireless Networks, volume 9. Old City Publishing, 2010. [WWW ]
     
  2. O. Dalle and G. Wainer, editors. SIMULATION: Transactions of the Society of Modeling and Simulation International. Special Issue on Software Tools, Techniques and Architectures for Computer Simulation, volume 86. Sage, 2010.
     
  3. F. Giroire and D. Mazauric, editors. 11es Journées Doctorales en Informatique et Réseaux (JDIR 2010), number 11, Sophia Antipolis, France, March 2010. Mascotte, INRIA, I3S(CNRS / Univ. of Nice-Sophia). [WWW ]
     
  4. D. Coudert. Algorithmique et optimisation dans les réseaux de télécommunications. Habilitation à Diriger des Recherches, Université de Nice Sophia-Antipolis (UNS), March 2010. [WWW ] [PDF ]
     
  5. Julian Monteiro. Modeling and Analysis of Reliable Peer-to-Peer Storage Systems. PhD thesis, Ecole doctorale STIC, Université de Nice-Sophia Antipolis, November 2010. [WWW ]
    Abstract:
    Large scale peer-to-peer systems are foreseen as a way to provide highly reliable data storage at low cost. To ensure high durability and high resilience over a long period of time the system must add redundancy to the original data. It is well-known that erasure coding is a space efficient solution to obtain a high degree of fault-tolerance by distributing encoded fragments into different peers of the network. Therefore, a repair mechanism needs to cope with the dynamic and unreliable behavior of peers by continuously reconstructing the missing redundancy. Consequently, the system depends on many parameters that need to be well tuned, such as the redundancy factor, the placement policies, and the frequency of data repair. These parameters impact the amount of resources, such as the bandwidth usage and the storage space overhead that are required to achieve a desired level of reliability, i.e., probability of losing data. This thesis aims at providing tools to analyze and predict the performance of general large scale data storage systems. We use these tools to analyze the impact of different choices of system design on different performance metrics. For instance, the bandwidth consumption, the storage space overhead, and the probability of data loss should be as small as possible. Different techniques are studied and applied. First, we describe a simple Markov chain model that harnesses the dynamics of a storage system under the effects of peer failures and of data repair. Then we provide closed-form formulas that give good approximations of the model. These formulas allow us to understand the interactions between the system parameters. Indeed, a lazy repair mechanism is studied and we describe how to tune the system parameters to obtain an efficient utilization of bandwidth. We confirm by comparing to simulations that this model gives correct approximations of the system average behavior, but does not capture its variations over time. We then propose a new stochastic model based on a fluid approximation that indeed captures the deviations around the mean behavior. These variations are most of the time neglected by previous works, despite being very important to correctly allocate the system resources. We additionally study several other aspects of a distributed storage system: we propose queuing models to calculate the repair time distribution under limited bandwidth scenarios; we discuss the trade-offs of a Hybrid coding (mixing erasure codes and replication); and finally we study the impact of different ways to distribute data fragments among peers, i.e., placement strategies.

     
  6. N. Nepomuceno. Network optimization for wireless microwave backhaul. PhD thesis, Ecole doctorale STIC, Université de Nice-Sophia Antipolis, December 2010. [WWW ] [PDF ]
    Keywords: Wireless communications, Mathematical programming, Network optimization, Multicommodity flows, Microwave backhaul networks.
    Abstract:
    Technological breakthroughs have transformed the telecommunications industry aiming at providing capacity and efficiency to support the increasing demand for wireless broadband services. With the advances in access technologies, the capacity bottleneck of cellular networks is gradually moving from the radio interface towards the backhaul -- the portion of the network infrastructure that provides interconnectivity between the access and core networks. The ability for microwave to be rapidly and cost-effectively deployed is being a crucial point for successfully tackling the backhaul bottleneck problem. However, backhaul solutions available with this technology have received little attention from the scientific community. Nevertheless, the growth of microwave backhaul networks and their increasing complexity give rise to many interesting optimization problems. In fact, unlike wired networks, the capacity of a microwave radio link is prone to variations, either due to external factors (e.g., weather) or by the action of the network operator. This fundamental difference raises a variety of new issues to be addressed appropriately. Therefore, more refined approaches for dealing with network optimization in wireless microwave backhaul need to be conceived. In this thesis, we investigate network optimization problems related to the design and configuration of wireless microwave backhaul. We are concerned with a general class of problems expressed in terms of minimum cost multicommodity flows with discontinuous step increasing cost functions on the links of the network. These problems are among the most important and challenging problems in network optimization. Generally, they are computationally very difficult and, in practice, can only be solved approximately. We introduce mathematical models for some of these problems and present solution approaches essentially based on general mixed integer programming, chance-constrained programming, relaxation techniques, cutting plane methods, as well as hybrid metaheuristics. This work was done in collaboration with the SME~3Roam, and partially developed within the scope of the joint project RAISOM (R\'eseaux de collecte IP sans fil optimis\'es), among INRIA Sophia

     
  7. S. Pérennes. Contribution à l'algorithmique des réseaux de télécommunications. Habilitation à Diriger des Recherches, Université de Nice Sophia-Antipolis (UNS), March 2010. [WWW ]
     
  8. A. Casamayou, N. Cohen, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N.M. Thiéry, and P. Zimmermann. Calcul mathématique avec Sage, chapter Théorie des graphes. 2010. [WWW ]
     
  9. A. Casamayou, N. Cohen, G. Connan, T. Dumont, L. Fousse, F. Maltey, M. Meulien, M. Mezzarobba, C. Pernet, N. M. Thiéry, and P. Zimmermann. Calcul mathématique avec Sage, chapter Programmation Linéaire. 2010. [WWW ]
     
  10. T. Cinkler, D. Coudert, M. Flammini, G. Monaco, L. Moscardelli, X. Muñoz, I. Sau, M. Shalom, and S. Zaks. Graphs and Algorithms in Communication Networks: Studies in Broadband, Optical, Wireless, and Ad Hoc Networks, volume XXVII of EATCS Texts in Theoretical Computer Science, chapter Traffic Grooming: Combinatorial Results and Practical Resolutions, pages 63-94. Springer, A. Koster and X. Muñoz edition, 2010. [WWW ] [PDF ]
    Abstract:
    In an optical network using the wavelength division multiplexing (WDM) technology, routing a request consists in assigning it a route in the physical network and a wavelength. If each request uses $1/g$ of the bandwidth of the wavelength, we will say that the grooming factor is $g$. That means that on a given edge of the network we can groom (group) at most $g$ requests on the same wavelength. With this constraint the objective can be either to minimize the number of wavelengths (related to the transmission cost) or minimize the number of Add Drop Multiplexers\index{add drop multiplexer} (shortly ADM) used in the network (related to the cost of the nodes). Here, we first survey the main theoretical results obtained for different grooming factors on various topologies: complexity, (in)approximability, optimal constructions, approximation algorithms, heuristics, etc. Then, we give an ILP formulation for multilayer traffic grooming and present some experimental results.

     
  11. L. Addario-Berry, W.S. Kennedy, A.D. King, Z. Li, and B. Reed. Finding the maximum-weight induced $k$-partite subgraph of an $i$-triangulated graph. Discrete Applied Mathematics, 158(7):765-770, April 2010. [WWW ]
    Abstract:
    An i-triangulated graph is a graph in which every odd cycle has two non-crossing chords; i-triangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are clique-separable graphs. A graph is clique-separable precisely if every induced subgraph either has a clique cutset, or is a complete multipartite graph or a clique joined to an arbitrary bipartite graph. We exhibit a polynomial time algorithm for finding a maximum-weight induced k-partite subgraph of an i-triangulated graph, and show that the problem of finding a maximum-size bipartite induced subgraph in a clique-separable graph is View the MathML source-complete.

     
  12. O. Amini, F. Giroire, F. Huc, and S. Pérennes. Minimal selectors and fault tolerant networks. Networks, 55(4):326-340, July 2010. [WWW ] [PDF ]
    Abstract:
    In this paper we study a combinatorial optimization problem issued from on-board networks in satellites. In this kind of networks the entering signals (inputs) should be routed to amplifiers (outputs). The connections are made via expensive switches with four links available. The paths connecting inputs to outputs should be link-disjoint. More formally, we call {it $\plk-$network } an undirected graph with $p+\lambda$ inputs, $p+k$ outputs and internal vertices of degree four. A $\plk-$network is \emph{valid} if it is tolerant to a restricted number of faults in the network, i.e. if for any choice of at most $k$ faulty inputs and $\lambda$ faulty outputs, there exist $p$ edge-disjoint paths from the remaining inputs to the remaining outputs. In the special case $\lambda=0$, a $\plk-$network is already known as a \emph{selector}. Our optimization problem consists of determining $N\plk$, the minimum number of nodes in a valid $\plk-$network. For this, we present validity certificates and a gluing lemma from which derive lower bounds for $N\plk$. We also provide constructions, and hence upper bounds, based on expanders. The problem is very sensitive to the order of $\lambda$ and $k$. For instance, when $\lambda$ and $k$ are small compared to $p$, the question reduces to avoid certain forbidden local configurations. For larger values of $\lambda$ and $k$, the problem is to find graphs with a good expansion property for small sets. This leads us to introduce a new parameter called \emph{$\alpha$-robustness}. We use $\alpha$-robustness to generalize our constructions to higher order values of $k$ and $\lambda$. In many cases, we provide asymptotically tight bounds for $N\plk$.

     
  13. O. Amini, F. Havet, F. Huc, and S. Thomassé. WDM and directed star arboricity. Combinatorics, Probability and Computing, 19:161--182, 2010. [PDF ]
    Abstract:
    A digraph is $m$-labelled if every arc is labelled by an integer in $\{1, \dots ,m\}$. Motivated by wavelength assignment for multicasts in optical networks, we introduce and study $n$-fibre colourings of labelled digraphs. These are colourings of the arcs of $D$ such that at each vertex $v$, and for each colour $\alpha$, $in(v,\alpha)+out(v,\alpha)\leq n$ with $in(v,\alpha)$ the number of arcs coloured $\alpha$ entering $v$ and $out(v,\alpha)$ the number of labels $l$ such that there is at least one arc of label $l$ leaving $v$ and coloured with $\alpha$. The problem is to find the minimum number of colours $\lambda_n(D)$ such that the $m$-labelled digraph $D$ has an $n$-fibre colouring. In the particular case when $D$ is $1$-labelled, $\lambda_1(D)$ is called the directed star arboricity of $D$, and is denoted by $dst(D)$. We first show that $dst(D)\leq 2\Delta^-(D)+1$, and conjecture that if $\Delta^-(D)\geq 2$, then $dst(D)\leq 2\Delta^-(D)$. We also prove that for a subcubic digraph $D$, then $dst(D)\leq 3$, and that if $\Delta^+(D), \Delta^-(D)\leq 2$, then $dst(D)\leq 4$. Finally, we study $\lambda_n(m,k)=\max\{\lambda_n(D) \tq D \mbox{ is $m$-labelled} \et \Delta^-(D)\leq k\}$. We show that if $m\geq n$, then $\ds \left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil\leq \lambda_n(m,k) \leq\left\lceil\frac{m}{n}\left\lceil \frac{k}{n}\right\rceil + \frac{k}{n} \right\rceil + C \frac{m2\log k}{n}$ for some constant $C$. We conjecture that the lower bound should be the right value of $\lambda_n(m,k)$.

     
  14. M. Asté, F. Havet, and C. Linhares Sales. Grundy number and products of graphs. Discrete Mathematics, 310(9):1482--1490, 2010. [PDF ]
    Abstract:
    The {\em Grundy number} of a graph $G$, denoted by $\Gamma (G)$, is the largest $k$ such that $G$ has a {\em greedy} $k$-colouring, that is a colouring with $k$ colours obtained by applying the greedy algorithm according to some ordering of the vertices of $G$. In this paper, we study the Grundy number of the lexicographic and the cartesian products of two graphs in terms of the Grundy numbers of these graphs. Regarding the lexicographic product, we show that $\Gamma(G)\times \Gamma(H)\leq \Gamma(G[H])\leq 2^{\Gamma(G)-1}(\Gamma(H)-1)+\Gamma(G)$. In addition, we show that if $G$ is a tree or $\Gamma(G)=\Delta(G)+1$, then $\Gamma(G[H])=\Gamma(G)\times\Gamma(H)$. We then deduce that for every fixed $c\geq 1$, given a graph $G$, it is CoNP-Complete to decide if $\Gamma(G)\leq c\times \chi(G)$ and it is CoNP-Complete to decide if $\Gamma(G)\leq c\times \omega(G)$. Regarding the cartesian product, we show that there is no upper bound of $\Gamma(G\square H)$ as a function of $\Gamma(G)$ and $\Gamma(H)$. Nevertheless, we prove that $\Gamma(G\square H) \leq \Delta(G)\cdot 2^{\Gamma(H)-1} + \Gamma(H)$.

     
  15. J-C. Bermond, C. J. Colbourn, L. Gionfriddo, G. Quattrocchi, and I. Sau. Drop Cost and Wavelength Optimal Two-Period Grooming with Ratio 4. SIAM Journal on Discrete Mathematics, 24(2):400-419, 2010. [PDF ]
    Abstract:
    We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and $C=4$ and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.

     
  16. J-C. Bermond, L. Gargano, and A.A. Rescigno. Gathering with minimum completion time in sensor tree networks. JOIN, 11(1-2):1-33, 2010.
    Note: A preliminary version has been presented at Sirocco08. [PDF ]
    Abstract:
    Data gathering is a fundamental operation in wireless sensor networks in which data packets generated at sensor nodes are to be collected at a base station. In this paper we suppose that each sensor is equipped with an half–duplex interface; hence, a node cannot receive and transmit at the same time. Moreover, each node is equipped with omnidirectional antennas allowing the transmission over distance R. The network is a multi-hop wireless network and the time is slotted so that one–hop transmission of one data item consumes one time slot. We model the network with a graph where the vertices represent the nodes and two nodes are connected if they are in the transmission range of each other. We suppose that the interference range is the same as the transmission range; therefore due to interferences a collision happens at a node if two or more of its neighbors try to transmit at the same time. Furthermore we suppose that an intermediate node should forward a message as soon as it receives it. We give an optimal collision free gathering schedule for tree networks whenever each node has exactly one data packet to send.

     
  17. J-C. Bermond, F. Havet, F. Huc, and C. Linhares Sales. Improper colouring of weighted grid and hexagonal graphs. Discrete Mathematics, Algorithms and Applications, 2(3):395-411, 2010. [PDF ]
    Abstract:
    {W}e study a weighted improper colouring problem motivated by a frequency allocation problem. {I}t consists of associating to each vertex a set of $p(v)$ (weight) distinct colours (frequencies), such that the set of vertices having a given colour induces a graph of degree at most $k$ (the case $k=0$ corresponds to proper colouring). {T}he objective is to minimize the number of colours. We propose approximation algorithms to compute such a colouring for general graphs. {W}e apply these to obtain good approximation ratio for grid and hexagonal graphs. {F}urthermore we give exact results for the 2-dimensional grid and the triangular lattice when the weights are all the same.

     
  18. J-C. Bermond and M-L. Yu. Optimal gathering algorithms in multi-hop radio tree networks with interferences. Ad Hoc and Sensor Wireless Networks, 9(1-2):109-128, 2010. [PDF ]
    Abstract:
    We study the problem of gathering information from the nodes of a multi-hop radio network into a pre-defined destination node under the interference constraints. In such a network, a message can only be properly received if there is no interference from another message being simultaneously transmitted. The network is modeled as a graph, where the vertices represent the nodes and the edges, the possible com- munications. The interference constraint is modeled by a fixed integer dI ? 1, which implies that nodes within distance d I in the graph from one sender cannot receive messages from another node. In this paper, we suppose that it takes one unit of time (slot) to transmit a unit-length message. A step (or round) consists of a set of non interfering (compat- ible) calls and uses one slot. We present optimal algorithms that give minimum number of steps (delay) for the gathering problem with buffer- ing possibility, when the network is a tree, the root is the destination and dI = 1. In fact we study the equivalent personalized broadcasting problem instead.

     
  19. I. Caragiannis, A. Ferreira, C. Kaklamanis, S. Pérennes, and H. Rivano. Fractional Path Coloring in Bounded Degree Trees with Applications. Algorithmica, 58(2):516-540, 2010. [WWW ] [PDF ]
    Abstract:
    This paper studies the natural linear programming relaxation of the path coloring problem. We prove constructively that finding an optimal fractional path coloring is Fixed Parameter Tractable (FPT), with the degree of the tree as parameter: the fractional coloring of paths in a bounded degree trees can be done in a time which is linear in the size of the tree, quadratic in the load of the set of paths, while exponential in the degree of the tree. We give an algorithm based on the generation of an efficient polynomial size linear program. Our algorithm is able to explore in polynomial time the exponential number of different fractional colorings, thanks to the notion of trace of a coloring that we introduce. We further give an upper bound on the cost of such a coloring in binary trees and extend this algorithm to bounded degree graphs with bounded treewidth. Finally, we also show some relationships between the integral and fractional problems, and derive a (1 + 5/3e) ~= 1.61 approximation algorithm for the path coloring problem in bounded degree trees, improving on existing results. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexing (WDM) optical networks.

     
  20. N. Cohen, D. Dimitrov, R. Krakovski, R. Skrekovski, and V. Vukasinovic. On Wiener Index of Graphs and Their Line Graphs. MATCH Commun. Math. Comput. Chem., 64(3):683-698, 2010. [PDF ]
    Abstract:
    The Wiener index of a graph $G$, denoted by $W(G)$, is the sum of distances between all pairs of vertices in $G$. In this paper, we consider the relation between the Wiener index of a graph, $G$, and its line graph, $L(G)$. We show that if $G$ is of minimum de\ gree at least two, then $W(G) ≤ W(L(G))$. We prove that for every non-negative integer g0, there exists $g > g_0$, such that there are infinitely many graphs $G$ of girth $g$, satisfying $W(G) = W(L(G))$. This partially answers a question raised by Dobrynin and Mel’nikov \ [8] and encourages us to conjecture that the answer to a stronger form of their question is affirmative.

     
  21. N. Cohen, F. V. Fomin, G. Gutin, E. Jung Kim, S. Saurabh, and A. Yeo. Algorithm for finding k-vertex out-trees and its application to k-internal out-branching problem. Journal of Computer and System Sciences, 76(7):650 - 662, 2010. [WWW ] [PDF ]
    Abstract:
    " An out-tree T is an oriented tree with only one vertex of in-degree zero. A vertex x of T is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given out-tree with k vertices. The algorithms are of running time O*(5.704k) and O*(6.14k), respectively. We apply the deterministic algorithm to obtain a deterministic algorithm of runtime O*(ck), where c is a constant, for deciding whether an input digraph contains a spanning out-tree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM'08)."

     
  22. N. Cohen and F. Havet. Planar graphs with maximum degree $\Delta\geq 9$ are ($\Delta+1$)-edge-choosable -- short proof. Discrete Mathematics, 310(21):3049--3051, 2010. [PDF ]
    Keywords: edge-colouring, list colouring, List Colouring Conjecture, planar graphs.
    Abstract:
    {W}e give a short proof of the following theorem due to {B}orodin~\cite{{B}or90}. {E}very planar graph with maximum degree $\{D}elta\geq 9$ is $(\{D}elta+1)$-edge-choosable.

     
  23. D. Coudert, N. Nepomuceno, and H. Rivano. Power-Efficient Radio Configuration in Fixed Broadband Wireless Networks. Computer Communications, Special Section on Hot Topics in Mesh Networking, 33(8):898-906, May 2010. [WWW ] [PDF ]
    Abstract:
    In this work, we investigate on determining feasible radio configurations in fixed broadband wireless networks, focusing on power efficiency. Under this scenario, a power-efficient configuration can be characterized by a modulation constellation size and a transmission power level. Every link holds a set of power-efficient configurations, each of them associating a capacity with its energy cost. We introduce a joint optimization of data routing and radio configuration that minimizes the total energy consumption while handling all the traffic requirements simultaneously. An exact mathematical formulation of the problem is presented. It relies on a minimum cost multicommodity flow with step increasing cost functions, which is very hard to optimize. We then propose a piecewise linear convex function, obtained by linear interpolation of power-efficient points, that provides a good approximation of the energy consumption on the links, and present a relaxation of the previous formulation that exploits the convexity of the cost functions. This yields lower bounds on the total energy expenditure, and finally heuristic algorithms based on the fractional optimum are employed to produce feasible configuration solutions. Our models are validated through extensive experiments that are reported and discussed. The results testify the potentialities behind this novel approach.

     
  24. O. Dalle, Q. Liu, G. Wainer, and B. P. Zeigler. Applying Cellular Automata and DEVS Methodologies to Digital Games: A Survey. Simulation & Gaming, 41(6):796-823, December 2010.
    Note: EA DISSIMINET (Associated Team). [WWW ]
    Abstract:
    Cellular automata were designed by John von Neumann in the 1940s, as a mathematical abstraction for modeling self-replicating algorithms. Since then, cellular automata have been widely studied theoretically and evolved into multiple variants. In the 1970s, Bernard P. Zeigler proposed a formalism rooted on systems theory principles, named DEVS (discrete-event systems specifications), which paved the way for component-based modeling and simulation and related methodologies. The purpose of this article is to survey how cellular automata and its variant, called cell-DEVS, may be used to implement computer simulations that can be used as digital serious games. The authors illustrate that implementation through some of the practical applications of such cellular automata. They show various serious game applications using real case studies: first, a simple bouncing ball and pinball game, a particle collision model, another on gossip propagation, and an application on human behavior at a metro station. Then, they show an application to social simulation using a voters game, a theoretical application (a model called Daisy World, which is derived from Gaia theory), and applications to physical phenomena such as a sandpile formation model or, finally, a three-dimensional model of a "virtual clay" that changes its shape when it is subject to pressure effects.

     
  25. N. Eggemann, F. Havet, and S. Noble. k-L(2,1)-Labelling for Planar Graphs is NP-Complete for $k\geq 4$. Discrete Applied Mathematics, 158(16):1777--1788, 2010. [WWW ] [PDF ]
    Abstract:
    A mapping from the vertex set of a graph $G=(V,E)$ into an interval of integers $\{0, \dots ,k\}$ is an $L(2,1)$-labelling of $G$ of span $k$ if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbour are mapped onto distinct integers. It is known that for any fixed $k\ge 4$, deciding the existence of such a labelling is an NP-complete problem while it is polynomial for $k\leq 3$. For even $k\geq 8$, it remains NP-complete when restricted to planar graphs. In this paper, we show that it remains NP-complete for any $k \ge 4$ by reduction from Planar Cubic Two-Colourable Perfect Matching. Schaefer stated without proof that Planar Cubic Two-Colourable Perfect Matching is NP-complete. In this paper we give a proof of this.

     
  26. C. Eslahchi, H. Pezeshk, M. Sadeghi, P. Giabbanelli, F. Movahedi, and V. Dabbaghian. A Probabilistic Model for the Spread of HIV Infection among Injection Drug Users. World Journal of Modelling and Simulation (WJMS), 6(4):267-273, November 2010. [PDF ]
    Abstract:
    By sharing contaminated needles, injecting drug users contribute in a significant manner to the spread of the human immunodeficiency virus (HIV) in Asia and in some European countries. Furthermore, injecting drug users may also be sex workers, and risky sexual activities allow the virus to spread to other parts of the population. Mathematical models of needle sharing have been used to evaluate the success of needle exchange programs, and have led to advances such as new legislations. We use epidemiological classes to model how injecting drug users may start or cease sharing needles under social influences, and may become infected with HIV when sharing. Numerous models based on epidemiological classes were proposed regarding several aspects of HIV, and were commonly studied by differential equations. We instead show how to analyze the theoretical behaviour of the model using the technique of discrete Markov chains. Using simulations, we observed that the prevalence of HIV depended very little on the probability of transmission of HIV when sharing a needle, but almost only on the encouragement and discouragement regarding needle sharing in the community. By measuring the cost of resources required to decrease factors encouraging needle sharing and to increase discouraging ones, our model could be refined to provide an estimate of the expected prevalence of HIV among injecting drug users.

     
  27. A. Ferreira, A. Goldman, and J. Monteiro. Performance evaluation of routing protocols for MANETs with known connectivity patterns using evolving graphs. Wireless Networks, 16(3):627--640, 2010. [WWW ] [PDF ]
    Abstract:
    The assessment of routing protocols for mobile wireless networks is a difficult task, because of the networks’ dynamic behavior and the absence of benchmarks. However, some of these networks, such as intermittent wireless sensors networks, periodic or cyclic networks, and some delay tolerant networks (DTNs), have more predictable dynamics, as the temporal variations in the network topology can be considered as deterministic, which may make them easier to study. Recently, a graph theoretic model—the evolving graphs—was proposed to help capture the dynamic behavior of such networks, in view of the construction of least cost routing and other algorithms. The algorithms and insights obtained through this model are theoretically very efficient and intriguing. However, there is no study about the use of such theoretical results into practical situations. Therefore, the objective of our work is to analyze the applicability of the evolving graph theory in the construction of efficient routing protocols in realistic scenarios. In this paper, we use the NS2 network simulator to first implement an evolving graph based routing protocol, and then to use it as a benchmark when comparing the four major ad hoc routing protocols (AODV, DSR, OLSR and DSDV). Interestingly, our experiments show that evolving graphs have the potential to be an effective and powerful tool in the development and analysis of algorithms for dynamic networks, with predictable dynamics at least. In order to make this model widely applicable, however, some practical issues still have to be addressed and incorporated into the model, like adaptive algorithms. We also discuss such issues in this paper, as a result of our experience.

     
  28. A. Ferreira. Uma estratégia face à Revolução Digital. Teoria e Debate, 87:20-23, 2010.
    Abstract:
    A revolu{\c{c}}{\~a}o digital {\'e} o principal motor do atual ritmo acelerado do progresso cient{\'\i}fico e da inova{\c{c}}{\~a}o. O poder criativo e a produtividade tecnol{\'o}gica dos indiv{\'\i}duos est{\~a}o sendo ativados em propor{\c{c}}{\~o}es antes desconhecidas, produzindo ininterruptamente novos produtos e processos, em quase todas as {\'a}reas do conhecimento humano. O Information Economy Report 2007-2008 da CNUCED detalha como a ind{\'u}stria das Tecnologias da Informa{\c{c}}{\~a}o e da Comunica{\c{c}}{\~a}o (TIC) cresce mais rapidamente do que muitas ind{\'u}strias a n{\'\i}vel mundial. Atualmente, o setor das TIC representa cerca de 7\-5582248o PIB mundial e emprega mais de 15 milh{\~o}es de pessoas nos pa{\'\i}ses da OECD. Em dados de 2007, as receitas mundiais das 250 maiores empresas em TIC atingiram 3,8 trilh{\~o}es de d{\'o}lares. Como afirmado por Kofi Annan, antigo Secret{\'a}rio-Geral das Na{\c{c}}{\~o}es Unidas: \"Se o mundo pretende seriamente alcan{\c{c}}ar o Objectivo de Desenvolvimento do Mil{\^e}nio de reduzir em metade o n{\'u}mero de pessoas vivendo em extrema pobreza at{\'e} o ano de 2015, as TIC devem figurar proeminentemente neste esfor{\c{c}}o. Todos – governos, sociedade civil e as empresas do setor privado – devem ajudar a fomentar oportunidades na era digital e colocar as TIC ao servi{\c{c}}o do desenvolvimento.\" Surpreendentemente, por{\'e}m, mesmo se tal contribui{\c{c}}{\~a}o enorme do setor econ{\^o}mico das TIC ao PIB mundial {\'e} bem compreendida e reconhecida, o impacto real de todas as Ci{\^e}ncias e Tecnologias da Computa{\c{c}}{\~a}o e da Comunica{\c{c}}{\~a}o como facilitadoras e catalisadoras da inova{\c{c}}{\~a}o e do progresso em outros setores econ{\^o}micos e outras disciplinas cient{\'\i}ficas, como a gen{\^o}mica por exemplo, que tamb{\'e}m impactam a sociedade, {\'e} largamente ignorado. Neste artigo proponho-me a mostrar a import{\^a}ncia de um posicionamento estrat{\'e}gico em rela{\c{c}}{\~a}o {\`a} revolu{\c{c}}{\~a}o digital, informado por atividades multidisciplinares de prospectiva.

     
  29. M. Flammini, G. Monaco, L. Moscardelli, H. Shachnai, M. Shalom, T. Tamir, and S. Zaks. Minimizing Total Busy Time in Parallel Scheduling with Application to Optical Networks. Theoretical Computer Science, 411(40-42):3553-3562, September 2010.
    Abstract:
    We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of $n$ jobs $\mathcal{J}= \{J_1, \ldots , J_n \}$. Each job, $J_j$, is associated with an interval $[s_j, c_j]$ along which it should be processed. Also given is the parallelism parameter $g \ge 1$, which is the maximal number of jobs that can be processed simultaneously by a single machine. Each machine operates along a contiguous time interval, called its {\em busy interval}, which contains all the intervals corresponding to the jobs it processes. The goal is to assign the jobs to machines such that the total busy time of the machines is minimized. The problem is known to be NP-hard already for $g=2$. We present a $4$-approximation algorithm for general instances, and approximation algorithms with improved ratios for instances with bounded lengths, for instances where any two intervals intersect, and for instances where no interval is properly contained in another. Our study has important application in optimizing the switching costs of optical networks.

     
  30. F. V. Fomin, P. A. Golovach, J. Kratochvil, N. Nisse, and K. Suchan. Pursuing a fast robber on a graph. Theoretical Computer Science, 411(7-9):1167-1181, 2010. [WWW ] [PDF ]
    Abstract:
    The Cops and Robbers game as originally defined independently by Quillot and by Nowakowski and Winkler in the 1980â??s has been much studied, but very few results pertain to algorithmic and complexity aspects of it. In this paper we prove that computing the minimum number of cops that are guaranteed too catch a robber on a given graph is NP-hard and that the parametrized version of the problem is W[2]-hard; the proof extends to the case where the robber moves s time faster than the cops. We show that on split graphs, the problem is polynomially solvable if s=1 but is NP-hard if s=2. We further prove that on graphs of bounded cliquewidth the problem is polynomially solvable for s<=2. Finally, we show that for planar graphs the minimum number of cops is unbounded if the robber is faster than the cops.

     
  31. F. Havet, D. Král, J.-S. Sereni, and R. Skrekovski. Facial coloring using Hall's theorems. European Journal of Combinatorics, 31:1001--1019, 2010. [WWW ] [PDF ]
    Abstract:
    A vertex coloring of a plane graph is $\ell$-facial if every two distinct vertices joined by a facial walk of length at most $\ell$ receive distinct colors. It has been conjectured that every plane graph has an $\ell$-facial coloring with at most $3\ell+1$ colors. We improve the currently best known bound and show that every plane graph has an $\ell$-facial coloring with at most $\lfloor 7\ell/2\rfloor+6$ colors. Our proof uses the standard discharging technique, however, in the reduction part we have successfully applied Hall's Theorem, which seems to be quite an innovative approach in this area.

     
  32. C. Molle and M-E. Voge. A quantitative analysis of the capacity of wireless mesh networks. IEEE Communications Letters, 14(5):438-440, May 2010. [WWW ]
     
  33. C. Molle. Optimization of the Capacity of Wireless Mesh Networks. 4OR: A Quarterly Journal of Operations Research, 8(4):425-428, December 2010. [WWW ]
     
  34. H. Rivano, F. Theoleyre, and F. Valois. A Framework for the Capacity Evaluation of Multihop Wireless Networks. Ad Hoc and Sensor Wireless networks (AHSWN), 9(3-4):139-162, 2010. [PDF ]
    Abstract:
    The specific challenges of multihop wireles networks lead to a strong research effort on efficient protocols design where the offered capacity is a key objective. More specifically, routing strategy largely impacts the network capacity, i.e. the throughput offered to each flow. In this work, we propose a complete framework to compute the upper and the lower bounds of the network capacity according to a physical topology and a given routing protocol. The radio resource sharing principles of CSMA-CA is modeled as a set of linear constraints with two models of fairness. The first one assumes that nodes have a fair access to the channel, while the second one assumes that on the radio links. We then develop a pessimistic and an optimistic scenarios for radio resource sharing, yielding a lower bound and an upper bound on the network capacity for each fairness case. Our approach is independent of the network topology and the routing protocols, and provides therefore a relevant framework for their comparison. We apply our models to a comparative analysis of a well-known flat routing protocol OLSR against two main self-organized structure approaches, VSR and localized CDS.

     
  35. I. Sau and D. M. Thilikos. Subexponential Parameterized Algorithms for Degree-constrained Subgraph Problems on Planar Graphs. Journal of Discrete Algorithms, 8(3):330-338, September 2010. [WWW ] [PDF ]
    Abstract:
    We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounded maximum degree and with maximum number of edges (or vertices). These problems are natural generalisations of the \textsc{Longest Path} problem. Our approach uses bidimensionality theory combined with novel dynamic programming techniques over branch decompositions of the input graph. These techniques can be applied to a more general family of problems that deal with finding connected subgraphs under certain degree constraints.

     
  36. E. Alvarez-Miranda, A. Candia, X. Chen, X. Hu, and B. Li. Efficient Algorithms for the Prize Collecting Steiner Tree Problems with Interval Data. In Proceedings of the 6th International Conference on Algorithmic Aspects in Information and Management (AAIM), volume 6124 of Lecture Notes in Computer Science, Weihai, China, pages 13-24, July 2010. Springer. [WWW ] [PDF ]
    Abstract:
    Given a graph $G=(V,E)$ with a cost on each edge in $E$ and a prize at each vertex in $V$, and a target set $V'\subseteq V$, the Prize Collecting Steiner Tree (PCST) problem is to find a tree $T$ interconnecting vertices in $V'$ that has minimum total costs on edges and maximum total prizes at vertices in $T$. This problem is NP-hard in general, and it is polynomial-time solvable when graphs $G$ are restricted to 2-trees. In this paper, we study how to deal with PCST problem with uncertain costs and prizes. We assume that edge $e$ could be included in $T$ by paying cost $x_e\in[c_e^-,c_e^+]$ while taking risk $\frac{ c_e^+-x_e}{ c_e^+-c_e^-}$ of losing $e$, and vertex $v$ could be awarded prize $p_v\in [p_v^-,p_v^+]$ while taking risk $\frac{ y_v-p_v^-}{p_v^+-p_v^-}$ of losing the prize. We establish two risk models for the PCST problem, one minimizing the maximum risk over edges and vertices in $T$ and the other minimizing the sum of risks. Both models are subject to upper bounds on the budget for constructing a tree. We propose two polynomial-time algorithms for these problems on 2-trees, respectively. Our study shows that the risk models have advantages over the tradional robust optimization model, which yields NP-hard problems even if the original optimization problems are polynomial-time solvable.

     
  37. J. Araujo, C. Linhares Sales, and I. Sau. Weighted Coloring on $P_4$-sparse Graphs. In 11es Journées Doctorales en Informatique et Réseaux (JDIR 2010), Sophia Antipolis, France, pages 33--38, March 2010. [PDF ]
    Abstract:
    Given an undirected graph G = (V, E) and a weight function w : V → R+, a vertex coloring of G is a partition of V into independent sets, or color classes. The weight of a vertex coloring of G is defined as the sum of the weights of its color classes, where the weight of a color class is the weight of a heaviest vertex belonging to it. In the WEIGHTED COLORING problem, we want to determine the minimum weight among all vertex colorings of G [1]. This problem is NP-hard on general graphs, as it reduces to determining the chromatic number when all the weights are equal. In this article we study the WEIGHTED COLORING problem on P4-sparse graphs, which are defined as graphs in which every subset of five vertices induces at most one path on four vertices [2]. This class of graphs has been extensively studied in the literature during the last decade, and many hard optimization problems are known to be in P when restricted to this class. Note that cographs (that is, P4-free graphs) are P4-sparse, and that P4-sparse graphs are P5-free. The WEIGHTED COLORING problem is in P on cographs [3] and NP-hard on P5-free graphs [4]. We show that WEIGHTED COLORING can be solved in polynomial time on a subclass of P4-sparse graphs that strictly contains cographs, and we present a 2-approximation algorithm on general P4-sparse graphs. The complexity of WEIGHTED COLORING on P4- sparse graphs remains open.

     
  38. J. Beauquier and J. Burman. Self-stabilizing Synchronization in Mobile Sensor Networks with Covering. In Distributed Computing in Sensor Systems, 6th IEEE International Conference, DCOSS 2010, volume 6131 of Lecture Notes in Computer Science, pages 362-378, 2010. Springer. [PDF ]
    Abstract:
    Synchronization is widely considered as an important service in distributed systems which may simplify protocol design. \emph{Phase clock} is a general synchronization tool that provides a form of a logical time. This paper presents a \emph{self-stabilizing} (a tolerating state-corrupting transient faults) phase clock algorithm suited to the model of \emph{population protocols with covering}. This model has been proposed recently for sensor networks with a very large, possibly \emph{unknown} number of \emph{anonymous} mobile agents having \emph{small memory}. Agents interact in pairs in an \emph{asynchronous} way subject to the constraints expressed in terms of the \emph{cover times} of agents. The cover time expresses the ``frequency'' of an agent to communicate with all the others and abstracts agent's communication characteristics (e.g. moving speed/patterns, transmitting/receiving capabilities). We show that a phase clock is impossible in the model with only constant-state agents. Hence, we assume an existence of resource-unlimited agent - the base station. The clock size and duration of each phase of the proposed phase clock tool are adjustable by the user. We provide application examples of this tool and demonstrate how it can simplify the design of protocols. In particular, it yields a solution to Group Mutual Exclusion problem.

     
  39. J. Beauquier, J. Burman, J. Clement, and S. Kutten. On Utilizing Speed in Networks of Mobile Agents. In Proceedings of the 29th Annual ACM Symposium on Principles of Distributed Computing, PODC 2010, pages 305-314, 2010. ACM. [PDF ]
    Abstract:
    Population protocols are a model presented recently for networks with a very large, possibly unknown number of mobile agents having small memory. This model has certain advantages over alternative models (such as DTN) for such networks. However, it was shown that the computational power of this model is limited to semi-linear predicates only. Hence, various extensions were suggested. We present a model that enhances the original model of population protocols by introducing a (weak) notion of speed of the agents. This enhancement allows us to design fast converging protocols with only weak requirements (for example, suppose that there are different types of agents, say agents attached to sick animals and to healthy animals, two meeting agents just need to be able to estimate which of them is faster, e.g., using their types, but not to actually know the speeds of their types). Then, using the new model, we study the gathering problem, in which there is an unknown number of anonymous agents that have values they should deliver to a base station (without replications). We develop efficient protocols step by step searching for an optimal solution and adapting to the size of the available memory. The protocols are simple, though their analysis is somewhat involved. We also present a more involved result - a lower bound on the length of the worst execution for any protocol. Our proofs introduce several techniques that may prove useful also in future studies of time in population protocols.

     
  40. J-C. Bermond, D. Mazauric, V. Misra, and P. Nain. A Distributed Scheduling Algorithm for Wireless Networks with Constant Overhead and Arbitrary Binary Interference. In SIGMETRICS 2010, pages 2p, 2010. ACM. [PDF ]
    Abstract:
    This work investigates distributed transmission scheduling in wireless networks. Due to interference constraints, "neighboring links" cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We follow the model described by Bui, Sanghavi, and Srikant in SBS07,SBS09. We suppose that time is slotted and during each slot we have two phases: one control phase which determines what links will be activated and send data during the second phase. We assume random arrivals on each link during each slot, therefore a queue is associated to each link. Since nodes do not have a global knowledge of the network, our aim (like in SBS07,SBS09) is to design for the control phase, a distributed algorithm which determines a set of non interfering links. To be efficient the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead). In this article we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues); and it needs no knowledge. Indeed contrary to other existing algorithms, we do not need to know the values of the queues of the "neighboring links", which are difficult to obtain in a wireless network with interference. We prove that this algorithm gives a maximal set of active links (in each interference set, there is at least one active edge). We also give sufficient conditions for stability under Markovian assumptions. Finally the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.

     
  41. C. Caillouet, F. Huc, N. Nisse, S. Pérennes, and H. Rivano. Stability of a localized and greedy routing algorithm. In 12th Workshop on Advances in Parallel and Distributed Computational Models, pages 8p, 2010. IEEE. [WWW ] [PDF ]
    Abstract:
    In this work, we study the problem of routing packets between undifferentiated sources and sinks in a network modeled by a multigraph. We consider a distributed and local algorithm that transmits packets hop by hop in the network and study its behavior. At each step, a node transmits its queued packets to its neighbors in order to optimize a local gradient. This protocol is greedy since it does not require to record the history about the past actions, and localized since nodes only need information about their neighborhood. A transmission protocol is \emph{stable} if the number of packets in the network does not diverge. To prove the stability, it is sufficient to prove that the number of packets stored in the network remains bounded as soon as the sources inject a flow that another method could have exhausted. The localized and greedy protocol considered has been shown to be stable in some specific cases related to the arrival rate of the packets. We investigate its stability in a more general context and therefore reinforce results from the literature that worked for differentiated suboptimal flows. We show that, to prove the stability of this protocol, it is sufficient to prove the intuitive following conjecture: roughly, if the protocol is stable when all sources inject the maximum number of packets at each turn and no packets are lost, then the protocol is stable whatever be the behavior of the network (i.e., when less packets are injected and some of them may be lost).

     
  42. C. Caillouet, S. Perennes, and H. Rivano. Cross line and column generation for the cut covering problem in wireless networks. In International Symposium on Combinatorial Optimization (ISCO), pages 8p, March 2010.
    Note: To appear. [WWW ] [PDF ]
    Abstract:
    In this paper, we address the problem of bandwidth allocation and routing in wire- less networks. A first model of this problem is known as the Round Weighting Problem (RWP) in which a weight is assigned to the set of rounds, i.e. a set of pairwise non-interfering links. We present a new formulation that forgets about the routing and concentrate on the capacity available on the network cuts. We use the maximum flow/minimum cut theorem known in graph theory to develop the Cut Covering Problem (CCP) and prove that it computes equivalent optimal round weights than RWP. We develop a primal/dual algorithm combining line and column generation to deal with the exponential number of variables and constraints of CCP.

     
  43. S. Caron, F. Giroire, D. Mazauric, J. Monteiro, and S. Pérennes. P2P Storage Systems: Data Life Time for Different Placement Policies. In Maria Gradinariu Potop-Butucaru et Hervé Rivano, editor, 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Belle Dune France, pages 4p, 2010. [WWW ] [PDF ]
    Keywords: P2P storage system, data placement, performance, data durability, Markov chain model.
    Abstract:
    {L}es syst{\`e}mes pair-{\`a}-pair {\`a} grande {\'e}chelle repr{\'e}sentent un moyen fiable pour stocker des donn{\'e}es {\`a} faible co{\^u}t. {A}fin d'assurer la p{\'e}rennit{\'e} des donn{\'e}es des utilisateurs, il est n{\'e}cessaire d'ajouter de la redondance. {A}insi {\`a} partir de s fragments initiaux composant un bloc de donn{\'e}es, s+r fragments sont g{\'e}n{\'e}r{\'e}s et r{\'e}partis entre les pairs du r{\'e}seau. {N}ous {\'e}tudions dans ce papier l'impact des diff{\'e}rentes politiques de placement sur la dur{\'e}e de vie des donn{\'e}es. {P}lus particuli{\`e}rement nous d{\'e}crivons des m{\'e}thodes pour calculer et approximer le temps moyen avant que le syst{\`e}me perde une donn{\'e}e ({M}ean {T}ime to {D}ata {L}oss). {N}ous comparons cette m{\'e}trique pour trois politiques de placement: deux sont locales, distribuant les fragments sur des voisins logiques, et la troisi{\`e}me est globale.

     
  44. S. Caron, F. Giroire, D. Mazauric, J. Monteiro, and S. Pérennes. Data Life Time for Different Placement Policies in P2P Storage Systems. In Proceedings of the 3rd Intl. Conference on Data Management in Grid and P2P Systems (Globe), volume 6265 of Lecture Notes in Computer Science, Bilbao, Spain, pages 75--88, September 2010. [PDF ]
    Keywords: P2P storage system, data placement, performance, data durability, Markov chain model.
    Abstract:
    Peer-to-peer systems are foreseen as an efficient solution to achieve reliable data storage at low cost. To deal with common P2P problems such as peer failures or churn, such systems encode the user data into redundant fragments and distribute them among peers. The way they distribute it, known as placement policy, has a significant impact on their behavior and reliability. In this paper, we study the impact of different placement policies on the data life time. More precisely, we describe methods to compute and approximate the mean time before the system loses data (Mean Time to Data Loss). We compare this metric for three placement policies: two of them local, in which the data is stored in logical peer neighborhoods, and one of them global in which fragments are parted uniformly at random among the different peers.

     
  45. J. Chalopin, V. Chepoi, N. Nisse, and Y. Vaxes. Cop and robber games when the robber can hide and ride. In 8th French Combinatorial Conference, Orsay, June 2010.
    Note: Selection on abstract.
    Abstract:
    In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G = (V , E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as dismantlable graphs. In this talk, we will characterize in a similar way the class CWFR(s, s') of cop-win graphs in the game in which the cop and the robber move at different speeds s' and s, s' ? s. We also establish some connections between cop-win graphs for this game with s'< s and Gromov’s hyperbolicity. In the particular case s' = 1 and s = 2, we prove that the class of cop-win graphs is exactly the well-known class of dually chordal graphs. We show that all classes CWFR(s,1), s ? 3, coincide and we provide a structural characterization of these graphs. We also investigate several dismantling schemes necessary or sufficient for the cop-win graphs (which we call k-winnable and denote by CWW(k)) in the game in which the robber is visible only every k moves for a fixed integer k > 1. We characterize the graphs which are k-winnable for any value of k.

     
  46. N. Cohen, D. Coudert, D. Mazauric, N. Nepomuceno, and N. Nisse. Tradeoffs in routing reconfiguration problems. In Maria Gradinariu Potop-Butucaru et Hervé Rivano, editor, 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), Belle Dune France, pages 4p, 2010. [WWW ] [PDF ]
    Abstract:
    {N}ous {\'e}tudions le probl{\`e}me du reroutage d'un ensemble de connexion dans un r{\'e}seau. {I}l consiste {\`a} passer d'un routage initial (ensemble de chemins reliant des paires de noeuds) {\`a} un autre, en traitant s{\'e}quentiellement chaque connexion. {I}l est parfois indispensable d'en interrompre temporairement certaines au cours du processus de reconfiguration, ce qui nous am{\`e}ne {\`a} {\'e}tudier les compromis possibles entre deux mesures d'efficacit{\'e} : le nombre total de connexions interrompues et le nombre maximum de connexions interrompues simultan{\'e}ment. {N}ous prouvons qu'{\'e}tablir de tels compromis m{\`e}ne {\`a} des probl{\`e}mes {NP}-complets et difficiles {\`a} approcher ({APX}-difficiles voir non {APX}). {N}ous montrons ensuite que de bons compromis sont impossibles en g{\'e}n{\'e}ral. {E}nfin, nous exhibons une classe d'instances de reroutage pour laquelle il est possible de minimiser le nombre de requ{\^e}tes interrompues simultan{\'e}ment sans "trop" augmenter le nombre total de connexions interrompues. {C}es r{\'e}sultats sont obtenus en mod{\'e}lisant ce probl{\`e}me par un jeu {\`a} l'aide d'agents mobiles.

     
  47. N. Cohen, D. Coudert, D. Mazauric, N. Nepomuceno, and N. Nisse. Tradeoffs in process strategy games with application in the WDM reconfiguration problem. In P. Boldi and L. Gargano, editors, Fifth International conference on Fun with Algorithms (FUN 2010), volume 6099 of Lecture Notes in Computer Science, Ischia Island, Italy, pages 121-132, June 2010. Springer.
    Note: Http://hal.inria.fr/inria-00495443. [WWW ] [PDF ]
    Abstract:
    We consider a variant of the graph searching games that is closely related to the routing reconfiguration problem in WDM networks. In the digraph processing game, a team of agents is aiming at clearing, or processing, the vertices of a digraph D. In this game, two important measures arise: 1) the total number of agents used, and 2) the total number of vertices occupied by an agent during the processing of D. Previous works have studied the problem of minimizing each of these parameters independently. In particular, both of these optimization problems are not in APX. In this paper, we study the tradeoff between both these conflicting objectives. More precisely, we prove that there exist some instances for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even in the case of basic network topologies. On the other hand, we exhibit classes of instances where good tradeoffs can be achieved. We also show that minimizing one of these parameters while the other is constrained is not in APX.

     
  48. D. Coudert. Graph searching games for the WDM reconfiguration problem. In 24th European Conference on Operational Research (EURO), Lisbon, Portugal, pages 1p, July 2010.
    Note: Invited talk. [WWW ]
    Abstract:
    The routing reconfiguration problem in WDM networks is to schedule the switching's of a set of lightpaths from one routing to a new predetermined one. This problem is modeled as a digraph processing game, closely related to graph searching games, in which a team of agents is aiming at clearing, or processing, the vertices of a digraph. In this talk, we will survey the main results on digraph processing games, and in particular the complexity and hardness of optimizing tradeoffs between the total number of agents used and the total number of vertices occupied by an agent during the strategy

     
  49. P. Giabbanelli, A. Alimadad, V. Dabbaghian, and D. T. Finegood. Modeling the influence of social networks and environment on energy balance and obesity. In XI International Conference on Obesity (ICO), July 2010.
    Note: Acceptance rate 8.6%.
     
  50. P. Giabbanelli. Impact of complex network properties on routing in backbone networks. In Proceedings of the IEEE Globecom 2010 Workshop on Complex and Communication Networks (CCNet 2010), 2010. [PDF ]
    Abstract:
    The properties found in complex networks (e.g., small-world, scale-free) have been used to characterize the behaviour of several processes such as epidemics or oscillators. We analyze the impact of such properties on the quality of a routing process. Using a Mixed Integer/Linear Program, the routing minimizes the number of ports installed in the network. Ports are network components which we use as a simplification of the capital cost in communication networks. Using data mining techniques, we are able to predict the minimal number of ports of a network with small error rate given the network’s properties and under the assumption of a realistic traffic distribution. We find that the average betweenness and the average path length are good indicators of the number of ports. We then present exploratory work on the dynamic aspects by considering that nodes join the network, which corresponds to the deployment of communication equipment. We consider several approaches to deploy the equipment, and report on the number of ports for each approach. By comparing approaches, having less edges can still yield better performances which motivates investigations on the design. Furthermore, this dynamic case confirms the static one since a tradeoff between the average betweenness and the average path length seems to be a key element in efficient designs.

     
  51. P. Giabbanelli, D. Mazauric, and J-C. Bermond. Average path length of deterministic and stochastics recursive networks. In Proceedings of the 2nd Workshop on Complex Networks (CompleNet), volume 116 of Communications in Computer and Information Science (CCIS), pages 1--12, 2010. Springer-Verlag. [PDF ]
    Abstract:
    The average shortest path distance between all pairs of nodes in real-world networks tends to be small compared to the number of nodes. Providing a closed-form formula for remains challenging in several network models, as shown by recent papers dedicated to this sole topic. For example, Zhang et al. proposed the deterministic model ZRG and studied an upper bound on . In this paper, we use graph-theoretic techniques to establish a closed-form formula for in ZRG. Our proof is of particular interests for other network models relying on similar re- cursive structures, as found in fractal models. We extend our approach to a stochastic version of ZRG in which layers of triangles are added with probability p. We find a first-order phase transition at the critical probability pc = 0.5, from which the expected number of nodes becomes infinite whereas expected distances remain finite. We show that if tri- angles are added independently instead of being constrained in a layer, the first-order phase transition holds for the very same critical probabil- ity. Thus, we provide an insight showing that models can be equivalent, regardless of whether edges are added with grouping constraints. Our detailed computations also provide thorough practical cases for readers unfamiliar with graph-theoretic and probabilistic techniques.

     
  52. P. Giabbanelli, D. Mazauric, and S. Pérennes. Computing the average path length and a label-based routing in a small-world graph. In 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'10), Belle Dune France, pages 4p, 2010. [WWW ] [PDF ]
    Keywords: Recursive graph, Labeling scheme, Decentralized routing.
    Abstract:
    {W}e study two characteristics of a small-world graph proposed by {Z}hang et al. to model complex networks. {O}ur study relies on the recursive structure of the graph. {F}irstly, we use it to design a labelling scheme in order to create an implicit routing (i.e., a routing scheme based on the label of vertices). {S}econdly, proving the average distance in this graph was arduous, thus {Z}hang et al. chose to study the diameter: we establish a closed-form formula of the average distance, proved using the recursive structure. {T}hus, we characterize that the graph is small-world and not ultra small-world as was still possible. {O}ur proof is of particular interest for other graphs based on similar recursive structures.

     
  53. F. Giroire, D. Mazauric, J. Moulierac, and B. Onfroy. Minimizing Routing Energy Consumption: from Theoretical to Practical Results. In IEEE/ACM International Conference on Green Computing and Communications (GreenCom'10), Hangzhou, China, pages 8, 2010. [PDF ]
    Abstract:
    Several studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. Hence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces, line cards, base chassis,... The goal thus is to find a routing that minimizes the (weighted) number of active network elements used when routing. In this paper, we consider a simplified architecture where a connection between two routers is represented as a link joining two network interfaces. When a connection is not used, both network interfaces can be turned off. Therefore, in order to reduce power consumption, the goal is to find the routing that minimizes the number of used links while satisfying all the demands. We first define formally the problem and we model it as an integer linear program. Then, we prove that this problem is not in APX, that is there is no polynomial-time constant-factor approximation algorithm. We propose a heuristic algorithm for this problem and we also prove some negative results about basic greedy and probabilistic algorithms. Thus we present a study on specific topologies, such as trees, grids and complete graphs, that provide bounds and results useful for real topologies. We then exhibit the gain in terms of number of network interfaces (leading to a global reduction of approximately 33 MWh for a medium-sized backbone network) for a set of existing network topologies: we see that for almost all topologies more than one third of the network interfaces can be spared for usual ranges of operation. Finally, we discuss the impact of energy efficient routing on the stretch factor and on fault tolerance.

     
  54. F. Giroire, J. Monteiro, and S. Pérennes. Peer-to-Peer Storage Systems: a Practical Guideline to be Lazy. In Proceedings of the IEEE Global Communications Conference (GLOBECOM), Miami, EUA, pages 1-6, 12 2010. [WWW ] [PDF ]
    Abstract:
    Distributed and peer-to-peer storage systems are foreseen as an alternative to the traditional data centers and in-house backup solutions. In the past few years many peer-to- peer storage systems have been proposed. Most of them rely on the use of erasure codes to introduce redundancy to the data. This kind of system depends on many parameters that need to be well tuned, such as the factor of redundancy, the frequency of data repair and the size of a data block. In this paper we give closed-form mathematical expressions that estimate the system average behavior. These expressions are derived from a Markov chain. Our contribution is a guideline to system designers and administrators to choose the best set of parameters. That is, how to tune the system parameters to obtain a desired level of reliability under a given constraint of bandwidth consumption. We confirm that a lazy repair strategy can be employed to amortize the repairing cost. Moreover, we propose a formula to calculate the optimal threshold value that minimizes the bandwidth consumption. Finally, we additionally discuss the impact of different system characteristics on the performance metrics, such as the number of peers, the amount of stored data, and the disk failure rate. To the best of our knowledge this is the first work to give close-form formulas to estimate the bandwidth consumption for a lazy repair, and the loss rate taking into account the repair time.

     
  55. N. Hanusse, D. Ilcinkas, A. Kosowski, and N. Nisse. Locating a target with an agent guided by unreliable local advice. In 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC'10), volume XXXX, pages 10p, 2010. ACM.
    Note: To appear. [PDF ]
    Abstract:
    {W}e study the problem of finding a destination node $t$ by a mobile agent in an unreliable network having the structure of an unweighted graph, in a model first proposed by {H}anusse {\it et al.}~\cite{{HKK}00,{HKKK}08}. {E}ach node of the network is able to give advice concerning the next node to visit so as to go closer to the target $t$. {U}nfortunately, exactly $k$ of the nodes, called \emph{liars}, give advice which is incorrect. {I}t is known that for an $n$-node graph ${G}$ of maximum degree $\{D}elta \geq 3$, reaching a target at a distance of $d$ from the initial location may require an expected time of $2^{\{O}mega(\min\{d,k\})}$, for any $d,k={O}(\log n)$, even when ${G}$ is a tree. {T}his paper focuses on strategies which efficiently solve the search problem in scenarios in which, at each node, the agent may only choose between following the local advice, or randomly selecting an incident edge. {T}he strategy which we put forward, called \algo{{R}/{A}}, makes use of a timer (step counter) to alternate between phases of ignoring advice (\algo{{R}}) and following advice (\algo{{A}}) for a certain number of steps. {N}o knowledge of parameters $n$, $d$, or $k$ is required, and the agent need not know by which edge it entered the node of its current location. {T}he performance of this strategy is studied for two classes of regular graphs with extremal values of expansion, namely, for rings and for random $\maxdeg$-regular graphs (an important class of expanders). {F}or the ring, \algo{{R}/{A}} is shown to achieve an expected searching time of $2d+k^{\{T}heta(1)}$ for a worst-case distribution of liars, which is polynomial in both $d$ and $k$. {F}or random $\maxdeg$-regular graphs, the expected searching time of the \algo{{R}/{A}} strategy is ${O}(k3 \log3 n)$ a.a.s. {T}he polylogarithmic factor with respect to $n$ cannot be dropped from this bound; in fact, we show that a lower time bound of $\{O}mega (\log n)$ steps holds for all $d,k=\{O}mega(\log\log n)$ in random $\maxdeg$-regular graphs a.a.s.\ and applies even to strategies which make use of some knowledge of the environment. {F}inally, we study oblivious strategies which do not use any memory (in particular, with no timer). {S}uch strategies are essentially a form of a random walk, possibly biased by local advice. {W}e show that such biased random walks sometimes achieve drastically worse performance than the \algo{{R}/{A}} strategy. {I}n particular, on the ring, no biased random walk can have a searching time which is polynomial in $d$ and $k$

     
  56. N. Hanusse, D. Ilcinkas, A. Kosowski, and N. Nisse. Comment battre la marche aléatoire en comptant ?. In 12ème Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'10), pages 4p, 2010. [WWW ] [PDF ]
    Abstract:
    Nous \'etudions le probl\`eme consistant \`a trouver une destination t dans un r\'eseau, non fiable, gr\^ace \`a un agent mobile. Chaque noeud du r\'eseau peut donner un conseil quant au prochain sommet \`a visiter pour se rapprocher de t. Malheureusement, k noeuds, appel\'es menteurs, donnent de mauvais conseils. Il est connu que pour un graphe G de n sommets et de degr\'e maximum Delta >= 3, atteindre une cible \`a distance d de la position initiale peut demander un temps moyen de 2^{Omega(min{d,k})}, pour tout d,k=O(log n), même lorsque G est un arbre. Ce papier \'etudie une strat\'egie, appel\'ee R/A, utilisant un compteur (d'\'etapes) pour alterner entre les phases al\'eatoires (R) où l'agent choisit al\'eatoirement une arête incidente, et celles (A) où l'agent suit le conseil local. Aucune connaissance des param\`etres n, d, ou k n'est requise, et l'agent n'a pas besoin de se rappeler par quel lien il est entr\'e dans le sommet qu'il occupe. Nous \'etudions les performances de cette strat\'egie pour deux classes de graphes, extrêmes pour ce qui est de l'expansion: les anneaux et les graphes r\'eguliers al\'eatoires (une importante classe d' expanders). Pour l'anneau, l'algorithme R/A requiert un temps moyen de 2d+k^{Theta(1)} (polynomial en d et k) pour une distribution des menteurs la plus d\'efavorable. A l'oppos\'e, nous montrons que dans un anneau, une marche al\'eatoire biais\'ee requiert un temps moyen exponentiel en d et k. Pour les graphes al\'eatoires r\'eguliers, le temps de recherche moyen de l'algorithme R/A est O(k3 log3 n) a.a.s.\ Le terme polylogarithmique de cette borne ne peut pas être am\'elior\'e, puisque nous montrons une borne inf\'erieure de Omega(log n) pour d,k=Omega(log log n) dans les graphes al\'eatoires r\'eguliers a.a.s. qui s'applique même lorsque l'agent a le sens de l'orientation.

     
  57. F. Havet and L. Sampaio. On the Grundy number of a graph. In Proceedings of the International Symposium on Parameterized and Exact Computation(IPEC), number 6478 of Lecture Notes on Computer science, pages 170-179, December 2010. [PDF ]
    Abstract:
    The Grundy number of a graph $G$, denoted by $\Gamma (G)$, is the largest $k$ such that $G$ has a greedy $k$-colouring, that is a colouring with $k$ colours obtained by applying the greedy algorithm according to some ordering of the vertices of $G$. Trivially $\Gamma(G)\leq \Delta(G)+1$. In this paper, we show that deciding if $\Gamma(G)\leq \Delta(G)$ is NP-complete. We then show that deciding if $\Gamma(G)\geq |V(G)|-k$ is fixed parameter tractable with respect to the parameter $k$.

     
  58. L. Hogie, D. Papadimitriou, I. Tahiri, and F. Majorczyk. Simulating routing schemes on large-scale topologies. In 24th ACM/IEEE/SCS Workshop on Principles of Advanced and Distributed Simulation (PADS), Atlanta, pages 8p, May 2010. [WWW ] [PDF ]
    Abstract:
    The expansion of the Internet routing system results in a number of research challenges, in particular, the Border Gateway Protocol (BGP) starts to show its limits a.o. in terms of the number of routing table entries it can dynamically process and control. Dynamic routing protocols showing better scaling properties are thus under investigation. However, because deploying under-development routing protocols on the Internet is not practicable at a large-scale (due to the size of the Internet topology), simulation is an unavoidable step to validate the properties of a newly proposed routing scheme. Unfortunately, the simulation of inter-domain routing protocols over large networks (order of tens of thousands of nodes) poses real challenges due to the limited memory and computational power that computers impose. This paper presents the Dynamic Routing Model simulator \drmsim which addresses the specific problem of large-scale simulations of (inter-domain) routing models on large networks. The motivation for developing a new simulator lies in the limitation of existing simulation tools in terms of the number of nodes they can handle and in the models they propose.

     
  59. B. Jaumard, N.N. Bhuiyan, S. Sebbah, F. Huc, and D. Coudert. A New Framework for Efficient Shared Segment Protection Scheme for WDM Networks. In IEEE High Performance Switching and Routing (HPSR), Richardson, TX, USA, pages 8p, June 2010. IEEE. [WWW ] [PDF ]
    Abstract:
    This work introduces a new shared segment protection scheme that ensures both node and link protection in an efficient manner in terms of cost and bandwidth, while taking full advantage of the optical hop endpoints of the primary logical hops (induced by the routing) without adding extra ones for protection. As opposed to the link or path protection schemes, the segment protection scheme has been less studied although it offers an interesting compromise between those two protection schemes, attempting to encompass all their advantages. We investigate two different Shared Segment Protection (SSP) schemes: Basic Shared Segment Protection (BSSP) and Shared Segment Protection with segment Overlap (SSPO), and propose a design of 100\(null)ingle segment protections. In SSPO, we study the extra protection capabilities, node failure and dual link failure survivability, offered by the single 100\ingle segment protection. For both BSSP and SSPO schemes, we propose two novel efficient ILP formulations, based on a column generation mathematical modeling. While (SSPO) offers the advantage over (BSSP) to ensure both node and link protection, it is not necessarily much more costly. Indeed, depending on the network topology and the traffic instances, it can be shown that none of the two SSP schemes dominates the other one. Therefore, the SSPO protection scheme should be favored as it offers more protection, i.e., it adds the node protection to the link protection at the expense of a minor additional cost.

     
  60. B. Jaumard, N.N. Bhuiyan, S. Sebbah, F. Huc, and D. Coudert. A New Framework for Efficient Shared Segment Protection Scheme for WDM Networks. In 10th INFORMS Telecommunications Conference, Montréal, Canada, pages 2p, May 2010. Informs. [WWW ]
    Abstract:
    This work introduces a new shared segment protection scheme that ensures both node and link protection in an efficient manner in terms of cost and bandwidth, while taking full advantage of the optical hop endpoints of the primary logical hops (induced by the routing) without adding extra ones for protection. As opposed to the link or path protection schemes, the segment protection scheme has been less studied although it offers an interesting compromise between those two protection schemes, attempting to encompass all their advantages. We investigate two different Shared Segment Protection (SSP) schemes: Basic Shared Segment Protection (BSSP) and Shared Segment Protection with segment Overlap (SSPO), and propose a design of 100\(null)ingle segment protections. In SSPO, we study the extra protection capabilities, node failure and dual link failure survivability, offered by the single 100\ingle segment protection. For both BSSP and SSPO schemes, we propose two novel efficient ILP formulations, based on a column generation mathematical modeling. While (SSPO) offers the advantage over (BSSP) to ensure both node and link protection, it is not necessarily much more costly. Indeed, depending on the network topology and the traffic instances, it can be shown that none of the two SSP schemes dominates the other one. Therefore, the SSPO protection scheme should be favored as it offers more protection, i.e., it adds the node protection to the link protection at the expense of a minor additional cost.

     
  61. G. B. Mertzios, I. Sau, and S. Zaks. The Recognition of Tolerance and Bounded Tolerance Graphs. In Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS), volume 5 of LIPIcs, pages 585-596, 2010. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. [WWW ] [PDF ]
    Abstract:
    Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure and its numerous applications. Several efficient algorithms for optimization problems that are NP-hard on general graphs have been designed for tolerance graphs. In spite of this, the recognition of tolerance graphs --~namely, the problem of deciding whether a given graph is a tolerance graph~-- as well as the recognition of their main subclass of bounded tolerance graphs, have been the most fundamental open problems on this class of graphs (cf.~the book on tolerance graphs~\cite{GolTol04}) since their introduction in 1982~\cite{GoMo82}. In this article we prove that both recognition problems are NP-complete, even in the case where the input graph is a trapezoid graph. The presented results are surprising because, on the one hand, most subclasses of perfect graphs admit polynomial recognition algorithms and, on the other hand, bounded tolerance graphs were believed to be efficiently recognizable as they are a natural special case of trapezoid graphs (which can be recognized in polynomial time) and share a very similar structure with them. For our reduction we extend the notion of an \emph{acyclic orientation} of permutation and trapezoid graphs. Our main tool is a new algorithm that uses \emph{vertex splitting} to transform a given trapezoid graph into a permutation graph, while preserving this new acyclic orientation property. This method of vertex splitting is of independent interest; very recently, it has been proved a powerful tool also in the design of efficient recognition algorithms for other classes of graphs~\cite{MC-Trapezoid}.

     
  62. J. Monteiro and S. Pérennes. Systèmes de stockage P2P : un guide pratique. In 11es Journées Doctorales en Informatique et Réseaux (JDIR 2010), Sophia Antipolis France, pages 15--20, 2010. [WWW ]
    Abstract:
    {L}es syst{\`e}mes pair-{\`a}-pair {\`a} grande {\'e}chelle ont {\'e}t{\'e} propos{\'e} comme un moyen fiable d'assurer un stockage de donn{\'e}e {\`a} faible c{\^o}ut. {P}our assurer la p{\'e}rennit{\'e} des donn{\'e}es, ces syst{\`e}mes codent les fichiers des utilisateurs en un ensemble de fragments redondants qui sont répartis entre les pairs. {N}ous étudions dans ce rapport l'impact des différents param{\`e}tres de configuration du syst{\`e}me, comme par exemple, le facteur de redondance et la fr{\'e}quence de r{\'e}paration des donn{\'e}es. {P}lus particulièrement, dans ce papier nous derivons des formules approch{\'e}es {\`a} partir d'une chaine de {M}arkov. {C}es formules nous donnent une estimation de la bande passante n{\'e}cessaire pour maintenir la redondance et de la probabilit{\'e} de perdre un bloc de donn{\'e}e.

     
  63. N. Nisse. Graph Searching and Graph Decompositions. In 24th European Conference on Operational Research (EURO), Lisbon, Portugal, pages 1p, July 2010.
    Note: Invited talk. [WWW ]
    Abstract:
    Graph searching is a game where a team of mobile agents must catch a fugitive hidden in a network (modelled by a graph). Equivalently, graph search- ing may be defined in terms of clearing a contaminated network. Besides of its practical interests, graph searching has been widely studied for its relationship with important graph parameters, in particular pathwidth and treewidth. Many versions of graph searching problems have been considered. They all look for a strategy that allows to catch the fugitive using the minimum number of agents. Variants of graph searching differ on various parameters. We first give a brief survey of the numerous research directions in this field. Then, we focus on the relationship between search games and graph decompositions (path- and tree- decompositions). Namely, search games provide a very interesting algorithmic interpretation of the pathwidth and the treewidth of graphs. we explain the equivalence between theses games and graph decompositions through an impor- tant property of these two search games: the monotonicity. This point of view allowed us to obtain new duality results generalyzing those obtained by Robert- son and Seymour in the Graph Minors Theory

     
  64. J. Ribault, O. Dalle, D. Conan, and S. Leriche. OSIF: A Framework To Instrument, Validate, and Analyze Simulations. In In Proc. of 3rd Intl. ICST Conference on Simulation Tools and Techniques (SIMUTools'2010), Torremolinos, Spain, 15-19 March 2010. [WWW ]
    Abstract:
    {I}n most existing simulators, the outputs of a simulation run consist either in a simulat ion report generated at the end of the run and summarizing the statistics of interest, or in a (set of) trace file(s) containing raw data samples produced and saved regularly during the run, for later post-processing. {I}n this paper, we address issues related to the management of these data and their on-line processing, such as: (i)~the instrumentation code is mixed in the modeling code; (ii)~the amount of data to be stored may be enormous, and often, a significant part of these data are useless while their collect may consume a significant amount of the computing resources; and (iii)~it is difficult to have confidence in the treatment applied to the data and then make comparisons between studies since each user (model developer) builds its own ad-hoc instrumentation and data processing. {I}n this paper, we propose {OSIF}, a new component-based instrumentation framework designed to solve the above mentioned issues. {OSIF} is based on several mature software engineering techniques and frameworks, such as {COSMOS}, {F}ractal and its {ADL}, and {AOP}.

     
  65. P. Uribe, J-C. Maureira Bravo, and O. Dalle. Extending INET Framework for Directional and Asymmetrical Wireless Communications. In Proc. of the 2010 Intl. ICST Workshop on OMNeT++ (OMNeT++ 2010), Torremolinos, Spain, pages 1--8, 15-19 March 2010.
     
  66. J. Bang-Jensen, F. Havet, and N. Trotignon. Finding an induced subdivision of a digraph. Research Report 7430, INRIA, 10 2010. [WWW ] [PDF ]
    Abstract:
    We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) $G$, does it contain an induced subdivision of a prescribed digraph $D$? The complexity of this problem depends on $D$ and on whether $H$ must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial instances as well as several NP-completeness proofs.

     
  67. L. Barrière, P. Flocchini, F. V. Fomin, P. Fraigniaud, N. Nisse, N. Santoro, and D. Thilikos. Connected Graph Searching. Research Report 7363, INRIA, August 2010. [WWW ] [PDF ]
    Abstract:
    In graph searching game the opponents are a set of searchers and a fugitive in a graph. The searchers try to capture the fugitive by applying some sequence moves that include placement, removal, or sliding of a searcher along an edge. The fugitive tries to avoid capture by moving along unguarded paths. The search number of a graph is the minimum number of searchers required to guarantee the capture of the fugitive. In this paper, we initiate the study of this game under the natural restriction of connectivity where we demand that in each step of the search the locations of the graph that are clean (i.e. non-accessible to the fugitive) remain connected. We give evidence that many of the standard mathematical tools used so far in the classic graph searching fail under the connectivity requirement. We also settle the question on ``the price of connectivity'' that is how many searchers more are required for searching a graph when the connectivity demand is imposed. We make estimations of the price of connectivity on general graphs and we provide tight bounds for the case of trees. In particular, for an $n$-vertex graph the ratio between the connected searching number and the non-connected one is $O(\log n)$ while for trees this ratio is always at most 2. We also conjecture that this constant-ratio upper bound for trees holds also for all graphs. Our combinatorial results imply a complete characterization of connected graph searching on trees. It is based on a forbidden-graph characterization of the connected search number. We prove that the connected search game is monotone for trees, i.e. restricting search strategies to only those where the clean territories increase monotonically does not require more searchers. A consequence of our results is that the connected search number can be computed in polynomial time on trees, moreover, we show how to make this algorithm distributed. Finally, we reveal connections of this parameter to other invariants on trees such as the Horton-Stralher number.

     
  68. F. Becker, M. Matamala, N. Nisse, I. Rapaport, K. Suchan, and I. Todinca. Adding a referee to an interconnection network: What can(not) be computed in one round. Research Report arXiv:1009.4447, arXiv, September 2010. [WWW ] [PDF ]
    Abstract:
    {In this paper we ask which properties of a distributed network can be computed from a few amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model and it is close to the simultaneous messages (communication complexity) model defined by Babai, Kimmel and Lokam. More precisely, each of these n nodes -which only knows its own ID and the IDs of its neighbors is allowed to send a message of O(log n) bits to some central entity, called the referee. Is it possible for the referee to decide some basic structural properties of the network topology G? We show that simple questions like, "does G contain a square?", "does G contain a triangle?" or "Is the diameter of G at most 3?” cannot be solved in general. On the other hand, the referee can decode the messages in order to have full knowledge of $G$ when $G$ belongs to many graph classes such as planar graphs, bounded treewidth graphs and, more generally, bounded degeneracy graphs. We leave open questions related to the connectivity of arbitrary graphs. }, OPTx-editorial-board={yes}, OPTx-proceedings={no}, OPTx-international-audience={yes}, sorte = "Rapports",

     
  69. J-C. Bermond, F. Havet, F. Huc, and C. Linhares Sales. Improper colouring of weighted grid and hexagonal graphs. Research Report RR-7250, INRIA, April 2010. [WWW ] [PDF ]
    Keywords: Improper colouring, Weighted colouring, Approximation algorithms.
    Abstract:
    {W}e study a weighted improper colouring problem on graph, and in particular of triangular and hexagonal grid graphs. {T}his problem is motivated by a frequency allocation problem. {W}e propose approximation algorithms to compute such colouring.

     
  70. V. Campos, A. Gyárfás, F. Havet, C. Linhares Sales, and F. Maffray. New bounds on the Grundy number of products of graphs. Research Report 7243, INRIA, April 2010. [WWW ] [PDF ]
    Abstract:
    The Grundy number of a graph $G$ is the largest $k$ such that $G$ has a greedy $k$-colouring, that is, a colouring with $k$ colours obtained by applying the greedy algorithm according to some ordering of the vertices of $G$. In this paper, we give new bounds on the Grundy number of the product of two graphs.

     
  71. S. Caron, F. Giroire, D. Mazauric, J. Monteiro, and S. Pérennes. P2P Storage Systems: Data Life Time for Different Placement Policies. Research Report RR-7209, INRIA, February 2010. [WWW ] [PDF ]
    Keywords: P2P storage system, data placement, data life time, mean time to data loss, performance evaluation, Markov chains.
    Abstract:
    {P}eer-to-peer systems are foreseen as an efficient solution to achieve reliable data storage at low cost. {T}o deal with common {P}2{P} problems such as peer failures or churn, such systems encode the user data into redundant fragments and distribute them among peers. {T}he way they distribute it, known as placement policy, has a significant impact on their behavior and reliability. {I}n this report, after a brief state-of-the-art of the technology used in {P}2{P} storage systems, we compare three different placement policies: two of them local, in which the data is stored in logical peer neighborhoods, and on of them global in which fragments are parted at random among the different peers. {F}or each policy, we give either {M}arkov {C}hain {M}odels to efficiently compute the {M}ean {T}ime {T}o {D}ata {L}oss (which is closely related to the probability to lose data) or approximations of this quantity under certain assumptions. {W}e also attempt to give lower bounds on {P}2{P} storage systems introducing the {BIG} system, in which we consider information globally. {W}e propose various ways to compute a bound on the probability to lose data, in relation with parameters such as the peer failure rate of the peer bandwidth.

     
  72. J. Chalopin, V. Chepoi, N. Nisse, and Y. Vaxès. Cop and robber games when the robber can hide and ride.. Technical report INRIA-RR7178, INRIA, January 2010. [WWW ] [PDF ]
    Abstract:
    In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G=(V,E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as graphs admitting a dismantling scheme. In this paper, we characterize in a similar way the cop-win graphs in the game in which the cop and the robber move at different speeds s' and s, s'<= s. We also investigate several dismantling schemes necessary or sufficient for the cop-win graphs in the game in which the robber is visible only every k moves for a fixed integer k>1. We characterize the graphs which are cop-win for any value of k.

     
  73. N. Cohen and F. Havet. Linear and 2-frugal choosability of graphs of small maximum average degree. Research Report RR-7213, INRIA, 02 2010. [WWW ]
    Abstract:
    {A} proper vertex colouring of a graph ${G}$ is {\it 2-frugal} (resp. {\it linear}) if the graph induced by the vertices of any two colour classes is of maximum degree 2 (resp. is a forest of paths). {A} graph ${G}$ is {\it 2-frugally} (resp. {\it linearly}) {\it ${L}$-colourable} if for a given list assignment ${L}:{V}({G})\mapsto 2^{\mathbb {N}}$, there exists a 2-frugal (resp. linear) colouring $c$ of ${G}$ such that $c(v)\in {L}(v)$ for all $v\in {V}({G})$. {I}f ${G}$ is 2-frugally (resp. linearly) ${L}$-list colourable for any list assignment such that $|{L}(v)|\ge k$ for all $v\in{V}({G})$, then ${G}$ is {\it 2-frugally} (resp. {\it linearly}) {\it $k$-choosable}. {I}n this paper, we improve some bounds on the 2-frugal choosability and linear choosability of graphs with small maximum average degree.

     
  74. F. Giroire, D. Mazauric, J. Moulierac, and B. Onfroy. Minimizing Routing Energy Consumption: from Theoretical to Practical Results. Research Report inria-00464318, May 2010. [WWW ] [PDF ]
    Keywords: power consumption, energy-efficient routing, graphs, linear programming.
    Abstract:
    {S}everal studies exhibit that the traffic load of the routers only has a small influence on their energy consumption. {H}ence, the power consumption in networks is strongly related to the number of active network elements, such as interfaces, line cards, base chassis,... {T}he goal thus is to find a routing that minimizes the (weighted) number of active network elements used when routing. {I}n this paper, we consider a simplified architecture where a connection between two routers is represented as a link joining two network equipments. {W}hen a connection is not used, both network equipments can be turned off. {T}herefore, in order to reduce power consumption, the goal is to find the routing that minimizes the number of used links while satisfying all the demands. {W}e first present a study on specific topologies, such as trees and complete graphs, that provide bounds and results useful for real topologies. {W}e model the problem as a linear program and propose a heuristic to solve large instances. {W}e exhibit the gain in terms of number of network equipments (leading to a global reduction of the power consumption) for a set of network topologies: we see that for almost all topologies more than one third of the network equipments can be spared for usual ranges of operation. {F}inally, we discuss the impact of energy efficient routing on the stretch factor and on fault tolerance.

     
  75. N. Hanusse, D. Ilcinkas, A. Kosowski, and N. Nisse. How to beat the random walk when you have a clock?. Research Report RR-7210, INRIA, February 2010. [WWW ] [PDF ]
    Abstract:
    {W}e study the problem of finding a destination node $t$ by a mobile agent in an unreliable network having the structure of an unweighted graph, in a model first proposed by {H}anusse {\it et al.}~\cite{{HKK}00,{HKKK}08}. {E}ach node of the network is able to give advice concerning the next node to visit so as to go closer to the target $t$. {U}nfortunately, exactly $k$ of the nodes, called \emph{liars}, give advice which is incorrect. {I}t is known that for an $n$-node graph ${G}$ of maximum degree $\{D}elta \geq 3$, reaching a target at a distance of $d$ from the initial location may require an expected time of $2^{\{O}mega(\min\{d,k\})}$, for any $d,k={O}(\log n)$, even when ${G}$ is a tree. {T}his paper focuses on strategies which efficiently solve the search problem in scenarios in which, at each node, the agent may only choose between following the local advice, or randomly selecting an incident edge. {T}he strategy which we put forward, called \algo{{R}/{A}}, makes use of a timer (step counter) to alternate between phases of ignoring advice (\algo{{R}}) and following advice (\algo{{A}}) for a certain number of steps. {N}o knowledge of parameters $n$, $d$, or $k$ is required, and the agent need not know by which edge it entered the node of its current location. {T}he performance of this strategy is studied for two classes of regular graphs with extremal values of expansion, namely, for rings and for random $\maxdeg$-regular graphs (an important class of expanders). {F}or the ring, \algo{{R}/{A}} is shown to achieve an expected searching time of $2d+k^{\{T}heta(1)}$ for a worst-case distribution of liars, which is polynomial in both $d$ and $k$. {F}or random $\maxdeg$-regular graphs, the expected searching time of the \algo{{R}/{A}} strategy is ${O}(k3 \log3 n)$ a.a.s. {T}he polylogarithmic factor with respect to $n$ cannot be dropped from this bound; in fact, we show that a lower time bound of $\{O}mega (\log n)$ steps holds for all $d,k=\{O}mega(\log\log n)$ in random $\maxdeg$-regular graphs a.a.s.\ and applies even to strategies which make use of some knowledge of the environment. {F}inally, we study oblivious strategies which do not use any memory (in particular, with no timer). {S}uch strategies are essentially a form of a random walk, possibly biased by local advice. {W}e show that such biased random walks sometimes achieve drastically worse performance than the \algo{{R}/{A}} strategy. {I}n particular, on the ring, no biased random walk can have a searching time which is polynomial in $d$ and $k$

     
  76. F. Havet, C. Linhares Sales, and L. Sampaio. b-coloring of tight graphs. Research Report 7241, INRIA, March 2010. [WWW ] [PDF ]
    Abstract:
    A coloring $c$ of a graph $G = (V, E)$ is a \emph{$b$-coloring} if in every color class there is a vertex whose neighborhood intersects every other color classes. The \emph{$b$-chromatic number} of $G$, denoted $\chi_b(G)$, is the greatest integer $k$ such that $G$ admits a $b$-coloring with $k$ colors. A graph $G$ is \emph{tight} if it has exactly $m(G)$ vertices of degree $m(G) - 1$, where $m(G)$ is the largest integer $m$ such that $G$ has at least $m$ vertices of degree at least $m-1$. Determining the $b$-chromatic number of a tight graph $G$ is NP-hard even for a connected bipartite graph \cite{KTV02}. In this paper we show that it is also NP-hard for a tight chordal graph. We also show that the $b$-chromatic number of a split graph can be computed is polynomial. Then we define the $b$-closure and the partial $b$-closure of a tight graph, and use these concepts to give a characterization of tight graphs whose $b$-chromatic number is equal to $m(G)$. This characterization is used to develop polynomial time algorithms for deciding whether $\chi_b(G) = m(G)$, for tight graphs that are complement of bipartite graphs, $P_4$-sparse and block graphs. We generalize the concept of pivoted tree introduced by Irving and Manlove \cite{IM99} and show its relation with the $b$-chromatic number of tight graphs. Finally, we give an alternative formulation of the Erd\"os-Faber-Lov\'asz conjecture in terms of $b$-colorings of tight graphs.

     
  77. P. Uribe, J-C. Maureira Bravo, and O. Dalle. Extending INET Framework for Directional and Asymmetrical Wireless Communications. Research Report RR-7120, INRIA, 03 2010. [WWW ] [PDF ]
    Keywords: OMNeT++, INET Framework, Directional Radios, Asymmetrical communication.
    Abstract:
    {T}his paper reports our work on extending the {O}mnet {INET} {F}ramework with a directional radio model, putting a special emphasis on the implementation of asymmetrical communications. {W}e first analyze the original {INET} radio model, focusing on its design and components. {T}hen we discuss the modifications that have been done to support directional communications. {O}ur preliminary results show that the new model is flexible enough to allow the user to provide any antenna pattern shape, with only an additional reasonable computational cost.

     
  78. N. Cohen. Several Graph Problems and their LP formulation, 2010. [PDF ]
    Abstract:
    In this document are given Linear Program formulations of several graph problems involving acyclicity constraints without the use of constraint generations.

     
2009
  1. O. Dalle, J. R. Heath, and G. A. Wayne, editors. Mobile Networks and Applications (MONET) : Special Issue on Development Tools and Techniques for Mobile Telecommunications. Springer Netherlands, December 2009.
    Note: Online publication. [WWW ]
     
  2. O. Dalle, L.-F. Perrone, G. Stea, and G. A. Wainer, editors. 2nd International Conference on Simulation Tools and Techniques (SIMUTools 2009), Rome, Italy, March 2009.
     
  3. C. Gomes. Radio Mesh Networks and the Round Weighting Problem. PhD thesis, Université de Nice-Sophia Antipolis (UNS), December 1st 2009. [WWW ] [PDF ]
    Keywords: Radio Mesh Networks, Multi-objective Optimization, Bandwidth allocation problem, Flow problem, Coloring Problem, Fairness, Column Generation method, Convex Problems.
    Abstract:
    In this thesis, we address the joint routing and slot assignment problem between the routers and the gateways in radio mesh access networks. We model the problem as a Round Weighting Problem (RWP) in which the objective is to minimize the overall period of slot activations providing enough capacity to satisfy the bandwidth requirements of the routers. Solving the full problem means generating an exponential set of simultaneous transmission rounds which is intractable even for small networks. To cope with this issue, we implement a mathematical multi-objective model to solve the problem using a column generation method. We observe that the bottleneck is usually located in a limited region around a gateway. We propose a method to obtain lower bounds (considering only a limited probable bottleneck region) and upper bounds for general graphs. Our methods are applied to grid graphs providing closed formulae for the case of uniform demands, and also optimal routing strategies considering non-uniform demands. Motivated by the results of the existence of a limited (bottleneck) region capable of representing the whole network, we consider a variant of the RWP dealing also with bandwidth allocation, but considering SINR conditions in a CDMA network. We give sufficient conditions for the whole network to be reduced to a single-hop around the gateway. It is due to the fact that the problem is convex under some conditions that are often met.

     
  4. C. Molle. Optimisation de la capacité des réseaux radio maillés. PhD thesis, Ecole doctorale STIC, Université de Nice-Sophia Antipolis, October 2009. [WWW ] [PDF ]
    Keywords: Optimisation, programmation linéaire, réseaux radio maillés, capacité, génération de colonnes.
    Abstract:
    Dans cette th\`ese, nous nous int\'eressons aux probl\'ematiques d'optimisation de la capacit\'e des r\'eseaux radio maill\'es. Cette architecture de r\'eseau d'acc\`es est particuli\`erement pertinente en milieu urbain ou en situation op\'erationnelle militaire. Nous d\'efinissons la capacit\'e d'un r\'eseau comme la quantit\'e de flot que peut r\'epartir \'equitablement une topologie aux utilisateurs qu'elle sert. Afin d'obtenir des bornes th\'eoriques sur les performances du r\'eseau, nous d\'eveloppons des mod\`eles d'optimisation int\'egrant les caract\'eristiques inter-couche des communications radio. Nous \'etudions plus pr\'ecis\'ement le probl\`eme joint du routage et de l'ordonnancement. Nous d\'eveloppons, pour la relaxation lin\'eaire de ce probl\`eme, une m\'ethode de r\'esolution efficace utilisant la g\'en\'eration de colonnes. Nous d\'erivons ensuite une formulation qui \'elimine le routage pour se concentrer sur la capacit\'e de transport disponible sur les coupes du r\'eseau. L'\ 'equivalence des solutions optimales est d\'emontr\'ee, et le processus de r\'esolution est adapt\'e en une g\'en\'eration crois\'ee de lignes et de colonnes. Ces \'etudes mettent en \'evidence la pr\'esence d'une zone de contention autour de chaque point d'acc\`es qui contraint la capacit\'e du r\'eseau. Ces r\'esultats permettent une \'etude quantitative des effets du trafic d'acquittement sur la capacit\'e. Nous pr\'esentons enfin une \'etude de la stabilit\'e d'un protocole routant du trafic inject\'e de mani\`ere arbitraire au cours du temps. Nous am\'eliorons les r\'esultats existants en d\'emontrant la stabilit\'e quand le trafic inject\'e est un flot maximum. L'ensemble de ces travaux a \'et\'e impl\'ement\'e dans la biblioth\`eque open source MASCOPT (Mascotte Optimisation) d\'edi\'ee aux probl\`emes d'optimisation des r\'eseaux.

     
  5. G. Monaco. Optimization and Non-Cooperative Issues in Communication Networks. PhD thesis, University of l'Aquila, October 2009. [WWW ] [PDF ]
    Abstract:
    Communication networks and more in general distributed systems are undergoing rapid advancements. The last few years have experienced a steep growth in research on different related aspects. However, although the great promise for our future communication capabilities, several challenges need still to be addressed. A crucial ingredient for the successful development end employment of the corresponding arising technologies is the design of networks better suited for the management of large bandwidth and high quality services, as required by the emerging tasks, such as on-demand-video, multimedia and data integrated networks, seamless and ubiquitous access to system resources in mobile environments, secure on-demand data, and so forth. In this thesis we focus on the analysis of the performance and complexity of distributed systems such as optical networks (representing the main contribution of the thesis) and wireless networks. More specifically, we consider classical combinatorial optimization problems arising in communication networks from two different perspectives. In the first part we consider the design of classical centralized polynomial time (approximation or exact) algorithms. Such an investigation is conducted under a traditional computational complexity setting in which time constraints must be taking into account for tractability and efficiency matters. The above perspective implicitly or explicitly assumes that the resources of the system are directly accessible and controllable by a centralized authority, but this assumption in highly distributed systems might be too strong or unrealistic. Therefore, in the second part of the thesis we consider communication problems arising in networks with autonomous or non-cooperative users. In such a scenario users pursue an own often selfish strategy and the system evolves as a consequence of the interactions among them. The interesting arising scenario is thus characterized by the conflicting needs of the users aiming to maximize their personal profit and of the system wishing to compute a socially efficient solution. Algorithmic Game theory is considered the most powerful tool dealing with such non-cooperative environments in which the lack of coordination yields inefficiencies. In such a scenario we consider the pure Nash equilibrium as the outcome of the game and in turn as the concept capturing the notion of stable solution of the system. Under the above perspectives, the thesis makes different progresses on the understanding of a variety of problems in communication networks. Our results include: polynomial time algorithms, NP-complete results, approximation algorithms and inapproximability results; analysis of performances, convergence and existence of Nash equilibria in selfish scenarios.

     
  6. J.-P. Perez Seva. Les optimisations d'algorithmes de traitement du signal sur les architectures modernes parallèles et embarquées. PhD thesis, Ecole doctorale STIC, Université de Nice-Sophia Antipolis, August 2009.
     
  7. P. Reyes. Data Gathering in Radio Networks. PhD thesis, Ecole doctorale STIC, Université de Nice-Sophia Antipolis, August 2009. [WWW ]
    Keywords: combinatorial optimization, algorithms, graph coloring, data gathering, wireless networks, sensor networks.
    Abstract:
    This thesis concerns the study of the algorithmic and the complexity of the communications in radio networks. In particular, we were interested in the problem of gathering information from the nodes of a radio network in a central node. This problem is motivated by a question of France Telecom (Orange Labs): How to bring Internet in villages. Nodes represent the houses of the villages which communicate between them by radio, the goal being to reach a gateway connected to Internet by a satellite link. The same problem can be found in sensor networks where the question is to collect data from sensors to a base station. A peculiarity of radio networks is that the transmission distance is limited and that the transmissions interfere between them (interference phenomena). We model these constraints by saying that two nodes (radio devices) can communicate if they are at distance at most dT and a node interferes with another one if their distance is at most dI. The distances are considered in a graph representing the network. Thus, a communication step will consist in a compatible (non interfering) set of transmissions. Our goal is to find the minimum number of steps needed to achieve such a gathering and design algorithms achieving this minimum. For special topologies such as the path and the grid, we have proposed optimal or near optimal solutions. We also considered the systolic (or continuous) case where we want to maximize the throughput (bandwidth) offered to each node.

     
  8. I. Sau. Optimization in Graphs under Degree Constraints. Application to Telecommunication Networks. PhD thesis, Université de Nice-Sophia Antipolis (UNS) and Universitat Politècnica de Catalunya (UPC), October 2009. [PDF ]
    Keywords: Graph theory, traffic grooming, optical networks, graph partitioning, computational complexity, approximation algorithms, parameterized complexity, branchwidth, dynamic programming, graphs on surfaces.
    Abstract:
    The first part of this thesis is devoted to traffic grooming, which is a central problem in optical networks. It refers to packing low-rate signals into higher-speed streams, in order to improve bandwidth utilization and reduce the network cost. The objective is to minimize the number of Add-Drop Multiplexers (ADMs), which are devices that insert/extract low-rate traffic to/from a high-speed stream. In graph-theoretical terms, the problem can be translated into finding a partition of the edges of a request graph into subgraphs with bounded number of edges, the objective being to minimize the total number of vertices of the partition. We first focus in Chapter~1 on a general request graph when the topology is a ring or a path. We provide the first inapproximability result for traffic grooming for fixed values of the \emph{grooming factor} $C$, answering affirmatively to a conjecture in the literature. We also provide a polynomial-time approximation algorithm for traffic grooming in rings and paths, with an approximation ratio independent of C. We introduce in Chapter~2 a new model of traffic grooming in unidirectional rings, in order to design networks being able to support \emph{any} request graph with bounded maximum degree. We show that the problem is essentially equivalent to finding the least integer $M(C,\Delta)$ such that the edges of any graph with maximum degree at most $\Delta$ can be partitioned into subgraphs with at most $C$ edges and each vertex appears in at most $M(C,\Delta)$ subgraphs, and we establish the value of $M(C,\Delta)$ for almost all values of $C$ and $\Delta$. In Chapter~3 we focus on traffic grooming in bidirectional rings with symmetric shortest path routing and all-to-all unitary requests, providing general lower bounds and infinite families of optimal solutions for $C=1,2,3$ and $C$ of the form $k(k+1)/2$. In Chapter~4 we study traffic grooming for two-period optical networks, a variation of the traffic grooming problem for WDM unidirectional ring networks with two grooming factors $C$ and $C'$ that allows some dynamism on the traffic. Using tools of graph decompositions, we determine the minimum number of ADMs for $C=4$, and $C'=1,2,3$. The study of the traffic grooming problem leads naturally to the study of a family of graph-theoretical problems dealing with general constraints on the degree. This is the topic of the second part of this thesis. We begin in Chapter~5 by studying the computational complexity of several families of degree-constrained problems, giving hardness results and polynomial-time approximation algorithms. We then study in Chapter~6 the parameterized complexity of finding degree-constrained subgraphs, when the parameter is the size of the subgraphs. We prove hardness results in general graphs and provide explicit fixed-parameter tractable algorithms for minor-free graphs. We obtain in Chapter~7 subexponential parameterized and exact algorithms for several families of degree-constrained subgraph problems on planar graphs, using bidimensionality theory combined with novel dynamic programming techniques. Finally, we provide in Chapter~8 a framework for the design of dynamic programming algorithms for surface-embedded graphs with single exponential dependence on branchwidth. Our approach is based on a new type of branch decomposition called \emph{surface cut decomposition}, which generalizes sphere cut decompositions for planar graphs. The existence of such algorithms is proved using diverse techniques from topological graph theory and analytic combinatorics.

     
  9. V. Bilò, I. Caragiannis, A. Fanelli, M. Flammini, C. Kaklamanis, G. Monaco, and L. Moscardelli. Graphs and Algorithms in Communication Networks: Studies in Broadband, Optical, Wireless, and Ad Hoc Networks, volume XXVII of EATCS Texts in Theoretical Computer Science, chapter Game-Theoretic Approaches to Optimization Problems in Communication Networks, pages 241-264. Springer, A. Koster and X. Muñoz edition, November 2009. [WWW ] [PDF ]
    Abstract:
    In this chapter we consider fundamental communication problems arising in networks with non-cooperative users. The uncoordinated users’ behavior, addressing communication primitives in an individualistic and selfish manner, poses several intriguing questions ranging from the definition of reasonable and practical models, to the quantification of the efficiency loss due to the lack of users' cooperation. We present several results lately achievied in this research area and propose interesting future research directions.

     
  10. I. Sau and J. Zerovnik. Graphs and Algorithms in Communication Networks: Studies in Broadband, Optical, Wireless, and Ad Hoc Networks, volume XXVII of EATCS Texts in Theoretical Computer Science, chapter Permutation Routing and $(\ell,k)$-Routing on Plane Grids, pages 265-279. Springer, A. Koster and X. Muñoz edition, November 2009. [WWW ] [PDF ]
    Abstract:
    The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the $(\ell,k)$-routing problem, each node can send at most $\ell$ packets and receive at most $k$ packets. Permutation routing is the particular case $\ell=k=1$. In the $r$-centralrouting problem, all nodes at distance at most $r$ from a fixed node $v$ want to send a packet to $v$.Here we survey the results on permutation routing, the $r$-central routing and the general $(\ell,k)$-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We assume the \emph{store-and-forward} $\Delta$-port model, and we consider both full and half-duplex networks.

     
  11. L. Addario-Berry, N. Broutin, and B. Reed. Critical random graphs and the structure of a minimum spanning tree. Random Structures and Algorithms, 35:323--347, 2009. [WWW ] [PDF ]
    Abstract:
    We consider the complete graph on n vertices whose edges are weighted by independent and identically distributed edge weights and build the associated minimum weight spanning tree. We show that if the random weights are all distinct, then the expected diameter of such a tree is Θ(n1-3). This settles a question of Frieze and Mc-Diarmid (Random Struct Algorithm 10 (1997), 5–42). The proofs are based on a precise analysis of the behavior of random graphs around the critical point. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009

     
  12. L. Addario-Berry and B. Reed. Minima in branching random walks. Annals of Probability, 37:1044--1079, 2009. [WWW ] [PDF ]
    Abstract:
    Given a branching random walk, let $M_n$ be the minimum position of any member of the $n$th generation. We calculate $\mathbf{E}M_n$ to within O(1) and prove exponential tail bounds for $\mathbf{P}\{|M_n-\mathbf{E}M_n|>x\}$, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89--108], our results fully characterize the possible behavior of $\mathbf {E}M_n$ when the branching random walk has bounded branching and step size.

     
  13. O. Amini, F. Huc, and S. Pérennes. On the pathwidth of planar graphs. SIAM Journal of Discrete Mathematics, 23(3):1311-1316, August 2009. [WWW ] [PDF ]
    Abstract:
    In this paper, we present a result concerning the relation between the path-with of a planar graph and the path-width of its dual. More precisely, we prove that for a 3-connected planar graph $G$, $pw(G) \leq 3pw(G^*)+2$. For $4$-connected planar graphs, and more generally for Hamiltonian planar graphs, we prove a stronger bound $\pw(G^*) \leq 2 \ \pw(G)+c$. The best previously known bound was obtained by Fomin and Thilikos who proved that $\pw(G^*) \leq 6 \ \pw(G)+cte$. The proof is based on an algorithm which, given a fixed spanning tree of $G$, transforms any given decomposition of $G$ into one of $G^*$. The ratio of the corresponding parameters is bounded by the maximum degree of the spanning tree.

     
  14. O. Amini, F. Mazoit, N. Nisse, and S. Thomassé. Submodular partition functions. Discrete Mathematics, 309(20):6000-6008, 2009. [WWW ] [PDF ]
    Abstract:
    Adapting the method introduced in Graph Minors X, we propose a new proof of the duality between the bramble-number of a graph and its tree-width. Our approach is based on a new definition of submodularity on partition functions which naturally extends the usual one on set functions. The proof does not rely on Menger's theorem, and thus greatly generalises the original one. It thus provides a dual for matroid tree-width. One can also derive all known dual notions of other classical width-parameters from it.

     
  15. O. Amini, S. Pérennes, and I. Sau. Hardness and Approximation of Traffic Grooming. Theoretical Computer Science, 410(38-40):3751-3760, 2009. [PDF ]
    Abstract:
    Traffic grooming is a central problem in optical networks. It refers to packing low rate signals into higher speed streams, in order to improve bandwidth utilization and reduce network cost. In WDM networks, the most accepted criterion is to minimize the number of electronic terminations, namely the number of SONET Add-Drop Multiplexers (ADMs). In this article we focus on ring and path topologies. On the one hand, we provide an inapproximability result for Traffic Grooming for fixed values of the grooming factor g, answering authorrmatively the conjecture of Chow and Lin (Networks, 44:194-202, 2004 ). More precisely, we prove that Ring Traffic Grooming for fixed $g\leq 1$ and Path Traffic Grooming for fixed $g \leq 2$ are Apx-complete. That is, they do not accept a PTAS unless P = NP. Both results rely on the fact that finding the maximum number of edge-disjoint triangles in a tripartite graph (and more generally cycles of length $2g + 1$ in a $(2g + 1)$-partite graph of girth $2g + 1$) is Apx-complete. On the other hand, we provide a polynomial-time approximation algorithm for Ring and Path Traffic Grooming, based on a greedy cover algorithm, with an approximation ratio independent of $g$. Namely, the approximation guarantee is ${\mathcal O} (n^{1/3}\log^2(n))$ for any $g\leq 1$, $n$ being the size of the network. This is useful in practical applications, since in backbone networks the grooming factor is usually greater than the network size. Finally, we improve this approximation ratio under some extra assumptions about the request graph.

     
  16. J-C. Bermond, R. Correa, and M-L. Yu. Optimal Gathering Protocols on Paths under Interference Constraints. Discrete Mathematics, 309(18):5574-5587, September 2009.
    Note: A preliminary version has been presented at CIAC06. [WWW ] [PDF ]
    Abstract:
    We study the problem of gathering information from the nodes of a multi-hop radio network into a predefined destination node under reachability and interference constraints. In such a network, a node is able to send messages to other nodes within reception distance, but doing so it might create interference with other communications. Thus, a message can only be properly received if the receiver is reachable from the sender and there is no interference from another message being transmitted simultaneously. The network is modeled as a graph, where the vertices represent the nodes of the network and the edges, the possible communications. The interference constraint is modeled by a fixed integer d?1, which implies that nodes within distance d in the graph from one sender cannot receive messages from another node. In this paper, we suppose that each node has one unit-length message to transmit and, furthermore, we suppose that it takes one unit of time (slot) to transmit a unit-length message and during such a slot we can have only calls which do not interfere (called compatible calls). A set of compatible calls is referred to as a round. We give protocols and lower bounds on the minimum number of rounds for the gathering problem when the network is a path and the destination node is either at one end or at the center of the path. These protocols are shown to be optimal for any d in the first case, and for 1?d?4, in the second case.

     
  17. E. Birmelé, J. A. Bondy, and B. Reed. Tree-width of graphs without a 3 by 3 grid minor. Discrete Applied Mathematics, 157:2577--2598, 2009. [WWW ] [PDF ]
    Abstract:
    We show that graphs with no minor isomorphic to the 3x3 grid have tree-width at most 7.

     
  18. R. Correa, F. Havet, and J-S. Sereni. About a Brooks-type theorem for improper colouring. Australasian Journal of Combinatorics, 43:219--230, 2009. [PDF ]
    Abstract:
    A graph is $k$-improperly \l-colourable if its vertices can be partitioned into \l parts such that each part induces a subgraph of maximum degree at most $k$. A result of Lov\'asz states that for any graph $G$, such a partition exists if $\l\ge\left\lceil\frac{\Delta(G)+1}{k+1}\right\rceil$. When $k=0$, this bound can be reduced by Brooks' Theorem, unless $G$ is complete or an odd cycle. We study the following question, which can be seen as a generalisation of the celebrated Brooks' Theorem to improper colouring: does there exist a polynomial-time algorithm that decides whether a graph $G$ of maximum degree $\Delta$ has $k$-improper chromatic number at most $\lceil \frac{\Delta + 1}{k + 1} \rceil - 1$? We show that the answer is no, unless $\mathcal P = \mathcal NP$, when $\Delta = \ell(k + 1)$, $k \geq 1$ and $\ell + \sqrt{\ell} \leq 2k + 3$. We also show that, if $G$ is planar, $k=1$ or $k=2$, $\Delta = 2k + 2$, and $\ell = 2$, then the answer is still no, unless $\mathcal P = \mathcal NP$. These results answer some questions of Cowen et al. [Journal of Graph Theory 24(3):205-219, 1997].

     
  19. F. V. Fomin, P. Fraigniaud, and N. Nisse. Nondeterministic Graph Searching: From Pathwidth to Treewidth. Algorithmica, 53(3):358-373, 2009. [WWW ] [PDF ]
    Abstract:
    We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this game-theoretic approach and graph decompositions called q -branched tree decompositions, which can be interpreted as a parameterized version of tree decompositions. Path decomposition and (standard) tree decomposition are two extreme cases of q-branched tree decompositions. The equivalence between nondeterministic graph searching and q-branched tree decomposition enables us to design an exact (exponential time) algorithm computing q-branched treewidth for all q, which is thus valid for both treewidth and pathwidth. This algorithm performs as fast as the best known exact algorithm for pathwidth. Conversely, this equivalence also enables us to design a lower bound on the amount of nondeterminism required to search a graph with the minimum number of searchers.

     
  20. J. Galtier. Real-time resource allocation for LEO satellite constellations. Wireless Networks, 15(6):791-803, August 2009. [WWW ]
    Abstract:
    The paper addresses the need of controling the access of terminals with guaranteed ressources on the high dynamic systems offered by LEO satellite constellations. A call-access-control scheme that guarantees the reservation of permanent resources of satellite constellations in $O(\sqrt{n}\log(n))$ time, where n is the number of user present in the system, is described. A tradeoff between computational time of call-access-control and optimization of the use of the spectrum is identified. Some experimental results are presented.

     
  21. J. Geelen, B. Gerards, B. Reed, P. Seymour, and A. Vetta. On the odd-minor variant of Hadwiger's conjecture. Journal of Combinatorial Theory Ser. B, 99:20--29, 2009. [WWW ] [PDF ]
    Abstract:
    A Kl-expansion consists of l vertex-disjoint trees, every two of which are joined by an edge. We call such an expansion odd if its vertices can be two-coloured so that the edges of the trees are bichromatic but the edges between trees are monochromatic. We show that, for every l, if a graph contains no odd Kl-expansion then its chromatic number is View the MathML source. In doing so, we obtain a characterization of graphs which contain no odd Kl-expansion which is of independent interest. We also prove that given a graph and a subset S of its vertex set, either there are k vertex-disjoint odd paths with endpoints in S, or there is a set X of at most 2k−2 vertices such that every odd path with both ends in S contains a vertex in X. Finally, we discuss the algorithmic implications of these results.

     
  22. F. Giroire. Order statistics and estimating cardinalities of massive data sets. Discrete Applied Mathematics, 157(2):406-427, 2009. [WWW ] [PDF ]
    Abstract:
    A new class of algorithms to estimate the cardinality of very large multisets using constant memory and doing only one pass on the data is introduced here. It is based on order statistics rather than on bit patterns in binary representations of numbers. Three families of estimators are analyzed. They attain a standard error of using M units of storage, which places them in the same class as the best known algorithms so far. The algorithms have a very simple internal loop, which gives them an advantage in terms of processing speed. For instance, a memory of only 12 kB and only few seconds are sufficient to process a multiset with several million elements and to build an estimate with accuracy of order 2 percent. The algorithms are validated both by mathematical analysis and by experimentations on real internet traffic.

     
  23. F. Havet, R. Kang, T. Müller, and J.-S. Sereni. Circular choosability. Journal of Graph Theory, 61(4):241--334, 2009. [PDF ]
    Abstract:
    We study circular choosability, a notion recently introduced by Mohar and by Zhu. First, we provide a negative answer to a question of Zhu about circular cliques. We next prove that $\cch(G) = O\left( \ch(G) + \ln |V(G)| \right)$ for every graph $G$. We investigate a generalisation of circular choosability, the circular $f$-choosability, where $f$ is a function of the degrees. We also consider the circular choice number of planar graphs. Mohar asked for the value of $\tau := \sup {\cch(G) : G\text{ is planar}}$, and we prove that $6\le\tau\le8$, thereby providing a negative answer to another question of Mohar. We also study the circular choice number of planar and outerplanar graphs with prescribed girth, and graphs with bounded density.

     
  24. F. Havet, R. Kang, and J.-S. Sereni. Improper Colouring of Unit Disk Graphs. Networks, 54(3):150--164, 2009.
    Abstract:
    Motivated by a satellite communications problem, we consider a generalised colouring problem on unit disk graphs. A colouring is \emph{$k$-improper} if no more than $k$ neighbours of every vertex have the same colour as that assigned to the vertex. The \emph{$k$-improper chromatic number $\chi^k(G)$} is the least number of colours needed in a $k$-improper colouring of a graph $G$. The main subject of this work is analysing the complexity of computing $\chi^k$ for the class of unit disk graphs and some related classes, e.g.~hexagonal graphs and interval graphs. We show NP-completeness in many restricted cases and also provide both positive and negative approximability results. Due to the challenging nature of this topic, many seemingly simple questions remain: for example, it remains open to determine the complexity of computing $\chi^k$ for unit interval graphs.

     
  25. F. Havet and S. Thomassé. Complexity of $(p,1)$-total labelling. Dicrete Applied Mathematics, 157:2859--2870, 2009. [PDF ]
    Abstract:
    A {\it $(p,1)$-total labelling} of a graph $G=(V,E)$ is a total coloring $L$ from $V\cup E$ into ${0,\dots ,l}$ such that $|L(v)-L(e)|\geq p$ whenever an edge $e$ is incident to a vertex $v$. The minimum $l$ for which $G$ admits a $(p,1)$-total labelling is denoted by $\lambda_p(G)$. The case $p=1$ corresponds to the usual notion of total colouring, which is NP-hard to compute even for cubic bipartite graphs~\cite{MDSA94}. In this paper we assume $p\geq 2$. It is easy to show that $\lambda_p(G)\geq \Delta +p-1$, where $\Delta$ is the maximum degree of $G$. Moreover, when $G$ is bipartite, $\Delta +p$ is an upper bound for $\lambda_p(G)$, leaving only two possible values. In this paper, we completely settle the computational complexity of deciding whether $\lambda_p(G)$ is equal to $\Delta +p-1$ or to $\Delta +p$ when $G$ is bipartite. This is trivial when $\Delta \leq p$, polynomial when $\Delta =3$ and $p=2$, and NP-complete in the remaining cases.

     
  26. F. Havet. Choosability of the square of planar subcubic graphs with large girth. Discrete Mathematics, 309:3553--3563, 2009. [PDF ]
    Abstract:
    We show that the choice number of the square of a subcubic graph with maximum average degree less than $18/7$ is at most $6$. As a corollary, we get that the choice number of the square of a subcubic planar graph with girth at least $9$ is at most $6$. We then show that the choice number of the square of a subcubic planar graph with girth at least $13$ is at most $5$.

     
  27. F. Huc, I. Sau, and J. Zerovnik. $(\ell,k)$-Routing on Plane Grids. Journal of Interconnection Networks, 10(1-2):27-57, 2009. [PDF ]
    Abstract:
    The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the $(\ell,k)$-routing problem, each node can send at most $\ell$ packets and receive at most $k$ packets. Permutation routing is the particular case $\ell=k=1$. In the $r$-central routing problem, all nodes at distance at most $r$ from a fixed node $v$ want to send a packet to $v$. In this article we study the permutation routing, the $r$-central routing and the general $(\ell,k)$-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the \emph{store-and-forward} $\Delta$-port model, and we consider both full and half-duplex networks. The main contributions are the following: \begin{itemize} \item[1.] Tight permutation routing algorithms on full-duplex hexagonal grids, and half duplex triangular and hexagonal grids. \item[2.] Tight $r$-central routing algorithms on triangular and hexagonal grids. \item[3.] Tight $(k,k)$-routing algorithms on square, triangular and hexagonal grids. \item[4.] Good approximation algorithms (in terms of running time) for $(\ell,k)$-routing on square, triangular and hexagonal grids, together with new lower bounds on the running time of any algorithm using shortest path routing. \end{itemize} \noindent All these algorithms are completely distributed, i.e. can be implemented independently at each node. Finally, we also formulate the $(\ell,k)$-routing problem as a \textsc{Weighted Edge Coloring} problem on bipartite graphs.

     
  28. D. Ilcinkas, N. Nisse, and D. Soguet. The Cost of Monotonicity in Distributed Graph Searching. Distributed Computing, 22(2):117-127, 2009. [WWW ] [PDF ]
    Abstract:
    Blin et al. (TCS 2008) proposed a dis- tributed protocol enabling the smallest possible num- ber of searchers to clear any unknown graph in a de- centralized manner. However, the strategy that is actu- ally performed lacks of an important property, namely the monotonicity. This paper deals with the smallest number of searchers that are necessary and sufficient to monotonously clear any unknown graph in a decen- tralized manner. The clearing of the graph is required to be connected, i.e., the clear part of the graph must remain permanently connected, and monotone, i.e., the clear part of the graph only grows. We prove that a dis- tributed protocol clearing any unknown n-node graph in a monotone connected way, in a decentralized set- ting, can achieve but cannot beat competitive ratio of Theta(log n /n), compared with the centralized minimum number of searchers. Moreover, our lower bound holds even in a synchronous setting, while our constructive upper bound holds even in an asynchronous setting.

     
  29. A. Jarry and S. Pérennes. Disjoint Path in symmetric Graphs. Discrete Applied Mathematics, 157(1):90-97, 2009.
     
  30. K. Kawarabayashi, O. Lee, and B. Reed. Removable cycles in non-bipartite graphs. Journal of Combinatorial Theory Ser. B, 99:30--38, 2009. [WWW ]
    Abstract:
    In this paper we prove the following result. Suppose that s and t are vertices of a 3-connected graph G such that G-s-t is not bipartite and there is no cutset X of size three in G for which some component U of G-X is disjoint from {s,t}. Then either (1) G contains an induced path P from s to t such that G-V(P) is not bipartite or (2) G can be embedded in the plane so that every odd face contains one of s or t. Furthermore, if (1) holds then we can insist that G-V(P) is connected, while if G is 5-connected then (1) must hold and P can be chosen so that G-V(P) is 2-connected.

     
  31. K. Kawarabayashi and B. Reed. Highly parity linked graphs. Combinatorica, 29:215--225, 2009. [WWW ]
    Abstract:
    A graph G is k-linked if G has at least 2k vertices, and for any 2k vertices x 1,x 2, …, x k ,y 1,y 2, …, y k , G contains k pairwise disjoint paths P 1, …, P k such that P i joins x i and y i for i = 1,2, …, k. We say that G is parity-k-linked if G is k-linked and, in addition, the paths P 1, …, P k can be chosen such that the parities of their length are prescribed. Thomassen [22] was the first to prove the existence of a function f(k) such that every f(k)-connected graph is parity-k-linked if the deletion of any 4k-3 vertices leaves a nonbipartite graph. In this paper, we will show that the above statement is still valid for 50k-connected graphs. This is the first result that connectivity which is a linear function of k guarantees the Erdős-Pósa type result for parity-k-linked graphs.

     
  32. R. Klasing, Z. Lotker, A. Navarra, and S. Pérennes. From Balls and Bins to Points and Vertices. Algorithmic Operations Research (AlgOR), 4(2):133-143, 2009.
    Abstract:
    Given a graph $G = (V, E)$ with $|V| = n$, we consider the following problem. Place $m = n$ points on the vertices of G independently and uniformly at random. Once the points are placed, relocate them using a bijection from the points to the vertices that minimizes the maximum distance between the random place of the points and their target vertices. We look for an upper bound on this maximum relocation distance that holds with high probability (over the initial placements of the points). For general graphs and in the case $m \leq n$, we prove the $\#P$-hardness of the problem and that the maximum relocation distance is ${\cal O}(\sqrt{n})$ with high probability. We present a Fully Polynomial Randomized Approximation Scheme when the input graph admits a polynomial-size family of witness cuts while for trees we provide a 2-approximation algorithm. Many applications concern the variation in which $m = (1 − q)n for some 0 < q < 1$. We provide several bounds for the maximum relocation distance according to different graph topologies.

     
  33. B. Lévêque, F. Maffray, B. Reed, and N. Trotignon. Coloring Artemis graphs. Theoretical Computer Science, 410:2234--2240, 2009. [WWW ] [PDF ]
    Abstract:
    We consider the class of graphs that contain no odd hole, no antihole, and no ''prism'' (a graph consisting of two disjoint triangles with three disjoint paths between them). We give an algorithm that can optimally color the vertices of these graphs in time O(n^2m).

     
  34. G. B. Mertzios, I. Sau, and S. Zaks. A New Intersection Model and Improved Algorithms for Tolerance Graphs. SIAM Journal on Discrete Mathematics, 23:1800-1813, 2009. [WWW ] [PDF ]
    Abstract:
    Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs, which generalizes in a natural way both interval and permutation graphs, has attracted many research efforts since their introduction in [10], as it finds many important applications in constraint-based temporal reasoning, resource allocation, and scheduling problems, among others. In this article we propose the first non-trivial intersection model for general tolerance graphs, given by three-dimensional parallelepipeds, which extends the widely known intersection model of parallelograms in the plane that characterizes the class of bounded tolerance graphs. Apart from being important on its own, this new representation also enables us to improve the time complexity of three problems on tolerance graphs. Namely, we present optimal $O(n log n)$ algorithms for computing a minimum coloring and a maximum clique, and an $O(n^2)$ algorithm for computing a maximum weight independent set in a tolerance graph with $n$ vertices, thus improving the best known running times $O(n^2)$ and $O(n^3)$ for these problems, respectively

     
  35. N. Nisse. Connected graph searching in chordal graphs. Discrete Applied Mathematics, 157(12):2603-2610, 2009. [WWW ] [PDF ]
    Abstract:
    Graph searching was introduced by Parson [T. Parson, Pursuit-evasion in a graph, in: Theory and Applications of Graphs, in: Lecture Notes in Mathematics, Springer-Verlag, 1976, pp. 426--441]: given a contaminated graph G (e.g., a network containing a hostile intruder), the search number s(G) of the graph G is the minimum number of searchers needed to clear the graph (or to capture the intruder). A search strategy is connected if, at every step of the strategy, the set of cleared edges induces a connected subgraph. The connected search number cs(G) of a graph G is the minimum k such that there exists a connected search strategy for the graph G using at most k searchers. This paper is concerned with the ratio between the connected search number and the search number. We prove that, for any chordal graph G of treewidth tw(G), cs(G)/s(G)=O(tw(G)). More precisely, we propose a polynomial-time algorithm that, given any chordal graph G, computes a connected search strategy for G using at most (tw(G)+2)(2s(G)-1) searchers. Our main tool is the notion of connected tree-decomposition. We show that, for any connected graph G of chordality k, there exists a connected search strategy using at most (tw(G)^{k/2}+2)(2s(T)-1) searchers where T is an optimal tree-decomposition of G.

     
  36. N. Nisse and D. Soguet. Graph Searching with Advice. Theoretical Computer Science, 410(14):1307-1318, 2009. [WWW ] [PDF ]
    Abstract:
    Fraigniaud et al. [L. Blin, P. Fraigniaud, N. Nisse, S. Vial, Distributing chasing of network intruders, in: 13th Colloquium on Structural Information and Communication Complexity, SIROCCO, in: LNCS, vol. 4056, Springer-Verlag, 2006, pp. 70--84] introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to clear a contaminated graph in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. Moreover, the clearing of the graph must be performed using the optimal number of searchers, i.e. the minimum number of searchers sufficient to clear the graph in a monotone connected way in a centralized setting. We show that the minimum number of bits of advice permitting the monotone connected and optimal clearing of a network in a distributed setting is $\Theta(nlogn)$, where n is the number of nodes of the network. More precisely, we first provide a labelling of the vertices of any graph G, using a total of O(nlogn) bits, and a protocol using this labelling that enables the optimal number of searchers to clear G in a monotone connected distributed way. Then, we show that this number of bits of advice is optimal: any distributed protocol requires $\Omega(nlogn)$ bits of advice to clear a network in a monotone connected way, using an optimal number of searchers.

     
  37. E. Altman, P. Nain, and J-C. Bermond. Distributed Storage Management of Evolving Files in Delay Tolerant Ad Hoc Networks. In INFOCOM 2009, Rio De Janeiro, Brazil, pages 1431 - 1439, April 2009. [WWW ] [PDF ]
    Abstract:
    This work focuses on a class of distributed storage systems whose content may evolve over time. Each component or node of the storage system is mobile and the set of all nodes forms a delay tolerant (ad hoc) network (DTN). The goal of the paper is to study efficient ways for distributing evolving files within DTNs and for managing dynamically their content. We specify to dynamic files where not only the latest version is useful but also previous ones; we restrict however to files where a file has no use if another more recent version is available. There are $N+1$ mobile nodes including a {\em single} source which at some points in time makes available a new version of a {\em single} file $F$. We consider both the cases when (a) nodes do not cooperate and (b) nodes cooperate. In case (a) only the source may transmit a copy of the latest version of $F$ to a node that it meets, while in case (b) any node may transmit a copy of $F$ to a node that it meets. A file management policy is a set of rules specifying when a node may send a copy of $F$ to a node that it meets. The objective is to find file management policies which maximize some system utility functions under a constraint on the resource consumption. Both myopic ({\em static}) and state-dependent ({\em dynamic}) policies are considered, where the state of a node is the age of the copy of $F$ it carries. Scenario (a) is studied under the assumption that the source updates $F$ at discrete times $t=0,1,\ldots$. During a slot $[t,t+1)$ the source meets any node with a fixed probability. We find the optimal static (resp. dynamic) policy which maximizes a general utility function under a constraint on the number of transmissions within a slot. In particular, we show the existence of a threshold dynamic policy. In scenario (b) $F$ is updated at random points in time, with the consequence that between two meetings with the source a node does not know the age evolution of the version of $F$ it holds. Under Markovian assumptions regarding nodes mobility and update frequency of $F$, we study the stability of the system (aging of the nodes) and derive an (approximate) optimal static policy. We then revisit scenario (a) when the source does not know parameter $N$ (node population) and $q$ (node meeting probability) and derive a stochastic approximation algorithm which we show to converge to the optimal static policy found in the complete information setting. Numerical results illustrate the respective performance of optimal static and dynamic policies as well as the benefit of node cooperation.

     
  38. J. Araujo, N. Cohen, F. Giroire, and F. Havet. Good edge-labelling of graphs. In proceedings of the Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS'09), volume 35 of Electronic Notes in Discrete Mathematics, Gramado, Brazil, pages 275--280, December 2009. Springer. [PDF ]
    Abstract:
    A good edge-labelling of a graph G is a labelling of its edges such that for any two distinct vertices u, v, there is at most one (u,v)-path with non-decreasing labels. This notion was introduced in [J-C. Bermond, M. Cosnard, and S. Pérennes. Directed acyclic graphs with unique path property. Technical Report RR-6932, INRIA, May 2009] to solve wavelength assignment problems for specific categories of graphs. In this paper, we aim at characterizing the class of graphs that admit a good edge-labelling. First, we exhibit infinite families of graphs for which no such edge-labelling can be found. We then show that deciding if a graph admits a good edge-labelling is NP-complete. Finally, we give large classes of graphs admitting a good edge-labelling: C3-free outerplanar graphs, planar graphs of girth at least 6, subcubic {C3,K2,3}-free graphs.

     
  39. J. Araujo and C. Linhares Sales. Grundy number on $P_4$-classes. In proceedings of the Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS'09), volume 35 of Electronic Notes in Discrete Mathematics, Gramado, Brazil, pages 21--27, December 2009. Springer. [PDF ]
    Abstract:
    In this article, we define a new class of graphs, the fat-extended P4-laden graphs, and we show a polynomial time algorithm to determine the Grundy number of the graphs in this class. This result implies that the Grundy number can be found in polynomial time for any graph of the following classes: P4-reducible, extended P4-reducible, P4-sparse, extended P4-sparse, P4-extendible, P4-lite, P4-tidy, P4-laden and extended P4-laden, which are all strictly contained in the fat-extended P4-laden class.

     
  40. J. Araujo, P. Moura, and M. Campêlo. Sobre a complexidade de Coloração Mista. In Encontro Regional de Pesquisa Operacional do Nordeste, Fortaleza, Brazil, pages 1--10, December 2009. [PDF ]
    Abstract:
    Grafos mistos s˜ao estruturas matem´aticas que mesclam caracter´ısticas de grafos direcionados e n˜ao-direcionados. Formalmente, um grafo misto pode ser definido por uma tripla GM = (V; A;E), onde V , A e E representam, respectivamente, um conjunto de v´ertices, de arcos e de arestas. Uma k-colorac¸ ˜ao mista de GM = (V; A;E) ´e func¸ ˜ao c : V ! f0; : : : ; k ¡ 1g tal que c(u) < c(v), se (u; v) 2 A, e c(u) 6= c(v), se [u; v] 2 E. O problema de Colorac¸ ˜ao Mista consiste em determinar o n´umero crom´atico misto de GM, denotado por ÂM(GM), que ´e menor inteiro k tal que GM admite uma k-colorac¸ ˜ao mista. Esse problema modela variac¸ ˜oes de problemas de escalonamento que consideram simultaneamente restric¸ ˜oes de precedˆencia e de compartilhamento de recursos. Neste trabalho, mostramos que Colorac¸ ˜ao Mista ´e NP-dif´ıcil para as classes dos grafos cordais, dos grafos linha de grafos bipartidos e dos grafos linha de grafos periplanares.

     
  41. D. Barman, J. Chandrashekar, N. Taft, M. Faloutsos, L. Huang, and F. Giroire. Impact of IT Monoculture on Behavioral End Host Intrusion Detection. In ACM SIGCOMM Workshop on Research on Enterprise Networking -- WREN, Barcelona, Spain, pages 27--36, August 2009. ACM. [PDF ]
    Abstract:
    In this paper, we study the impact of today's IT policies, defined based upon a monoculture approach, on the performance of endhost anomaly detectors. This approach leads to the uniform configuration of Host intrusion detection systems (HIDS) across all hosts in an enterprise networks. We assess the performance impact this policy has from the individual's point of view by analyzing network traces collected from 350 enterprise users. We uncover a great deal of diversity in the user population in terms of the “tail†behavior, i.e., the component which matters for anomaly detection systems. We demonstrate that the monoculture approach to HIDS configuration results in users that experience wildly different false positive and false negatives rates. We then introduce new policies, based upon leveraging this diversity and show that not only do they dramatically improve performance for the vast majority of users, but they also reduce the number of false positives arriving in centralized IT operation centers, and can reduce attack strength.

     
  42. J-C. Bermond, D. Coudert, J. Moulierac, S. Perennes, H. Rivano, I. Sau, and F. Solano Donado. MPLS label stacking on the line network. In L. Fratta et al., editor, IFIP Networking, volume 5550 of Lecture Notes in Computer Science, Aachen, Germany, pages 809-820, May 2009. Springer. [WWW ] [PDF ]
    Abstract:
    All-Optical Label Switching (AOLS) is a new technology that performs forwarding without any Optical-Electrical-Optical (OEO) conversions. In this report, we study the problem of routing a set of requests in AOLS networks with the aim of minimizing the number of labels required to ensure the forwarding. In order to spare the label space, we consider label stacking, allowing the configuration of tunnels. We study particularly this network design problem when the network is a line. We provide an exact algorithm for the case in which all the requests have a common source and present some approximation algorithms and heuristics when an arbitrary number of sources are distributed over the line. We contrast the performance of our proposed algorithms by simulations.

     
  43. J-C. Bermond, D. Coudert, J. Moulierac, S. Perennes, I. Sau, and F. Solano Donado. Designing Hypergraph Layouts to GMPLS Routing Strategies. In 16th International Colloquium on Structural Information and Communication Complexity (SIROCCO), volume 5869 of Lecture Notes in Computer Science, Piran, Slovenia, pages 57--71, May 2009. Springer. [WWW ] [PDF ]
    Abstract:
    All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any Optical-Electrical-Optical (OEO) conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formalize the problem by associating to each routing strategy a logical hypergraph whose hyperedges are dipaths of the physical graph, called \emph{tunnels} in GMPLS terminology. Such a hypergraph is called a \emph{hypergraph layout}, to which we assign a cost function given by its physical length plus the total number of hops traveled by the traffic. Minimizing the cost of the design of an AOLS network can then be expressed as finding a minimum cost hypergraph layout. We prove hardness results for the problem, namely $C \log n$ hardness for directed networks and non-existence of \textsc{PTAS} for undirected networks, where $C $ is a a positive constant and $n$ is the number of nodes of the network. These hardness results hold even is the traffic instance is a partial broadcast. On the other hand, we provide an $\mathcal{O}(\log n)$-approximation algorithm to the problem for a general network. Finally, we focus on the case where the physical network is a path, providing a polynomial-time dynamic programming algorithm for a bounded number of sources, thus extending the algorithm of~\cite{BCM+09b} for a single source.

     
  44. J-C. Bermond, D. Mazauric, and P. Nain. Algorithmes distribués d'ordonnancement dans les réseaux sans-fil. In 10èmes Journées Doctorales en Informatique et Réseaux (JDIR), Belfort, France, February 2009. [PDF ]
    Abstract:
    Nous consid\'erons dans cet article le probl\`eme d'ordonnancement distribu\'e dans les r\'eseaux sans-fil. En raison des interf\'erences dans ce type de r\'eseau, ne peuvent \^etre activ\'es simultan\'ement que des liens n'interf\'erant pas entre eux. Par exemple dans un mod\`ele primaire, on ne peut activer que des liens deux \`a deux non adjacents. Nous nous pla\c cons dans un contexte d'arriv\'ee al\'eatoire de messages et l'objectif est d'assurer un bon comportement du r\'eseau en particulier d'assurer la stabilit\'e des files d'attente, en limitant le nombre moyen de messages en attente. Des algorithmes centralis\'es permettant de d\'ecider quels liens sont activ\'es \`a chaque \'etape existent mais ils supposent une connaissance globale du r\'eseau et sont peu adapt\'es aux applications. Il est donc n\'ecessaire de concevoir des algorithmes distribu\'es qui utilisent une connaissance tr\`es locale du r\'eseau. Nous proposons dans cet article deux algorithmes distribu\'es, valides quelque soit le mod\`ele d'interf\'erence binaire et avec une phase de contr\^ole de dur\'ee constante, am\'eliorant les algorithmes existants v\'erifiant uniquement l'un ou l'autre de ces deux crit\`eres.

     
  45. J-C. Bermond, N. Nisse, P. Reyes, and H. Rivano. Minimum delay Data Gathering in Radio Networks. In Proceedings of the 8th international conference on Ad Hoc Networks and Wireless (AdHoc-Now), volume 5793 of Lecture Notes in Computer Science, pages 69-82, 2009. Springer. [WWW ] [PDF ]
    Abstract:
    The aim of this paper is to design efficient gathering algorithms (data collection) in a Base Station of a wireless multi hop grid network when interferences constraints are present. We suppose the time is slotted and that during one time slot (step) each node can transmit to one of its neighbours at most one data item. Each device is equipped with a half duplex interface; so a node cannot both receive and transmit simultaneously. During a step only non interfering transmissions can be done. In other words, the non interfering calls done during a step will form a matching. The aim is to minimize the number of steps needed to send to the base station a set of messages generated by the nodes, this completion time is also denoted makespan of the call scheduling. The best known algorithm for open-grids was a multiplicative 1.5-approximation algorithm [Revah, Segal 07]. In such topologies, we give a very simple +2 approximation algorithm and then a more involved +1 approximation algorithm. Moreover, our algorithms work when no buffering is allowed in intermediary nodes, i.e., when a node receives a message at some step, it must transmit it during the next step.

     
  46. J-C. Bermond, N. Nisse, P. Reyes, and H. Rivano. Fast Data Gathering in Radio Grid Networks. In 11èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'09), pages 4p, June 2009. [WWW ] [PDF ]
    Abstract:
    Nous présentons des algorithmes efficaces pour la collecte d'informations par une station de base au sein d'un réseau sans-fil multi sauts en présence d'interférences. Nous nous focalisons sur les réseaux en grille car ils sont un bon modèle des réseaux d'accès comme des réseaux aléatoires de capteurs. Le temps est divisé en étapes élémentaires. Au cours d'une étape, un nœud peut transmettre au plus un message à l'un de ces voisins. Chaque appareil est équipé d'un interface half duplex et ne peut donc émettre et recevoir à la même étape. Ainsi, au cours d'une étape, l'ensemble des transmissions valides induit un couplage de la grille. Le problème consiste à minimiser le nombre d'étapes nécessaires à la collecte de tous les messages par la station de base. Le meilleur algorithme connu était une 3/2 approximation. Nous donnons un algorithme très simple qui approche l'optimum à 2 près, puis nous présentons un algorithme plus évolué qui est une +1 approximation. Nos résultats sont valides lorsque les appareils ne disposent d'aucune mémoire tampon et doivent retransmettre un message à l'étape suivant sa réception.

     
  47. V. Bilò, M. Flammini, G. Monaco, and L. Moscardelli. On the performances of Nash Equilibria in Isolation Games. In Proceedings of the 15th International Computing and Combinatorics Conference (COCOON 2009), volume 5609 of Lecture Notes in Computer Science, Niagara Falls, New York, U.S.A., pages 17-26, July 2009. Springer. [WWW ] [PDF ]
    Abstract:
    We study the performances of Nash equilibria in isolation games, a class of competitive location games recently introduced by Zhao et all. For all the cases in which the existence of Nash equilibria has been shown, we give tight or asymptotically tight bounds on the prices of anarchy and stability under the two classical social functions mostly investigated in the scienti¯c literature, namely, the minimum utility per player and the sum of the players' utilities. Moreover, we prove that the convergence to Nash equilibria is not guaranteed in some of the not yet analyzed cases.

     
  48. A. Casteigts, S. Chaumette, and A. Ferreira. Characterizing Topological Assumptions of Distributed Algorithms in Dynamic Networks. In Proc. of 16th Intl. Conference on Structural Information and Communication Complexity (SIROCCO'09), volume 5869 of Lecture Notes in Computer Science, Piran, Slovenia, pages 126-140, May 2009. Springer-Verlag. [PDF ]
    Abstract:
    Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at their assumptions on the underlying network. This paper focuses on the study of such assumptions in dynamic networks, where the connectivity is expected to change, predictably or not, during the execution. Our main contribution is a theoretical framework dedicated to such analysis. By combining several existing components (local computations, graph relabellings, and evolving graphs), this framework allows to express detailed properties on the network dynamics and to prove that a given property is necessary, or sufficient, for the success of an algorithm. Consequences of this work include (i)~the possibility to compare distributed algorithms on the basis of their topological requirements, (ii)~the elaboration of a formal classification of dynamic networks with respect to these properties, and (iii)~the possibility to check automatically whether a network trace belongs to one of the classes, and consequently to know which algorithm should run on it.

     
  49. N. Cohen, F. V. Fomin, G. Gutin, E. J. Kim, S. Saurabh, and A. Yeo. Algorithm for Finding it -Vertex Out-trees and Its Application to it -Internal Out-branching Problem. In 15th Annual International Conference on Computing and Combinatorics (COCOON), volume 5609 of Lecture Notes in Computer Science, pages 37-46, 2009. [WWW ] [PDF ]
    Abstract:
    An out-tree T is an oriented tree with exactly one vertex of in-degree zero and a vertex x of T is called internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a subgraph isomorphic to a given out-tree with k vertices. Both algorithms run in O∗(5.704^k) time. We apply the deterministic algorithm to obtain an algorithm of runtime O∗(c^k), where c is a constant, for deciding whether an input digraph contains a spanning out-tree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM'08).

     
  50. N. Cohen, F. Havet, and T. Müller. Acyclic edge-colouring of planar graphs. In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2009), volume 34 of Electronic Notes on Discrete Mathematics, Bordeaux, France, pages 417-421, September 2009. [PDF ]
    Abstract:
    A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an {\it acyclic edge-colouring}. The {\it acyclic chromatic index} of a graph $G$, denoted $\chi'_a(G)$ is the minimum $k$ such that $G$ admits an {\it acyclic edge-colouring} with $k$ colours. We conjecture that if $G$ is planar and $\Delta(G)$ is large enough then $\chi'_a(G)=\Delta(G)$. We settle this conjecture for planar graphs with girth at least $5$ and outerplanar graphs. We also show that if $G$ is planar then $\chi'_a(G)\leq \Delta(G) + 25$.

     
  51. D. Coudert, F. Giroire, and I. Sau. Edge-Simple Circuits Through 10 Ordered Vertices in Square Grids. In J. Kratochvìl and M. Miller, editors, 20th International Workshop on Combinatorial Algorithms -- IWOCA, volume 5874 of Lecture Notes in Computer Science, Hradec nad Moravicì, Czech Republic, pages 134-145, June 2009. Springer. [WWW ] [PDF ]
    Abstract:
    A \emph{circuit} in a simple undirected graph $G=(V,E)$ is a sequence of vertices $\{v_1,v_2,\ldots,v_{k+1}\}$ such that $v_1=v_{k+1}$ and $\{v_i,v_{i+i}\} \in E$ for $i=1,\ldots,k$. A circuit $C$ is said to be \emph{edge-simple} if no edge of $G$ is used twice in $C$. In this article we study the following problem: which is the largest integer $k$ such that, given any subset of $k$ ordered vertices of an infinite square grid, there exists an edge-simple circuit visiting the $k$ vertices in the prescribed order? We prove that $k=10$. To this end, we first provide a counterexample implying that $k<11$. To show that $k\geq 10$, we introduce a methodology, based on the notion of core graph, to reduce drastically the number of possible vertex configurations, and then we test each one of the resulting configurations with an \textsc{ILP} solver.

     
  52. D. Coudert, F. Huc, D. Mazauric, N. Nisse, and J-S. Sereni. Reconfiguration of the Routing in WDM Networks with Two Classes of Services. In 13th Conference on Optical Network Design and Modeling (ONDM), Braunschweig, Germany, pages 6p, February 2009. IEEE. [WWW ]
    Abstract:
    In WDM backbone networks, the traffic pattern evolves constantly due to the nature of the demand itself or because of equipment failures leading to reroute affected connections. In this context, requests are routed greedily using available resources without changing the routing of pre-established connections. However, such a policy leads to a poor usage of resources and so higher blocking probability: new connection requests might be rejected while network resources are sufficient to serve all the traffic. Therefore, it is important to regularly reconfigure the network by rerouting established connections in order to optimize the usage of network resources. In this paper, we consider the network reconfiguration problem that consists in switching existing connections one after the other from the current routing to a new pre-computed routing. Due to cyclic dependencies between connections, some requests may have to be temporarily interrupted during this process. Clearly, the number of requests simultaneously interrupted has to be minimized. Furthermore, it might be impossible for the network operator to interrupt some connections because of the contract signed with the corresponding clients. In this setting, the network reconfiguration problem consists in going from a routing to another one given that some priority connections cannot be interrupted. The network reconfiguration problem without priority connections has previously been modeled as a cops-and-robber game in [CPPS05,CoSe07]. Here, we first extend this model to handle priority connections. Then we identify cases where no solution exists. Using a simple transformation, we prove that the reconfiguration problem with priority connections can be reduced to the problem without this constraint. Finally, we propose a new heuristic algorithm that improves upon previous proposals.

     
  53. D. Coudert, F. Huc, D. Mazauric, N. Nisse, and J-S. Sereni. Reconfiguration dans les réseaux optiques. In A. Chaintreau and C. Magnien, editors, 11ème Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'09), Carry le Rouet, pages 4p, June 2009. [WWW ] [PDF ]
    Abstract:
    L'\'evolution permanente du trafic, les op\'erations de maintenance et l'existence de pannes dans les r\'eseaux WDM, obligent \`a rerouter r\'eguli\`erement des connexions. Les nouvelles demandes de connexions sont rout\'ees en utilisant les ressources disponibles et, si possible, sans modifier le routage des connexions existantes. Ceci peut engendrer une mauvaise utilisation des ressources disponibles. Il est donc pr\'ef\'erable de reconfigurer r\'eguli\`erement l'ensemble des routes des diff\'erentes connexions. Un objectif particuli\`erement important est alors de minimiser le nombre de requ\^etes simultan\'ement interrompues lors de la reconfiguration. Nous proposons une heuristique pour r\'esoudre ce probl\`eme dans les r\'eseaux WDM. Les simulations montrent que cette heuristique r\'ealise de meilleures performances que celle propos\'ee par Jose et Somani (2003). Nous proposons \'egalement un mod\`ele permettant de prendre en compte diff\'erentes classes de clients, avec notamment la contrainte que des requ\^etes, dites prioritaires, ne peuvent pas \^etre interrompues. Une simple transformation permet de r\'eduire le probl\`eme avec requ\^etes prioritaires au probl\`eme initial. De ce fait, notre heuristique s'applique \'egalement au cas autorisant des requ\^etes prioritaires.

     
  54. D. Coudert, D. Mazauric, and N. Nisse. On Rerouting Connection Requests in Networks with Shared Bandwidth. In DIMAP workshop on Algorithmic Graph Theory (AGT09), volume 32 of Electronic Notes in Discrete Mathematics, Warwick, UK, pages 109-116, March 2009. Elsevier. [WWW ] [PDF ]
    Abstract:
    In this paper, we address the problem of scheduling the switching of a set of connection requests one after the other from current routing to another pre-determined routing. We propose a model that handles requests using only a constant fraction of the bandwidth of a link, thus generalizing the model proposed in [CoSe07,JoSo03] for WDM networks. Our main result is the proof that the problem of deciding whether it exists a scheduling of the rerouting of connection requests without traffic interruption is NP-complete even if requests use the third of the bandwidth of a link. Note that the problem is polynomial when the bandwidth of a link cannot be shared [CoSe07].

     
  55. D. Coudert, N. Nepomuceno, and H. Rivano. Minimizing Energy Consumption by Power-Efficient Radio Configuration in Fixed Broadband Wireless Networks. In First IEEE WoWMoM Workshop on Hot Topics in Mesh Networking (HotMESH), Kos, Greece, pages 6p, June 2009. IEEE. [WWW ] [PDF ]
    Abstract:
    "In this paper, we investigate on minimizing the energy consumption of a fixed broadband wireless network through a joint optimization of data routing and radio configuration. The network is modeled by a digraph in which the nodes represent radio base stations and the arcs denote radio links. Under this scenario, a power-efficient configuration can be characterized by a modulation constellation size and a transmission power level. Every link holds a set of power-efficient configurations, each of them associating a capacity with its energy cost. The optimization problem involves deciding the network's configuration and flows that minimize the total energy consumption, while handling all the traffic requirements simultaneously. An exact mathematical formulation of the problem is presented. It relies on a minimum cost multicommodity flow with step increasing cost functions, which is very hard to optimize. We then propose a piecewise linear convex function, obtained by linear interpolation of powerefficient configuration points, that provides a good approximation of the energy consumption on the links, and present a relaxation of the previous formulation that exploits the convexity of the energy cost functions. This yields lower bounds on the energy consumption, and finally a heuristic algorithm based on the fractional optimum is employed to produce feasible solutions. Our models are validated through extensive experiments that are reported and discussed. The results verify the potentialities behind this novel approach. In particular, our algorithm induces a satisfactory integrality gap in practice."

     
  56. D. Coudert, N. Nepomuceno, and H. Rivano. Joint Optimization of Routing and Radio Configuration in Fixed Wireless Networks. In A. Chaintreau and C. Magnien, editors, 11ème Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'09), Carry le Rouet, pages 4p, June 2009. [WWW ] [PDF ]
    Abstract:
    Nous étudions la minimisation de la consommation d'énergie des réseaux sans-fil fixes à transmission par liens micro-ondes, par l'optimisation jointe du routage des flux de données et la sélection de la configuration des liens. Nous présentons une formulation mathématique exacte basée sur un multiflot entier de coût minimum avec des fonctions de coût en escalier, rendant le problème très difficile à résoudre. Nous proposons ensuite une fonction linéaire par morceaux convexe, obtenue par interpolation linéaire des points de configuration efficaces en énergie, qui fournit une bonne approximation de la consommation d'énergie sur les liens, et présentons une relaxation qui exploite la convexité des fonctions de coût. Ceci rapporte des limites inférieures sur la consommation d'énergie, et finalement un algorithme heuristique basé sur l'optimum fractionnaire est utilisé pour produire des solutions réalisables. Les résultats attestent du potentiel de notre nouvelle approche.

     
  57. O. Dalle, F. Giroire, J. Monteiro, and S. Pérennes. Analysis of Failure Correlation Impact on Peer-to-Peer Storage Systems. In Proceedings of the 9th IEEE International Conference on Peer-to-Peer Computing (P2P), pages 184--193, September 2009. [WWW ] [PDF ]
    Abstract:
    Peer-to-peer storage systems aim to provide a reliable long-term storage at low cost. In such systems, peers fail continuously, hence, the necessity of self-repairing mechanisms to achieve high durability. In this paper, we propose and study analytical models that assess the bandwidth consumption and the probability to lose data of storage systems that use erasure coded redundancy. We show by simulations that the classical stochastic approach found in the literature, that models each block independently, gives a correct approximation of the system average behavior, but fails to capture its variations over time. These variations are caused by the simultaneous loss of multiple data blocks that results from a peer failing (or leaving the system). We then propose a new stochastic model based on a fluid approximation that better captures the system behavior. In addition to its expectation, it gives a correct estimation of its standard deviation. This new model is validated by simulations.

     
  58. O. Dalle, F. Giroire, J. Monteiro, and S. Pérennes. Analyse des Corrélations entre Pannes dans les Systèmes de Stockage Pair-à-Pair. In Augustin Chaintreau and Clemence Magnien, editors, 11ème rencontres francophones sur les Aspects Algorithmiques des Télécommunications (Algotel'2009), Carry-Le-Rouet France, pages 4p, 2009.
    Note: Best Student Paper Award. [WWW ] [PDF ]
    Abstract:
    {D}ans cet article, nous pr{\'e}sentons et {\'e}tudions des mod{\`e}les analytiques de syst{\`e}mes de stockage pair-{\`a}-pair fiables {\`a} long terme. {L}es pairs sont sujets {\`a} des pannes d{\'e}finitives (d{\'e}faillance du disque, d{\'e}part du pair) induisant la perte de toutes les donn{\'e}es stock{\'e}es par le pair. {C}es pannes ont lieu en continu. {A}fin de p{\'e}renniser les donn{\'e}es il est indispensable d'user de redondance et de maintenir celle-ci au moyen d'un processus permanent de reconstruction. {D}ans un premier temps nous consid{\'e}rons une approche classiquement utilis{\'e}e dans la litt{\'e}rature, consistant {\`a} mod{\'e}liser chaque bloc par une cha{\^i}ne de {M}arkov et {\`a} n{\'e}gliger les interd{\'e}pendances entre blocs. {S}i celle-ci permet le calcul du comportement moyen du syst{\`e}me (par exemple la demande moyenne en bande passante), elle est insuffisante pour en {\'e}valuer les fluctuations. {N}os simulations d{\'e}montrent que ces fluctuations sont tr{\`e}s importantes m{\^e}me pour des grands syst{\`e}mes comportant des milliers de pairs. {N}ous proposons alors un nouveau mod{\`e}le stochastique prenant en compte l'interd{\'e}pendance des pannes de blocs, et nous en donnons une approximation fluide. {C}eci nous permet de caract{\'e}riser le comportement du syst{\`e}me (calcul de tous les moments) mais aussi de le simuler efficacement, car il est ind{\'e}pendant de la taille du syst{\`e}me. {L}a pertinence de notre mod{\`e}le est valid{\'e}e en comparant les r{\'e}sultats obtenus par des simulations utilisant d'un c{\^o}t{\'e} notre mod{\`e}le fluide et de l'autre un mod{\`e}le {\`a} {\'e}v{\'e}nements discrets reproduisant fid{\`e}lement le comportement du syst{\`e}me.

     
  59. A. Ferreira. Road-mapping the Digital Revolution: Visions from COST Foresight 2030 (An exercise in multi-disciplinarity). In Proceedings of IEEE Wireless VITAE'09, Aalborg, Denmark, pages 5p, May 2009. IEEE Press. [PDF ]
    Abstract:
    From innovation triggered by user virtual communities to remote surgery and new financial instruments, the creative power of individuals is being fostered at proportions previously unseen. The main driver enabling such a pace of innovation, scientific progress, and user adoption is the Digital Revolution. One consequence is that interrelationships between science, technology and society are increasing in complexity and harder to understand. COST Foresight 2030 is an initiative encompassing a set of events designed to explore a multi-disciplinary vision for a future permeated and shaped by the digital revolution. This paper describes the vision behind COST Foresight 2030 and highlights several issues that are likely to become central in the next decades.

     
  60. M. Flammini, A. Marchetti-Spaccamela, G. Monaco, L. Moscardelli, and S. Zaks. On the complexity of the regenerator placement problem in optical networks. In Proceedings of the 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2009), Calgary, Canada, pages 154-162, August 2009. ACM. [WWW ] [PDF ]
    Abstract:
    Placement of regenerators in optical networks has attracted the attention of recent research works in optical networks. In this problem we are given a network, with an underlying topology of a graph G, and with a set of requests that correspond to paths in G. There is a need to put a regenerator every certain distance, because of a decrease in the power of the signal. In this work we investigate the problem of minimizing the number of locations to place the regenerators. We present analytical results regarding the complexity of this problem, in four cases, depending on whether or not there is a bound on the number of regenerators at each node, and depending on whether or not the routing is given or only the requests are given (and part of the solution is also to determine the actual routing). These results include polynomial time algorithms, NP-complete results, approximation algorithms, and inapproximability results.

     
  61. M. Flammini, G. Monaco, L. Moscardelli, H. Shachnai, M. Shalom, T. Tamir, and S. Zaks. Minimizing total busy time in parallel scheduling with application to optical networks. In Proceedings of the 23rd IEEE International Parallel and Distributed Processing Symposium (IPDPS 2009), Rome, Italy, pages 1-12, May 2009. IEEE. [WWW ] [PDF ]
    Abstract:
    We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J1,..., Jn}. Each job, Jj, is associated with an interval [sj, cj] along which it should be processed. Also given is the parallelism parameter g ges 1, which is the maximal number of jobs that can be processed simultaneously by a single machine. Each machine operates along a contiguous time interval, called its busy interval, which contains all the intervals corresponding to the jobs it processes. The goal is to assign the jobs to machines such that the total busy time of the machines is minimized. The problem is known to be NP-hard already for g = 2. We present a 4-approximation algorithm for general instances, and approximation algorithms with improved ratios for instances with bounded lengths, for instances where any two intervals intersect, and for instances where no interval is properly contained in another. Our study has important application in optimizing the switching costs of optical networks.

     
  62. N. Fountoulakis and B. Reed. A general critical condition for the emergence of a giant component in random graphs with given degrees. In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2009), volume 34 of Electronic Notes on Discrete Mathematics, Bordeaux, France, pages 639--645, September 2009.
     
  63. P. Giabbanelli. Why having in-person lectures when e-learning and podcasts are available?. In Proceedings of the 14th Western Canadian Conference on Computing Education (ACM SIGCSE), pages 42-44, 2009.
     
  64. F. Giroire, J. Chandrashekar, N. Taft, E. Schooler, and K. Papagiannaki. Exploiting Temporal Persistence to Detect Covert Botnet Channels. In Springer, editor, 12th International Symposium on Recent Advances in Intrusion Detection (RAID'09), volume 5758 of Lecture Notes in Computer Science, Saint Malo, France, pages 326--345, September 2009. [PDF ]
    Abstract:
    We describe a method to detect botnet command and control traffic and individual end-hosts. We introduce the notion of †destination traffic atoms†which aggregate the destinations and services that are communicated with. We then compute the †persistence†, which is a measure of temporal regularity and that we propose in this paper, for individual destination atoms. Very persistent destination atoms are added to a host's whitelist during a training period. Subsequently, we track the persistence of new destination atoms not already whitelisted, to identify suspicious C&C destinations. A particularly novel aspect is that we track persistence at multiple timescales concurrently. Importantly, our method does not require any a-priori information about destinations, ports, or protocols used in the C&C, nor do we require payload inspection. We evaluate our system using extensive user traffic traces collected from an enterprise network, along with collected botnet traces. We demonstrate that our method correctly identifies a botnet's C&C traffic, even when it is very stealthy. We also show that filtering outgoing traffic with the constructed whitelists dramatically improves the performance of traditional anomaly detectors. Finally, we show that the C&C detection can be achieved with a very low false positive rate.

     
  65. F. Giroire, J. Monteiro, and S. Pérennes. P2P Storage Systems: How Much Locality Can They Tolerate?. In Proceedings of the 34th IEEE Conference on Local Computer Networks (LCN), pages 320--323, October 2009. [PDF ]
    Keywords: P2P storage system, data placement, performance evaluation, data durability.
    Abstract:
    Large scale peer-to-peer systems are foreseen as a way to provide highly reliable data storage at low cost. To achieve high durability, such P2P systems encode the user data in a set of redundant fragments and distribute them among the peers. In this paper, we study the impact of different data placement strategies on the system performance when using erasure codes redundancy schemes. We compare three policies: two of them local, in which the data are stored in logical neighbors, and the other one global, in which the data are spread randomly in the whole system. We focus on the study of the probability to lose a data block and the bandwidth consumption to maintain enough redundancy. We use simulations to show that, without resource constraints, the average values are the same no matter which placement policy is used. However, the variations in the use of bandwidth are much more bursty under the local policies. When the bandwidth is limited, these bursty variations induce longer maintenance time and henceforth a higher risk of data loss. Finally, we propose a new external reconstruction strategy and a suitable degree of locality that could be introduced in order to combine the efficiency of the global policy with the practical advantages of a local placement.

     
  66. C. Gomes and J. Galtier. Optimal and Fair Transmission Rate Allocation Problem in Multi-hop Cellular Networks. In 8th International Conference on AD-HOC Networks & Wireless (ADHOC NOW), volume 5793 of Lecture Notes in Computer Science, Murcia, Spain, pages 327-340, September 2009. Springer. [PDF ]
    Abstract:
    We deal with the rate allocation problem for downlink in a Multi-hop Cellular Network. A mathematical model is provided to assign transmission rates in order to reach an optimal and fair solution. We prove that under some conditions that are often met, the problem can be reduced to a single-hop cellular network problem. The validity of our proof is confirmed experimentally.

     
  67. D. Gonçalves, F. Havet, A. Pinlou, and S. Thomassé. Spanning galaxies in digraphs. In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2009), volume 34 of Electronic Notes on Discrete Mathematics, Bordeaux, France, pages 139--143, September 2009. [PDF ]
    Abstract:
    A \emph{star} is an arborescence in which the root dominates all the other vertices. A \emph{galaxy} is a vertex-disjoint union of stars. The \emph{directed star arboricity} of a digraph $D$,denoted by $dst(D)$, is the minimum number of galaxies needed to cover $A(D)$. In this paper, we show that $dst(D)\leq \Delta(D)+1$ and that if $D$ is ascyclic then $dst(D)\leq \Delta(D)$. These results are proving by considering the existence of spanning galaxy in digraphs. Thus, we study the problem of deciding whether a digraph $D$ has a spanning galaxy or not. We show that it is NP-complete (even when restricted to acyclic digraphs) but that it becomes polynomial-time solvable when restricted to strongly connected digraphs.

     
  68. F. Guinand and B. Onfroy. MANET : étude de l'impact de la mobilité sur la connexité du réseau. In 11èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'09), pages 2p, June 2009.
    Note: Poster. [PDF ]
    Keywords: réseau mobile ad-hoc, graphe dynamique, MANET, connexité, algorithme.
    Abstract:
    Avec la multiplication des terminaux communiquant, les r\'eseaux ad-hoc dynamiques ont maintenant la capacit\'e de se d\'evelopper. Ces r\'eseaux ne poss\`edent pas d'infrastructure fixe, et les d\'eplacements rapides des terminaux rendent instables les voisins de ces noeuds mobiles. Dans l'objectif de concevoir des m\'ethodes d\'ecentralis\'ees efficaces, nos travaux actuels tentent d'\'evaluer l'impact des diff\'erents param\`etres de mobilit\'e sur la connexit\'e du graphe repr\'esentatif du r\'eseau form\'e par ces terminaux mobiles. Le mod\`ele de mobilit\'e \'etudi\'e est le Random Waypoint. L'objectif est donc de d\'eterminer quels param\`etres de mobilit\'e (vitesse de d\'eplacement, temps de pause, ...) ont un impact significatif sur la connexit\'e du r\'eseau.

     
  69. F. Havet and C. Linhares Sales. Combinatória e Problemas em Redes de Telecomunicações. In Colloque d'Informatique: Brésil / INRIA, Coopérations, Avancées et Défis, Bento Gonçalves, Brazil, pages 4p, July 2009. [PDF ]
    Abstract:
    In this paper, we summarize some problems arising in telecommunication networks which have been studied in the scope of the cooperation between our teams ParGO (UFC) and Mascotte (INRIA). We also present their modeling by graph coloring problems and some partial results we have ob- tained.

     
  70. J. Himmelspach, O. Dalle, and J. Ribault. Design considerations for M&S software. In D. Rossetti, R. R. Hill, B. Johansson, A. Dunkin, and R. G. Ingalls, editors, Proceedings of the Winter Simulation Conference (WSC'09), Austin, TX, pages 12p, December 2009.
    Note: Invited Paper. [WWW ] [PDF ]
    Abstract:
    The development of M&S products often seems to be driven by need: people start coding because they are interested in either a concrete simulation study, or they are interested in a (single) research subject of M&S methodology. We claim that discussing, designing, developing, and comparing M&S products should be based on software engineering concepts. We shortly introduce some of these engineering concepts and discuss how these relate to the M&S domain. By describing two examples, OSA and JAMES II, we illustrate that reuse might play an important role in the development of high quality M&S products as the examples allow reuse on the level of models and scenarios, on the level of "simulation studies", of algorithms (e.g., reuse of event queues, random number generators), across hardware architectures / operating systems, and of analysis tools.

     
  71. K. Kawarabayashi and B. Reed. A nearly linear time algorithm for the half integral parity disjoint paths packing problem. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithm (SODA 2009), pages 1183--1192, January 2009. [WWW ] [PDF ]
    Abstract:
    We consider the following problem, which is called the half integral parity disjoint paths packing problem. Input: A graph G, k pair of vertices (s1, t1), (s2, t2), ...,(sk, tk) in G (which are sometimes called terminals), and a parity li for each i with $1 \leq i \leq k$, where li = 0 or 1. Output: Paths P1, ..., Pk in G such that Pi joins si and ti for i = 1, 2, ..., k and parity of length of the path Pi is li, i.e, if li = 0, then length of Pi is even, and if li = 1, then length of Pi is odd for i = 1, 2, ..., k. In addition, each vertex is on at most two of these paths. We present an O(m \alpha(m, n) log n) algorithm for fixed k, where n, m are the number of vertices and the number of edges, respectively, and the function \alpha(m, n) is the inverse of the Ackermann function (see by Tarjan [43]). This is the first polynomial time algorithm for this problem, and generalizes polynomial time algorithms by Kleinberg [23] and Kawarabayashi and Reed [20], respectively, for the half integral disjoint paths packing problem, i.e., without the parity requirement. As with the Robertson-Seymour algorithm to solve the k disjoint paths problem, in each iteration, we would like to either use a huge clique minor as a "crossbar", or exploit the structure of graphs in which we cannot find such a minor. Here, however, we must maintain the parity of the paths and can only use an "odd clique minor". We must also describe the structure of those graphs in which we cannot find such a minor and discuss how to exploit it. We also have algorithms running in O(m(1 + \epsilon)) time for any \epsilon > 0 for this problem, if k is up to o(log log log n) for general graphs, up to o(log log n) for planar graphs, and up to o(log log n/g) for graphs on the surface, where g is Euler genus. Furthermore, if k is fixed, then we have linear time algorithms for the planar case and for the bounded genus case.

     
  72. K. Kawarabayashi and B. Reed. Hadwiger's Conjecture is decidable. In 41th ACM Symposium on Theory of Computing (STOC 2009), pages 445--454, 2009. [WWW ] [PDF ]
    Abstract:
    The famous Hadwiger's conjecture asserts that every graph with no Kt-minor is (t-1)-colorable. The case t=5 is known to be equivalent to the Four Color Theorem by Wagner, and the case t=6 is settled by Robertson, Seymour and Thomas. So far the cases t \geq 7 are wide open. In this paper, we prove the following two theorems: There is an O(n2) algorithm to decide whether or not a given graph G satisfies Hadwiger's conjecture for the case t. Every minimal counterexample to Hadwiger's conjecture for the case t has at most f(t) vertices for some explicit bound f(t). The bound f(t) is at most pppt, where p=101010t. Our proofs for both results use the well-known result by Thomassen [46] for 5-list-coloring planar graphs, together with some results (but not the decomposition theorem) of Graph Minors in [36]. Concerning the first result, we prove the following stronger theorem: For a given graph G and any fixed t, there is an O(n2) algorithm to output one of the following: a (t-1)-coloring of G, or a Kt- minor of G, or a minor H of G of order at most f(t) such that H does not have a Kt-minor nor is (t-1)-colorable. The last conclusion implies that H is a counterexample to Hadwiger's conjecture with at most f(t) vertices for the case t. The time complexity of the algorithm matches the best known algorithms for 4-coloring planar graphs (the Four Color Theorem), due to Appel and Hakken, and Robertson, Sanders, Seymour and Thomas, respectively. Let us observe that when t=5, the algorithm gives rise to an algorithm for the Four Color Theorem. The second theorem follows from our structure theorem, which has the following corollary: Every minimal counterexample G to Hadwiger's conjecture for the case t either has at most f(t) vertices, or has a vertex set Z of order at most t-5 such that G-Z is planar. It follows from the Four Color Theorem that the second assertion does not happen to any minimal counterexample to Hadwiger's conjecture for the case t. Thus in constant time, we can decide Hadwiger's conjecture for the case t.

     
  73. S. Kennedy, C. Meagher, and B. Reed. Fractionally Edge Colouring Graphs with Large Maximum Degree in Linear Time. In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2009), volume 34 of Electronic Notes on Discrete Mathematics, Bordeaux, France, pages 47--51, September 2009.
    Abstract:
    For any c>1, we describe a linear time algorithm for fractionally edge colouring simple graphs with maximum degree at least |V|/c.

     
  74. Z. Li and I. Sau. Graph Partitioning and Traffic Grooming with Bounded Degree Request Graph. In 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009), volume 5911 of Lecture Notes in Computer Science, pages 250-261,, June 2009.
    Note: Best student paper award. [PDF ]
    Abstract:
    We study a graph partitioning problem which arises from traffic grooming in optical networks. We wish to minimize the equipment cost in a SONET WDM ring network by minimizing the number of Add-Drop Multiplexers (ADMs) used. We consider the version introduced by Mu{\~n}oz and Sau~[Mu{\~n}oz and Sau, WG 08] where the ring is unidirectional with a grooming factor $C$, and we must design the network (namely, place the ADMs at the nodes) so that it can support \emph{any} request graph with maximum degree at most $\Delta$. This problem is essentially equivalent to finding the least integer $M(C,\Delta)$ such that the edges of any graph with maximum degree at most $\Delta$ can be partitioned into subgraphs with at most $C$ edges and each vertex appears in at most $M(C,\Delta)$ subgraphs~[Mu{\~n}oz and Sau, WG 08] . The cases where $\Delta=2$ and $\Delta=3,C\neq 4$ were solved by Mu{\~n}oz and Sau~[Mu{\~n}oz and Sau, WG 08] . In this article we establish the value of $M(C,\Delta)$ for many more cases, leaving open only the case where $\Delta \geq 5$ is odd, $\Delta \pmod{2C}$ is between $3$ and $C-1$, $C\geq 4$, and the request graph does not contain a perfect matching. In particular, we answer a conjecture of~[Mu{\~n}oz and Sau, WG 08] .

     
  75. C. Linhares Sales and L. Sampaio. b-coloring of m-tight graphs. In T. Liebling and J. Szwarcfiter, editors, LAGOS'09 - V Latin-American Algorithms, Graphs and Optimization Symposium, volume 35 of Electronic Notes in Discrete Mathematics, Gramado, Brazil, pages 209 - 214, March 2009. Elsevier. [WWW ] [PDF ]
     
  76. J-C. Maureira Bravo, D. Dujovne, and O. Dalle. Generation of Realistic 802.11 Interferences in the OMNeT++ INET Framework Based on Real Traffic Measurements. In Second International Workshop on OMNeT++, Rome, Italy, pages 8p, March 2009. [PDF ]
    Abstract:
    Realistic simulation of 802.11 traffic subject to high interference, for example in dense urban areas, is still an open issue. Many studies do not address the interference problem properly. In this paper, we present our preliminary work on a method to recreate interference traffic from real measurements. The method consists in capturing real traffic traces and generating interference patterns based on the recorded information. Furthermore, we assume that the coordinates of the sources of interference in the real scene are not known a priori. We introduce an extension to Omnet++ INET-Framework to replay the recreated interference in a transparent way into a simulation. We validate our proposed method by comparing it against the real measurements taken from the scene. Furthermore we present an evaluation of how the injected interference affects the simulated results on three arbitrary simulated scenarios.

     
  77. J-C. Maureira Bravo, P. Uribe, O. Dalle, T. Asahi, and J. Amaya. Component based approach using OMNeT++ for Train Communication Modeling. In Proceedings of 9th International Conference on ITS Telecommunication, Lille, France, pages 6p, October 2009. [PDF ]
    Abstract:
    This paper reports on our experience in using OMNeT++ to develop a network simulator focused on railway environments. Common design problems are analyzed, making emphasis on radio communication models. Scalability issues are raised when modeling the large topologies that are associated with railway communications. Our conclusions point out that model reusability must be reinforced and that a component-based design must be adopted in order to build a tool for generating valuable performance results.

     
  78. G. Mertzios, I. Sau, and S. Zaks. A New Intersection Model and Improved Algorithms for Tolerance Graphs. In 35th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2009), volume 5911 of Lecture Notes in Computer Science, pages 285-295, 06 2009. [PDF ]
    Abstract:
    Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in con ict. This class of graphs, which generalizes in a natural way both interval and permutation graphs, has attracted many research efforts since their introduction in [10], as it finds many important applications in constraint-based temporal reasoning, resource allocation and scheduling problems, among others. In this article we propose the first non-trivial intersection model for general tolerance graphs, given by three-dimensional parallelepipeds, which extends the widely known intersection model of parallelograms in the plane that characterizes the class of bounded tolerance graphs. Apart from being important on its own, this new representation also enables us to improve the time complexity of three problems on tolerance graphs. Namely, we present optimal ${\cal O}(n \log n)$ algorithms for computing a minimum coloring and a maximum clique, and an ${\cal O}(n2)$ algorithm for computing a maximum weight independent set in a tolerance graph with n vertices, thus improving the best known running times ${\cal O}(n2)$ and ${\cal O}(n3)$ for these problems, respectively.

     
  79. C. Molle and M-E. Voge. Effects of the Acknowledgment Traffic on the Capacity of Wireless Mesh Networks. In 69th IEEE Vehicular Technology Conference (VTC2009-Spring), Barcelona, Spain, pages 5p, April 2009. [PDF ]
    Abstract:
    Since the emergence of ubiquitous computing, evaluating wireless network performances has become one of the major economic issues. Among the existing performance indicators, the network {\em capacity}, defined as the maximal amount of flow carried by a topology during a fixed time period, is essential. Some cross-layer characteristics have to be taken into account in order to optimally allocate the common resources. In this article, a comparative study is done between interference consequences in the two following models: (i) usual IEEE 802.11 MAC layer with acknowledgments at each hop, and (ii) block acknowledgments reported at the transport layer that can be included in the IEEE 802.16 standard. Cross-layer properties are modeled in a linear programming formulation that is solved using the column generation process. We quantify the gain in capacity induced by the move of the MAC acknowledgments into the transport layer, and show the better load distribution obtained in the network with the second model.

     
  80. M. Molloy and B. A. Reed. Asymptotically optimal frugal colouring. In Proceedings of Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 106-114, 2009. [WWW ] [PDF ]
    Abstract:
    We prove that every graph with maximum degree \Delta can be properly (\Delta + 1)-coloured so that no colour appears more than O(log \Delta / log log \Delta) times in the neighbourhood of any vertex. This is best possible up to the constant factor in the O(−) term. We also provide an efficient algorithm to produce such a colouring.

     
  81. N. Nisse, I. Rapaport, and K. Suchan. Distributed computing of efficient routing schemes in generalized chordal graphs. In Proceedings of the 16th International Colloquium on Structural Information and Communication Complexity (SIROCCO), volume 5869 of Lecture Notes in Computer Science, Piran, Slovenia, pages 252-265, 2009. Springer-Verlag. [PDF ]
    Abstract:
    Efficient algorithms for computing routing tables should take advantage of the particular properties arising in large scale networks. There are in fact at least two properties that any routing scheme must consider: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Therefore, we propose a routing scheme that computes short routes in the class of k-chordal graphs, i.e., graphs with no chordless cycles of length more than k. We study the tradeoff between the length of routes and the time complexity for computing them. In the class of k-chordal graphs, our routing scheme achieves an additive stretch of at most k − 1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k − 1. In order to compute the routing tables of any n-node graph with diameter D we propose a distributed algorithm which uses O(log n)-bit messages and takes O(D) time. We then propose a slightly modified version of the algorithm for computing routing tables in time O(min{∆D, n}), where ∆ is the the maximum degree of the graph. Using these tables, our routing scheme achieves a better additive stretch of 1 in chordal graphs (notice that chordal graphs are 3-chordal graphs). The routing scheme uses addresses of size log n bits and local memory of size 2(d − 1) log n bits in a node of degree d.

     
  82. J. Ribault and O. Dalle. OSA : A Federative Simulation Platform. In Proceedings of the Winter Simulation Conference (WSC'09), Austin, TX, USA, 2009.
    Note: Ph.D. Colloquium. [WWW ]
    Abstract:
    {OSA} ({O}pen {S}imulation {A}rchitecture) is a collaborative platform for component-based discrete-event simulation. {I}t has been created to support both {M}\&{S} studies and research on {M}\&{S} techniques and methodology. {T}he {OSA} project started from the observation that despite no single simulation software seems to be perfect, most of the elements required to make a perfect simulator already exist as part of existing simulators. {H}ence, the particular area of research that motivated the {OSA} project is to investigate practical means of reusing and combining any valuable piece of {M}\&{S} software at large, including models, simulation engines and algorithms, and supporting tools for the {M}\&{S} methodology. {T}o achieve this goal, the {OSA} project investigates in advanced software engineering techniques such as component-based framework, layered patterns and aspect-oriented programming. {I}n cases studies, the {OSA} project is among others involved in a large-scale simulation, and a distributed simulation over the {REST}ful protocol.

     
  83. I. Sau and D. M. Thilikos. Subexponential Parameterized Algorithms for Bounded-Degree Connected Subgraph Problems on Planar Graphs. In DIMAP workshop on Algorithmic Graph Theory (AGT09), volume 32 of Electronic Notes in Discrete Mathematics, Warwick, UK, pages 59-66, March 2009. Elsevier. [PDF ]
    Abstract:
    We present subexponential parameterized algorithms on planar graphs for a family of problems that consist in, given a graph $G$, finding a connected subgraph $H$ with bounded maximum degree, while maximising the number of edges (or vertices) of $H$. These problems are natural generalisations of the \textsc{Longest Path} problem. Our approach uses bidimensionality theory to obtain combinatorial bounds, combined with dynamic programming techniques over a branch decomposition of the input graph. These techniques need to be able to keep track of the connected components of the partial solutions over the branch decomposition, and can be seen as an \emph{algorithmic tensor} that can be applied to a wide family of problems that deal with finding connected subgraphs under certain constraints.

     
  84. I. Sau and D. M. Thilikos. On Self-Duality of Branchwidth in Graphs of Bounded Genus. In 8th Cologne Twente Workshop on Graphs and Combinatorial Optimization (CTW), Paris, France, pages 19-22, June 2009. [PDF ]
    Abstract:
    A graph parameter is self-dual in some class of graphs embeddable in some surface if its value does not change in the dual graph more than a constant factor. Self-duality has been examined for several width-parameters, such as branchwidth in graphs in some surface. In this direction, we prove that ${\mathbf bw}(G^*) \leq 6\times {\mathbf bw}(G) +2g-4$ for any graph $G$ embedded in a surface of Euler genus $g$.

     
  85. A. Silva, P. Reyes, and M. Debbah. Congestion in Randomly Deployed Wireless Ad-Hoc and Sensor Networks. In International Conference on Ultra Modern Telecommunications, St. Petersburg, Russia, pages 10p, October 2009. [WWW ] [PDF ]
    Keywords: Random Matrix Theory, Random Graph Theory, Wireless Ad-Hoc Networks, Wireless Sensor Networks.
    Abstract:
    Congestion in wireless ad-hoc sensor networks not only causes packet loss and increases queueing delay, but also leads to unnecessary energy consumption. In these networks, two types of congestion can occur: node-level congestion, which is caused by buffer overflow in the node, or link-level congestion, when wireless channels are shared by several nodes arising in collisions. We study a measure of link-level congestion in static wireless ad-hoc and sensor networks randomly deployed over an area. The measure of congestion considered is the inverse of the greatest eigenvalue of the adjacency matrix of the random graph. This measure gives an approximation of the average quantity of wireless links of a certain length on the network. We review the results to find this measure in Bernoulli random graphs. We use tools from random graph and random matrix theory to extend this measure on Geometric random graphs.

     
  86. F. Solano Donado and J. Moulierac. Routing in All-Optical Label Switched-based Networks with Small Label Spaces. In 13th Conference on Optical Network Design and Modeling (ONDM), Braunschweig, Germany, pages 6p, February 2009. IFIP/IEEE. [WWW ]
    Abstract:
    With the development of All-Optical Label Switching (AOLS) network, nodes are capable of forwarding labeled packets without performing Optical-Electrical-Optical (OEO) conversions, speeding up the forwarding. However, this new technology also brings new constraints and, consequently, new problems have to be adressed. We study in this paper the problem of routing a set of demands in such a network, considering that routers have limited label space, preventing from the usage of label swapping techniques. Label stripping is a solution that ensures forwarding, concerning these constraints, of all the paths at expenses of increasing the stack size and wasting bandwith. We propose an intermediate feasible solution that keeps the GMPLS stack size smaller than label stripping, in order to gain bandwidth resources. After proposing an heuristic for this problem, we present simulations that show the performance of our solution.

     
  87. J. Araujo, N. Cohen, F. Giroire, and F. Havet. Good edge-labelling of graphs. Research Report 6934, INRIA, 2009. [WWW ] [PDF ]
    Keywords: graph theory, complexity, edge-labelling, planar graphs, matching-cut, channel assignment.
    Abstract:
    A {\em good edge-labelling} of a graph ${G}$ is a labelling of its edges such that, for any ordered pair of vertices $(x,y)$, there do not exist two paths from $x$ to $y$ with increasing labels. {T}his notion was introduced in~\cite{{BCP}} to solve wavelength assignment problems for specific categories of graphs. {I}n this paper, we aim at characterizing the class of graphs that admit a good edge-labelling. {F}irst, we exhibit infinite families of graphs for which no such edge-labelling can be found. {W}e then show that deciding if a graph admits a good edge-labelling is {NP}-complete. {F}inally, we give large classes of graphs admitting a good edge-labelling: forests, ${C}_3$-free outerplanar graphs, planar graphs of girth at least 6, subcubic ${{C}_3,{K}_{2,3}}$-free graphs.

     
  88. J-C. Bermond, C.J. Colbourn, L. Gionfriddo, G. Quattrocchi, and I. Sau. Drop cost and wavelength optimal two-period grooming with ratio 4. Technical report RR-7101, INRIA, November 2009. [PDF ]
    Abstract:
    We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time, there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and $C=4$ and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.

     
  89. J-C. Bermond, M. Cosnard, and S. Pérennes. Directed acyclic graphs with unique path property. Technical report 6932, INRIA, May 2009. [WWW ] [PDF ]
    Abstract:
    Let P be a family of dipaths of a DAG (Directed Acyclic Graph) G. The load of an arc is the number of dipaths containing this arc. Let π(G, P) be the maximum of the load of all the arcs and let w(G, P) be the minimum number of wavelengths (colors) needed to color the family of dipaths P in such a way that two dipaths with the same wavelength are arc-disjoint. There exist DAGs such that the ratio between w(G, P) and π(G, P) cannot be bounded. An internal cycle is an oriented cycle such that all the vertices have at least one prede- cessor and one successor in G (said otherwise every cycle contain neither a source nor a sink of G). We prove that, for any family of dipaths P, w(G, P) = π(G, P) if and only if G is without internal cycle. We also consider a new class of DAGs, which is of interest in itself, those for which there is at most one dipath from a vertex to another. We call these digraphs UPP-DAGs. For these UPP-DAGs we show that the load is equal to the maximum size of a clique of the conflict graph. We prove that the ratio between w(G, P) and π(G, P) cannot be bounded (a result conjectured in an other article). For that we introduce “good labelings” of the conflict graph associated to G and P, namely labelings of the edges such that for any ordered pair of vertices (x, y) there do not exist two paths from x to y with increasing labels.

     
  90. J-C. Bermond, D. Coudert, J. Moulierac, S. Perennes, H. Rivano, I. Sau, and F. Solano Donado. MPLS label stacking on the line network. Technical report RR-6803, INRIA, January 2009. [WWW ] [PDF ]
    Abstract:
    All-Optical Label Switching (AOLS) is a new technology that performs forwarding without any Optical-Electrical-Optical (OEO) conversions. In this report, we study the problem of routing a set of requests in AOLS networks with the aim of minimizing the number of labels required to ensure the forwarding. In order to spare the label space, we consider label stacking, allowing the configuration of tunnels. We study particularly this network design problem when the network is a line. We provide an exact algorithm for the case in which all the requests have a common source and present some approximation algorithms and heuristics when an arbitrary number of sources are distributed over the line. We contrast the performance of our proposed algorithms by simulations.

     
  91. J-C. Bermond, D. Coudert, J. Moulierac, S. Perennes, I. Sau, and F. Solano Donado. GMPLS Label Space Minimization through Hypergraph Layouts. Research Report RR-7071, INRIA, October 2009. [WWW ] [PDF ]
    Keywords: GMPLS, optical networks, label stacking, hypergraph layout, approximation algorithms, dynamic programming..
    Abstract:
    {A}ll-{O}ptical {L}abel {S}witching ({AOLS}) is a new technology that performs packet forwarding without any optical-electrical-optical conversions. {I}n this report, we study the problem of routing a set of requests in {AOLS} networks using {GMPLS} technology, with the aim of minimizing the number of labels required to ensure the forwarding. {W}e first formalize the problem by associating to each routing strategy a logical hypergraph, called a hypergraph layout, whose hyperarcs are dipaths of the physical graph, called tunnels in {GMPLS} terminology. {W}e define a cost function for the hypergraph layout, depending on its total length plus its total hop count. {M}inimizing the cost of the design of an {AOLS} network can then be expressed as finding a minimum cost hypergraph layout. {W}e prove hardness results for the problem, namely for general directed networks we prove that it is {NP}-hard to find a {C} log n-approximation, where {C} is a positive constant and n is the number of nodes of the network. {F}or symmetric directed networks, we prove that the problem is {APX}-hard. {T}hese hardness results hold even if the traffic instance is a partial broadcast. {O}n the other hand, we provide approximation algorithms, in particular an {O}(log n)-approximation for symmetric directed networks. {F}inally, we focus on the case where the physical network is a directed path, providing a polynomial-time dynamic programming algorithm for a fixed number k of sources running in {O}(n^{k+2}) time.

     
  92. J-C. Bermond, D. Coudert, J. Moulierac, S. Perennes, I. Sau, and F. Solano Donado. GMPLS Routing Strategies based on the Design of Hypergraph Layouts. Technical report RR-6842, INRIA, February 2009. [WWW ] [PDF ]
    Abstract:
    All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any Optical-Electrical-Optical (OEO) conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formalize the problem by associating to each routing strategy a logical hypergraph whose hyperedges are dipaths of the physical graph, called \emph{tunnels} in GMPLS terminology. Such a hypergraph is called a \emph{hypergraph layout}, to which we assign a cost function given by its physical length plus the total number of hops traveled by the traffic. Minimizing the cost of the design of an AOLS network can then be expressed as finding a minimum cost hypergraph layout. We prove hardness results for the problem, namely $C \log n$ hardness for directed networks and non-existence of \textsc{PTAS} for undirected networks, where $C$ is a a positive constant and $n$ is the number of nodes of the network. These hardness results hold even is the traffic instance is a partial broadcast. On the other hand, we provide an $\mathcal{O}(\log n)$-approximation algorithm to the problem for a general network. Finally, we focus on the case where the physical network is a path, providing a polynomial-time dynamic programming algorithm for a bounded number of sources, thus extending the algorithm of~\cite{BCM+09b} for a single source.

     
  93. J-C. Bermond, D. Coudert, and J. Peters. Online Distributed Traffic Grooming on Path Networks. Technical report RR-6833, INRIA, February 2009. [WWW ] [PDF ]
    Abstract:
    The {\em grooming factor} $C$ of a WDM optical network is the number of connections that can share the bandwidth of each wavelength and the process of grouping the requests that will share each wavelength is called {\em traffic grooming}. The goal of traffic grooming is either to reduce the transmission cost by reducing the number of wavelengths or to reduce the hardware cost by reducing the number of Add-Drop Multiplexors (ADM). In this paper, we investigate traffic grooming for directed path networks with online connection requests and distributed routing algorithms. When connection requests are online, the {\em virtual topology} that results from the assignment of ADMs to wavelengths cannot be changed with each request. The design of efficient virtual topologies that minimize either the number of ADMs needed to satisfy any set of connection requests or the blocking of connection requests depends strongly on the routing algorithm. We show how to design the best possible virtual topologies, independently of the routing algorithm, when each node is equipped with the same number of ADMs, and we analyze the performance of distributed greedy routing algorithms.

     
  94. J-C. Bermond, X. Muñoz, and I. Sau. Traffic Grooming in Bidirectional WDM Ring Networks. Technical report RR-7080, INRIA, October 2009. [WWW ] [PDF ]
    Abstract:
    We study the minimization of ADMs (Add-Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all-to-all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor $C$ and $N$, the size of the ring. We first study exhaustively the cases $C=1$, $C = 2$, and $C=3$, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case $C>3$, focusing specifically on the case $C = k(k+1)/2$ for some $k \geq 1$. We give optimal decompositions for several congruence classes of $N$ using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings.

     
  95. J-C. Bermond, N. Nisse, P. Reyes, and H. Rivano. Fast Data Gathering in Radio Grid Networks. Research Report RR-6851, INRIA, March 2009. [WWW ] [PDF ]
    Abstract:
    The aim of this paper is to design efficient gathering algorithms (data collection) in a Base Station of a wireless multi hop grid network when interferences constraints are present. We suppose the time is slotted and that during one time slot (step) each node can transmit to one of its neighbor at most one data item. Each device is equipped with a half duplex interface; so a node cannot both receive and transmit simultaneously. During a step only non interfering transmissions can be done. In other words, the non interfering calls done during a step will form a matching. The aim is to minimize the number of steps needed to send all messages to the base station, a.k.a. makespan or completion time. The best known algorithm for grids was a multiplicative 1.5-approximation algorithm. In such topologies, we give a very simple +2 approximation algorithm and then a more involved +1 approximation algorithm. Moreover, our algorithms work when no buffering is allowed in intermediary nodes, i.e., when a node receives a message at some step, it must transmit it during the next step.

     
  96. N. Cohen, D. Coudert, D. Mazauric, N. Nepomuceno, and N. Nisse. Tradeoffs when optimizing Lightpaths Reconfiguration in WDM networks.. Technical report RR-7047, INRIA, September 2009. [WWW ] [PDF ]
    Abstract:
    In this report, we study the problem of rerouting a set of lightpaths in WDM networks. The reconfiguration issue arises for instance when it is necessary to improve the usage of resources or when a maintenance operation is planned on a particular link of the network. In order to avoid service interruptions, old lightpaths should not be torn down before the new ones are set up. However, this may not be possible since establishing the new routes of lightpaths may require the release of resources previously seized by old routes. Then it could be important for the operator to minimize 1) the total number of temporarily disrupted lightpaths, and/or 2) the number of concurrent disrupted lightpaths. In this paper, we study the tradeoff between both these conflicting objectives. More precisely, we prove that there exist some instances for which minimizing one of these objectives arbitrarily impairs the quality of the solution for the other one. We show that such bad tradeoffs may happen even in the case of basic network topologies. On the other hand, we exhibit classes of instances where good tradeoffs can be achieved. Finally, we investigate instances from various networks through simulations.

     
  97. N. Cohen and F. Havet. Planar graphs with maximum degree $\Delta\geq 9$ are ($\Delta+1$)-edge-choosable -- short proof. Research Report RR-7098, November 2009. [WWW ]
    Keywords: edge-colouring, list colouring, List Colouring Conjecture, planar graphs.
    Abstract:
    {W}e give a short proof of the following theorem due to {B}orodin~\cite{{B}or90}. {E}very planar graph with maximum degree $\{D}elta\geq 9$ is $(\{D}elta+1)$-edge-choosable.

     
  98. N. Cohen, F. Havet, and T. Müller. Acyclic edge-colouring of planar graphs. Research Report 6876, INRIA, March 2009. [WWW ] [PDF ]
    Abstract:
    A proper edge-colouring with the property that every cycle contains edges of at least three distinct colours is called an {\it acyclic edge-colouring}. The {\it acyclic chromatic index} of a graph $G$, denoted $\chi'_a(G)$ is the minimum $k$ such that $G$ admits an {\it acyclic edge-colouring} with $k$ colours. We conjecture that if $G$ is planar and $\Delta(G)$ is large enough then $\chi'_a(G)=\Delta(G)$. We settle this conjecture for planar graphs with girth at least $5$ and outerplanar graphs. We also show that $\chi'_a(G)\leq \Delta(G) + 25$ for all planar graph $G$, which improves a previous result by Muthu et al.

     
  99. D. Coudert, F. Giroire, and I. Sau. Circuit visiting 10 ordered vertices in infinite grids. Technical report RR-6910, INRIA, 2009. [WWW ] [PDF ]
    Abstract:
    A \emph{circuit} in a simple undirected graph $G=(V,E)$ is a sequence of vertices ${v_1,v_2,\ldots,v_{k+1}}$ such that $v_1=v_{k+1}$ and ${v_i,v_{i+i}} \in E$ for $i=1,\ldots,k$. A circuit $C$ is said to be \emph{edge-simple} if no edge of $G$ is used twice in $C$. In this article we study the following problem: which is the largest integer $k$ such that, given any subset of $k$ ordered vertices of an infinite square grid, there exists an edge-simple circuit visiting the $k$ vertices in the prescribed order? We prove that $k=10$. To this end, we first provide a counterexample implying that $k<11$. To show that $k\geq 10$, we introduce a methodology, based on the notion of core graph, to reduce drastically the number of possible vertex configurations, and then we test each one of the resulting configurations with an \textsc{ILP} solver.

     
  100. D. Coudert, D. Mazauric, and N. Nisse. Routing Reconfiguration/Process Number: Networks with Shared Bandwidth.. Technical report RR-6790, INRIA, January 2009. [WWW ] [PDF ]
    Abstract:
    In this paper, we address the problem of scheduling the switching of a set of connection requests one after the other from current routing to another pre-determined routing. We propose a model that handles requests using only a constant fraction of the bandwidth of a link, thus generalizing the model proposed in~\cite{CoSe07,JoSo03} for WDM networks. Our main result is the proof that the problem of deciding whether it exists a scheduling of the rerouting of connection requests without traffic interruption is NP-complete even if requests use the third of the bandwidth of a link. Note that the problem is polynomial when the bandwidth of a link cannot be shared~\cite{CoSe07}

     
  101. N. Eggemann, F. Havet, and S. Noble. $k$-$L(2,1)$-Labelling for Planar Graphs is NP-Complete for $k\geq 4$. Research Report 6840, INRIA, February 2009. [WWW ] [PDF ]
    Abstract:
    A mapping from the vertex set of a graph $G=(V,E)$ into an interval of integers $0, \dots ,k$ is an $L(2,1)$-labelling of $G$ of span $k$ if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbour are mapped onto distinct integers. It is known that for any fixed $k\ge 4$, deciding the existence of such a labelling is an NP-complete problem while it is polynomial for $k\leq 3$. For even $k\geq 8$, it remains NP-complete when restricted to planar graphs. In this paper, we show that it remains NP-complete for any $k \ge 4$ by reduction from Planar Cubic Two-Colourable Perfect Matching. Schaefer stated without proof that Planar Cubic Two-Colourable Perfect Matching is NP-complete. In this paper we give a proof of this.

     
  102. R. Erman, F. Havet, B. Lidicky, and O. Pangrác. 5-colouring graphs with 4 crossings. Research Report 7110, INRIA, November 2009.
    Abstract:
    We disprove a conjecture of Oporowski and Zhao stating that every graph with crossing number at most 5 and clique number at most 5 is 5-colourable. However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5-colourable. We also show some colourability results on graphs that can be made planar by removing few edges. In particular, we show that if there exists three edges whose removal leaves the graph planar then it is $5$-colourable.

     
  103. F. Giroire, J. Monteiro, and S. Pérennes. P2P Storage Systems: How Much Locality Can They Tolerate?. Research Report RR-7006, INRIA, July 2009. [WWW ] [PDF ]
    Keywords: P2P storage system, data placement, performance evaluation, data durability.
    Abstract:
    {L}arge scale peer-to-peer systems are foreseen as a way to provide highly reliable data storage at low cost. {T}o achieve high durability, such {P}2{P} systems encode the user data in a set of redundant fragments and distribute them among the peers. {W}e study here the impact of different data placement strategies on the system performance when using erasure codes redundancy schemes. {S}everal practical factors (easier control, software reuse, latency) tend to favor data placement strategies that preserve some degree of locality. {I}n this paper, we compare three policies: two of them local, in which the data are stored in logical neighbors, and the other one global, in which the data are spread randomly in the whole system. {W}e focus on the study of the probability to lose a data block and the bandwidth consumption to maintain such redundancy. {W}e use simulations to show that, without resource constraints, the average values are the same no matter which placement policy is used. {H}owever, the variations in the use of bandwidth are much more bursty under the local policies. {W}hen the bandwidth is limited, these bursty variations induce longer maintenance time and henceforth a higher risk of data loss. {W}e then show that a suitable degree of locality could be introduced in order to combine the efficiency of the global policy with the practical advantages of a local placement. {F}inally, we propose a new external reconstruction strategy that greatly improves the performance of local placement strategies.

     
  104. F. Havet, S. Jendrol', R. Soták, and E. Skrabul'aková. Facial non-repetitive edge-colouring of plane graphs. Research Report 6873, INRIA, February 2009. [WWW ] [PDF ]
    Abstract:
    A sequence $r_1,r_2,\dots,r_{2n}$ such that $r_i=r_{n+i}$ for all $1\leq i \leq n$, is called a {\em repetition}. A sequence $S$ is called {\em non-repetitive} if no {\it block} (i.e. subsequence of consecutive terms of $S$) is a repetition. Let $G$ be a graph whose edges are coloured. A trail is called {\em non-repetitive} if the sequence of colours of its edges is non-repetitive. If $G$ is a plane graph, a {\em facial non-repetitive edge-colouring} of $G$ is an edge-colouring such that any {\it facial trail} (i.e. trail of consecutive edges on the boundary walk of a face) is non-repetitive. We denote $\pi'_f(G)$ the minimum number of colours of a facial non-repetitive edge-colouring of $G$. In this paper, we show that $\pi'_f(G)\leq 8$ for any plane graph $G$. We also get better upper bounds for $\pi'_f(G)$ in the cases when $G$ is a tree, a plane triangulation, a simple $3$-connected plane graph, a hamiltonian plane graph, an outerplanar graph or a Halin graph. The bound $4$ for trees is tight.

     
  105. L. Hogie, D. Papadimitriou, I. Tahiri, and F. Majorczyk. Simulating routing schemes on large-scale topologies. Technical report RT-0371, INRIA, November 2009. [WWW ] [PDF ]
    Abstract:
    The expansion of the Internet routing system results in a number of research challenges, in particular, the Border Gateway Protocol (BGP) starts to show its limits a.o. in terms of the number of routing table entries it can dynamically process and control. Dynamic routing protocols showing better scaling properties are thus under investigation. However, because deploying under-development routing protocols on the Internet is not practicable at a large-scale (due to the size of the Internet topology), simulation is an unavoidable step to validate the properties of a newly proposed routing scheme. Unfortunately, the simulation of inter-domain routing protocols over large networks (order of tens of thousands of nodes) poses real challenges due to the limited memory and computational power that computers impose. This paper presents the Dynamic Routing Model simulator \drmsim which addresses the specific problem of large-scale simulations of (inter-domain) routing models on large networks. The motivation for developing a new simulator lies in the limitation of existing simulation tools in terms of the number of nodes they can handle and in the models they propose.

     
  106. F. Huc, C. Molle, N. Nisse, S. Perennes, and H. Rivano. Stability of a local greedy distributed routing algorithm. Technical report RR-6871, INRIA, March 2009. [WWW ] [PDF ]
    Abstract:
    In this work, we study the problem of routing packets between undifferentiated sources and sinks in a network modeled by a multigraph. We provide a distributed and local algorithm that transmits packets hop by hop in the network and study its behaviour. At each step, a node transmits its queued packets to its neighbours in order to optimize a local gradient. This protocol is thus greedy since it does not require to record the history about the past actions, and lazy since it only needs informations of the neighborhood. We prove that this protocol is however optimal in the sense that the number of packets stored in the network stays bounded as soon as the sources injects a flow that another method could have exhausted. We therefore reinforce a result from the literature that worked for differentiated suboptimal flows.

     
  107. J-C. Maureira Bravo, D. Dujovne, and O. Dalle. Network Provisioning for High Speed Vehicles Moving along Predictable Routes - Part 1: Spiderman Handover. Research Report RR-6850, INRIA, 2009. [WWW ]
    Abstract:
    {T}his report presents our on-going work on a new system designed to provide a continuous network connectivity to communicating devices located on-board a vehicle moving at ”high speed” with a predictable trajectory such as trains, subways or buses. {T}he devices on-board the vehicle form a sub-network called the ”in-motion network”. {T}his system we propose is composed of two parts. {T}he mobile part, called {S}piderman {D}evice ({SD}), installed on the roof of the vehicle, and the fixed part is composed of multiples access points, called {W}ireless {S}witch {A}ccess {P}oints ({WS} {AP}s), installed along the predictable route of the vehicle. {T}o provide a continuous connectivity, we designed a new handover algorithm that relies on a two {IEEE}802.11 radio hardware placed in the {SD} device. {T}his dual-radio architecture allows to minimize or even hide the handover effects, achieving a seamless continuous data-link connection at high speeds, up-to 150 {K}m/h and possibly more. {T}he link between the {SD} and the {WS} {AP} forms a {L}ayer 2 {E}thernet {B}ridge, supporting any {L}ayer 3 protocol between the infrastructure network and the in-motion network. {T}his concept has been validated by simulations and is currently tested using a real prototype in order to assess the performances and practical feasibility of the system.

     
  108. J. Rué, I. Sau, and D. M. Thilikos. Dynamic Programming for Graphs on Surfaces. Technical report RR-7166, INRIA, December 2009. [PDF ]
    Abstract:
    We provide a framework for the design of $2^{\mathcal{O}(k)}\cdot n$ step dynamic programming algorithms for surface-embedded graphs on $n$ vertices of branchwidth at most $k$. Our technique applies to graph problems for which dynamic programming uses tables encoding set partitions. For general graphs, the best known algorithms for such problems run in $2^{\mathcal{O}(k\cdot \log k)}\cdot n$ steps. That way, we considerably extend the class of problems that can be solved by algorithms whose running times have a {\em single exponential dependence} on branchwidth, and improve the running time of several existing algorithms. Our approach is based on a new type of branch decomposition called {\em surface cut decomposition}, which generalizes sphere cut decompositions for planar graphs, and where dynamic programming should be applied for each particular problem. The construction of such a decomposition uses a new graph-topological tool called {\em polyhedral decomposition}. The main result is that if dynamic programming is applied on surface cut decompositions, then the time dependence on branchwidth is {\sl single exponential}. This fact is proved by a detailed analysis of how non-crossing partitions are arranged on surfaces with boundary and uses diverse techniques from topological graph theory and analytic combinatorics.

     
  109. A. Silva, P. Reyes, and M. Debbah. Congestion in Randomly Deployed Wireless Ad-Hoc and Sensor Networks. Research Report RR-6854, INRIA, March 2009. [WWW ] [PDF ]
    Abstract:
    Congestion in wireless ad-hoc and sensor networks not only causes packet loss, and increases queueing delay, but also leads to unnecessary energy consumption. In a wireless ad-hoc and sensor network, two types of congestion can occur: node-level congestion, which is caused by buffer overflow in the node, or link-level congestion, when wireless channels are shared by several nodes and collisions occur when multiple active nodes try to seize the channel at the same time. We study a measure of link-level congestion in a static wireless ad-hoc and sensor network randomly deployed over an area. The measure considered on this paper is the inverse of the greatest eigenvalue of the adjacency matrix of the random graph. This measure of congestion gives an approximation of the average quantity of wireless links of a certain length that a node have on the wireless ad-hoc and sensor network. We review the results to find this measure of congestion in a Bernoulli random graph and we use tools from random graph theory and random matrix theory to extend this measure of congestion on a Geometric random graph.

     
  110. F. Guinand and B. Onfroy. MANET : modèle de mobilité planifié. Ubimob'09, July 2009.
    Note: Demonstration. [PDF ]
    Keywords: réseau mobile ad-hoc, MANET, graphe dynamique, modèle de mobilité, mobilité planifiée, environnement urbain.
    Abstract:
    Avec la multiplication des terminaux communicants, les r\'eseaux mobiles ad-hoc ont maintenant la capacit\'e de se d\'evelopper. Ces r\'eseaux ne poss\`edent pas d'infrastructure fixe, et le d\'eplacement des terminaux rend leur voisinage instable. Il est tr\`es difficile d'effectuer des mesures r\'eelles sur ce type de r\'eseau afin d'en \'etudier la dynamique. Dans l'objectif de concevoir des m\'ethodes d\'ecentralis\'ees efficaces, il est donc important de pouvoir simuler une mobilit\'e pertinente en fonction de l'environnement et du support des mouvements (hommes, v\'ehicules, ...) afin de recr\'eer de facon globale un r\'eseau dynamique proche du r\'eel. De nombreux mod\`eles de mobilit\'e ont d\'ej\`a \'et\'e propos\'es afin d'\'etudier et d'analyser les protocoles de routage et de communication, ainsi que certains algorithmes (diffusion en particulier). Le but de cette d\'emonstration est de pr\'esenter une plate-forme de simulation de mod\`eles de mobilit\'e en environnements urbains. La mise en oeuvre d'un nouveau type de mobilit\'e ax\'ee sur la planification de d\'eplacements illustrera l'utilisation et le fonctionnement de cette plate-forme.

     
  111. J. Ribault, F. Peix, J. Monteiro, and O. Dalle. OSA: an Integration Platform for Component-Based Simulation. Second Intl. Conf. on Simulation Tools and Techniques (SIMUTools09), March 2009.
    Note: Poster abstract. [PDF ]
    Abstract:
    Many discrete-event simulators are developed concurrently, but with identical or similar purpose. This poster presents the Open Simulation Architecture (OSA), a discrete-event component-based simulation platform whose goal is to favor the reuse and integration of simulation software components and models. To favor reuse, OSA uses a layered approach to combine the modeling, simulation, and related concerns, such as instrumentation or deployment. OSA is both a testbed for experimenting new simulation techniques and a tool for real case studies. The ability of OSA to support challenging studies is illustrated by a Peer-to-peer system case study involving millions of components.

     
2008
  1. O. Dalle and G.A. Wainer, editors. 1st International Conference on Simulation and Techniques for Communications, Networks and Systems (SIMU Tools 2008), Marseille, France, March 2008.
     
  2. D. Coudert, V. Issarny, and N. Georgantas, editors. 1st International Workshop on Ad-hoc Ambient Computing (AdhocAmC), Sophia Antipolis, France, September 2008. I3S, CNRS, Université de Nice Sophia, INRIA. [WWW ]
     
  3. D. Coudert, S. Krco, and K. Wrona, editors. PhD workshop (PhD-NOW), Sophia Antipolis, France, September 2008. I3S, CNRS, Université de Nice Sophia, INRIA. [WWW ]
     
  4. D. Coudert, D. Simplot-Ryl, and I. Stojmenovic, editors. 7th International Conference on AD-HOC Networks & Wireless (AdHoc-NOW), volume 5198 of Lecture Notes in Computer Science, September 2008. Springer. [WWW ]
     
  5. J. Galtier. L'adaptativité dans les télécommunications. Habilitation à Diriger des Recherches, Université de Nice-Sophia Antipolis, February 2008.
     
  6. F. Huc. Conception de Réseaux Dynamiques Tolérants aux Pannes. PhD thesis, École doctorale STIC, Université de Nice-Sophia Antipolis, November 2008. [PDF ]
    Abstract:
    Cette thèse aborde différents aspects de la conception d'un réseau de télécommunications. Un tel réseau utilise des technologies hétérogènes: liens antennes-satellites, radio, fibres optiques ou bien encore réseaux embarqués dans un satellite. Les problématiques varient en fonction de la partie du réseau considérée, du type de requêtes et de l'objectif. Le cas des requêtes de type paquets est abordé dans le cadre des réseaux en forme de grille, mais le thème principal est le routage de requêtes de type connections (unicast et multicast). Les objectifs considérés sont : la conception d'un réseau embarqué dans un satellite de télécommunication, de taille minimum et tolérant des pannes de composants; le dimensionnement des liens d'un réseau afin qu'il supporte des pannes corrélées ou qu'il offre une bonne qualité de service, ou s'il autorise des connections multicast; le dimensionnement de la taille des buffers d'un réseau d'accés radio; et l'optimisation de l'utilisation des ressources d'un réseau dynamique orienté connections. Dans tous ces cas la problématique du routage de connections est centrale. Mon approche consiste à utiliser la complémentarité de techniques algorithmique et d'optimisation combinatoire ainsi que d'outils issus de la théorie des graphes tels la pathwidth et des notions reliées -process number, jeux de captures et treewidth-, différents types de coloration -impropre et pondérée, proportionnelle, directed star colouring-, les graphes d'expansion et des techniques de partitions telle la quasi partition.

     
  7. L. Addario-Berry and B. Reed. Horizons of Combinatorics, volume 17 of Bolyai Society Mathematical Studies, chapter Ballot Theorems, Old and New, pages 9-35. Springer, 2008.
     
  8. N. Nepomuceno, P.R. Pinheiro, and A.L.V. Coelho. A Hybrid Optimization Framework for Cutting and Packing Problems: Case Study on Constrained 2D Non-guillotine Cutting. In Recent Advances in Evolutionary Computation for Combinatorial Optimization, volume 153 of Studies in Computational Intelligence, chapter 6, pages 87-99. Springer, 2008. [WWW ] [PDF ]
    Abstract:
    This work presents a hybrid optimization framework for tackling cutting and packing problems, which is based upon a particular combination scheme between heuristic and exact methods. A metaheuristic engine works as a generator of reduced instances for the original optimization problem, which are formulated as mathematical programming models. These instances, in turn, are solved by an exact optimization technique (solver), and the performance measures accomplished by the respective models are interpreted as score (fitness) values by the metaheuristic, thus guiding its search process. As a means to assess the potentialities behind the novel approach, we provide an instantiation of the framework for dealing specifically with the constrained two-dimensional non-guillotine cutting problem. Computational experiments performed over standard benchmark problems are reported and discussed here, evidencing the effectiveness of the novel approach.

     
  9. L. Addario-Berry, M. Chudnovsky, F. Havet, B. Reed, and P. Seymour. Bisimplicial vertices in even-hole-free graphs. Journal of Combinatorial Theory Ser. B, 98(6):1119--1164, 2008. [PDF ]
    Abstract:
    A hole in a graph is an induced subgraph which is a cycle of length at least four. A hole is called even if it has an even number of vertices. An even-hole-free graph is a graph with no even holes. A vertex of a graph is bisimplicial if the set of its neighbours is the union of two cliques. In this paper we prove that every even-hole-free graph has a bisimplicial vertex, which was originally conjectured by Reed.

     
  10. L. Addario-Berry, K. Dalal, and B. Reed. Degree-Constrained Subgraphs. Discrete Applied Mathematics, 156:1168-1174, 2008.
     
  11. N. Ben Ali, B. Belghith, J. Moulierac, and M. Molnár. QoS multicast aggregation under multiple additive constraints. Computer Communications, 31(15):3564-3578, September 2008. [PDF ]
    Abstract:
    IP Multicast has been proposed in order to manage group communications over the Internet in a bandwidth efficient manner. Although such a proposition has been well studied, there are still some inherent problems for its widespread deployment. In this paper, we propose a new algorithm coined mQMA that deals with the two main problems of traditional IP multicast, i.e., multicast forwarding state scalability and multi-constrained QoS routing. The algorithm mQMA is a QoS multicast aggregation algorithm which handles multiple additive QoS constraints. It builds few trees and maintains few forwarding states for the groups thanks to the technique of multicast tree aggregation, which allows several groups to share the same delivery tree. Moreover, the algorithm mQMA builds trees satisfying multiple additive QoS constraints. We show via extensive simulations that mQMA reduces dramatically the number of trees to be maintained and reduces the utilization of the network resources, yet it leverages the same overall QoS performances as Mamcra which is the main known multi-constrained multicast routing algorithm.

     
  12. J-C. Bermond, D. Coudert, and B. Lévêque. Approximations for All-to-all Uniform Traffic Grooming on Unidirectional Ring. Journal of Interconnection Networks (JOIN), 9(4):471-486, December 2008. [WWW ] [PDF ]
    Abstract:
    Traffic grooming in a WDM network consists of assigning to each request (lightpath) a wavelength with the constraint that a given wavelength can carry at most C requests or equivalently a request uses at most 1/C of the bandwidth. C is known as the grooming ratio. A request (lightpath) need two SONET add-drop multiplexers (ADMs) at each end node~; using grooming different requests can share the same ADM. The so called traffic grooming problem consists of minimizing the total number of ADMs to be used (in order to reduce the overall cost of the network). Here we consider the traffic grooming problem in WDM unidirectional rings with all-to-all uniform unitary traffic. This problem has been optimally solved for specific values of the grooming ratio, namely C=2,3,4,5,6. In this paper we present various simple constructions for the grooming problem providing good approximation of the total number of ADMs. For that we use the fact that the problem corresponds to a partition of the edges of the complete graph into subgraphs, where each subgraph has at most C edges and where the total number of vertices has to be minimized.

     
  13. L. Blin, P. Fraigniaud, N. Nisse, and S. Vial. Distributed chasing of network intruders. Theoretical Computer Science, 399(1-2):12-37, 2008. [WWW ] [PDF ]
    Abstract:
    Graph searching is one of the most popular tools for analyzing the chase for a powerful and hostile software agent (called the "intruder"), by a set of software agents (called the "searchers") in a network. The existing solutions for the graph searching problem suffer however from a serious drawback: they are mostly centralized and assume a global synchronization mechanism for the searchers. In particular: (1) the search strategy for every network is computed based on the knowledge of the entire topology of the network, and (2) the moves of the searchers are controlled by a centralized mechanism that decides at every step which searcher has to move, and what movement it has to perform. This paper addresses the graph searching problem in a distributed setting. We describe a distributed protocol that enables searchers with logarithmic size memory to clear any network, in a fully decentralized manner. The search strategy for the network in which the searchers are launched is computed online by the searchers themselves without knowing the topology of the network in advance. It performs in an asynchronous environment, i.e., it implements the necessary synchronization mechanism in a decentralized manner. In every network, our protocol performs a connected strategy using at most k+1 searchers, where k is the minimum number of searchers required to clear the network in a monotone connected way using a strategy computed in the centralized and synchronous setting.

     
  14. M. Cerioli, L. Faria, T. Ferreira, C. Martinhon, F. Protti, and B. Reed. Partition into cliques for cubic graphs: Planar case, complexity and approximation. Discrete Applied Mathematics, 156:2270-2278, 2008.
     
  15. R. Chand, M. Cosnard, and L. Liquori. Powerful resource discovery for Arigatoni overlay network. Future Generation Computer Systems, 24:31--38, 2008. [WWW ] [PDF ]
     
  16. S. Fiorini, N. Hardy, B. Reed, and A. Vetta. Planar graph bipartization in linear time. Discrete Applied Mathematics, 156:1175-1180, 2008.
    Abstract:
    For each constant k, we present a linear time algorithm that, given a planar graph G, either finds a minimum odd cycle vertex transversal in G or guarantees that there is no transversal of size at most k.

     
  17. M. Flammini, R. Klasing, A. Navarra, and S. Pérennes. Tightening the Upper Bound for the Minimum Energy Broadcasting problem. Wireless Networks, 14(5):659--669, October 2008.
    Note: Special Issue associated to the 3rd International Symposium on Modelling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt 2005). [WWW ]
     
  18. M. Flammini, L. Moscardelli, A. Navarra, and S. Pérennes. Asymptotically Optimal Solutions for Small World Graphs. Theory of Computing Systems, 42(4):632-650, May 2008. [WWW ] [PDF ]
    Abstract:
    We consider the problem of determining constructions with an asymptotically optimal oblivious diameter in small world graphs under the Kleinberg’s model. In particular, we give the first general lower bound holding for any monotone distance distribution, that is induced by a monotone generating function. Namely, we prove that the expected oblivious diameter is Ω(log 2 n) even on a path of n nodes. We then focus on deterministic constructions and after showing that the problem of minimizing the oblivious diameter is generally intractable, we give asymptotically optimal solutions, that is with a logarithmic oblivious diameter, for paths, trees and Cartesian products of graphs, including d-dimensional grids for any fixed value of d.

     
  19. N. Fountoulakis and B. Reed. The evolution of the mixing rate of a simple random walk on the giant component of a random graph. Random Structures and Algorithms, 33:68-86, 2008.
     
  20. P. Fraigniaud and N. Nisse. Monotony Properties of Connected Visible Graph Searching. Information and Computation, 206(12):1383-1393, 2008.
    Abstract:
    {Search games are attractive for their correspondence with classical width parameters. For instance, the \emph{invisible} search number (a.k.a. \emph{node} search number) of a graph is equal to its pathwidth plus~1, and the \emph{visible} search number of a graph is equal to its treewidth plus~1. The \emph{connected} variants of these games ask for search strategies that are connected, i.e., at every step of the strategy, the searched part of the graph induces a connected subgraph. We focus on \emph{monotone} search strategies, i.e., strategies for which every node is searched exactly once. The monotone connected visible search number of an $n$-node graph is at most $O(\log n)$ times its visible search number. First, we prove that this logarithmic bound is tight. Precisely, we prove that there is an infinite family of graphs for which the ratio monotone connected visible search number over visible search number is $\Omega(\log n)$. Second, we prove that, as opposed to the non-connected variant of visible graph searching, ``recontamination helps" for connected visible search. Precisely, we prove that, for any $k \geq 4$, there exists a graph with connected visible search number at most $k$, and monotone connected visible search number $>k$.}, url = {http://www.informatik.uni-trier.de/~ley/db/conf/wg/wg2006.shtml}, pdf = {http://www-sop.inria.fr/members/Nicolas.Nisse/publications/WG06_nisse.ps}, OPTx-editorial-board={yes}, OPTx-proceedings={yes}, OPTx-international-audience={yes}, sorte = "rev-int",

     
  21. F. Havet, J.-S. Sereni, and R. Skrekovski. 3-facial colouring of plane graphs. SIAM Journal on Discrete Mathematics, 22(1):231--247, 2008. [WWW ] [PDF ]
    Abstract:
    A plane graph is \l-facially $k$-colourable if its vertices can be coloured with $k$ colours such that any two distinct vertices on a facial walk of length at most \l are coloured differently. We prove that every plane graph is $3$-facially $11$-colourable. As a consequence, we derive that every $2$-connected plane graph with maximum face-size at most $7$ is cyclically $11$-colourable. These two bounds are for one off from those that are proposed by the $(3\l+1)$-Conjecture and the Cyclic Conjecture.

     
  22. F. Havet, S. Thomassé, and A. Yeo. Hoang-Reed conjecture for tournaments. Discrete Mathematics, 308(15):3412--3415, August 2008. [PDF ]
    Abstract:
    Ho\`ang-Reed conjecture asserts that every digraph $D$ has a collection $\cal C$ of circuits $C_1,\dots,C_{\delta ^+}$, where $\delta ^+$ is the minimum outdegree of $D$, such that the circuits of $\cal C$ have a forest-like structure. Formally, $|V(C_i)\cap (V(C_1)\cup \dots \cup V(C_{i-1}))|\leq 1$, for all $i=2,\dots ,\delta^+$. We verify this conjecture for the class of tournaments.

     
  23. F. Havet and M-L. Yu. $(p,1)$-total labelling of graphs. Discrete Mathematics, 308(4):496--513, February 2008. [PDF ]
    Abstract:
    A $(p,1)$-total labelling of a graph $G$ is an assignment of integers to $V(G)\cup E(G)$ such that: (i) any two adjacent vertices of $G$ receive distinct integers, (ii) any two adjacent edges of $G$ receive distinct integers, and (iii) a vertex and its incident edge receive integers that differ by at least $p$ in absolute value. The {\it span} of a $(p,1)$-total labelling is the maximum difference between two labels. The minimum span of a $(p,1)$-total labelling of $G$ is called the {\it $(p,1)$-total number} and denoted by $\lambda_p^T(G)$. We provide lower and upper bounds for the $(p,1)$-total number. In particular, generalizing the Total Colouring Conjecture, we conjecture that $\lambda_p^T\leq \Delta+ 2p - 1$ and give some evidences to support it. Finally, we determine the exact value of $\lambda^T_p(K_n)$, except for even $n$ in the interval $[p+5, 6p2-10p+4]$ for which we show that $\lambda_p^T(K_n) \in n+2p-3, n+2p-2$.

     
  24. R. J. Kang, T. Müller, and J.-S. Sereni. Improper colouring of (random) unit disk graphs. Discrete Mathematics, 308:1438--1454, April 2008.
    Note: The Special Issue devoted to EuroComb 2005. [PDF ]
     
  25. K. Kawarabayashi, O. Lee, B. Reed, and P. Wollan. A weaker version of Lovasz' path removable conjecture. Journal of Combinatorial Theory (Series B), 98:972-979, 2008.
     
  26. K. Kawarabayashi and B. Reed. Fractional coloring and the odd Hadwiger's conjecture. European Journal of Combinatorics, 29(2):411-417, 2008.
    Abstract:
    Gerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, Wiley-Interscience, 1995], page 115) conjectured that if a graph has no odd complete minor of order p, then it is (p-1)-colorable. This is an analogue of the well known conjecture of Hadwiger, and in fact, this would immediately imply Hadwiger's conjecture. The current best known bound for the chromatic number of graphs without an odd complete minor of order p is O(plogp) by the recent result by Geelen et al. [J. Geelen, B. Gerards, B. Reed, P. Seymour, A. Vetta, On the odd variant of Hadwiger's conjecture (submitted for publication)], and by Kawarabayashi [K. Kawarabayashi, Note on coloring graphs without odd K"k-minors (submitted for publication)] (but later). But, it seems very hard to improve this bound since this would also improve the current best known bound for the chromatic number of graphs without a complete minor of order p. Motivated by this problem, we prove that the ''fractional chromatic number'' of a graph G without odd K"p-minor is at most 2p; that is, it is possible to assign a rational q(S)>=0 to every stable set SV(G) so that "S"vq(S)=1 for every vertex v, and "Sq(S)2p. This generalizes the result of Reed and Seymour [B. Reed, P.D. Seymour, Fractional chromatic number and Hadwiger's conjecture, J. Combin. Theory Ser. B 74 (1998) 147-152] who proved that the fractional chromatic number of a graph with no K"p"+"1-minor is at most 2p.

     
  27. R. Klasing, N. Morales, and S. Pérennes. On the Complexity of Bandwidth Allocation in Radio Networks. Theoretical Computer Science, 406(3):225-239, October 2008. [WWW ] [PDF ]
    Abstract:
    "We define and study an optimization problem that is motivated by bandwidth allocation in radio networks. Because radio transmissions are subject to interference constraints in radio networks, physical space is a common resource that the nodes have to share in such a way, that concurrent transmissions do not interfere. The bandwidth allocation problem we study under these constraints is the following. Given bandwidth (traffic) demands between the nodes of the network, the objective is to schedule the radio transmissions in such a way that the traffic demands are satisfied. The problem is similar to a multicommodity flow problem, where the capacity constraints are replaced by the more complex notion of non-interfering transmissions. We provide a formal specification of the problem that we call round weighting. By modeling non-interfering radio transmissions as independent sets, we relate the complexity of round weighting to the complexity of various independent set problems (e.g. maximum weight independent set, vertex coloring, fractional coloring). From this relation, we deduce that in general, round weighting is hard to approximate within n1−ε (n being the size of the radio network). We also provide polynomial (exact or approximation) algorithms e.g. in the following two cases: (a) when the interference constraints are specific (for instance for a network whose vertices belong to the Euclidean space), or (b) when the traffic demands are directed towards a unique node in the network (also called gathering, analogous to single commodity flow)."

     
  28. C. Linhares-Sales, F. Maffray, and B. Reed. On Planar Quasi-Parity Graphs. SIAM Journal of Discrete Mathematics, 22:329-347, 2008.
     
  29. F. Mazoit and N. Nisse. Monotonicity of non-deterministic graph searching. Theoretical Computer Science, 399(3):169-178, 2008. [WWW ] [PDF ]
    Abstract:
    In graph searching, a team of searchers are aiming at capturing a fugitive moving in a graph. In the initial variant, called invisible graph searching, the searchers do not know the position of the fugitive until they catch it. In another variant, the searchers permanently know the position of the fugitive, i.e. the fugitive is visible. This latter variant is called visible graph searching. A search strategy that catches any fugitive in such a way that the part of the graph reachable by the fugitive never grows is called monotone. A priori, monotone strategies may require more searchers than general strategies to catch any fugitive. This is however not the case for visible and invisible graph searching. Two important consequences of the monotonicity of visible and invisible graph searching are: (1) the decision problem corresponding to the computation of the smallest number of searchers required to clear a graph is in NP, and (2) computing optimal search strate gies is simplified by taking into account that there exist some that never backtrack. Fomin et al. [F.V. Fomin, P. Fraigniaud, N. Nisse, Nondeterministic graph searching: From pathwidth to treewidth, in: Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science, MFCS 2005, pp. 364--375] introduced an important graph searching variant, called non-deterministic graph searching, that unifies visible and invisible graph searching. In this variant, the fugitive is invisible, and the searchers can query an oracle that permanently knows the current position of the fugitive. The question of the monotonicity of non-deterministic graph searching was however left open. In this paper, we prove that non-deterministic graph searching is monotone. In particular, this result is a unified proof of monotonicity for visible and invisible graph searching. As a consequence, the decision problem corresponding to non-deterministic graph searching belongs to NP. Moreover, the exact algorithms designed by Fomin et al. do compute optimal non-deterministic search strategies.

     
  30. C. McDiarmid and B. Reed. On the maximum degree of a random planar graph. Combinatorics, Probability and Computing, 17:591-601, 2008.
     
  31. C. Meagher and B. Reed. Fractionally total colouring ${G}_{n,p}$. Discrete Applied Mathematics, 156:1112-1124, 2008.
     
  32. B. Reed. Skew Partitions in Perfect Graphs. Discrete Applied Mathematics, 156:1150-1156, 2008.
     
  33. I. Sau and J. Zerovnik. An Optimal Permutation Routing Algorithm on Full-Duplex Hexagonal Networks. Discrete Mathematics and Theoretical Computer Science, 10(3):49-62, 2008. [PDF ]
    Abstract:
    In the permutation routing problem, each processor is the origin of at most one packet and the destination of no more than one packet. The goal is to minimize the number of time steps required to route all packets to their respective destinations, under the constraint that each link can be crossed simultaneously by no more than one packet. We study this problem in a hexagonal network, i.e. a finite subgraph of a triangular grid, which is a widely used network in practical applications. We present an optimal distributed permutation routing algorithm for full-duplex hexagonal networks, using the addressing scheme described by F.G. Nocetti, I. Stojmenovi\'{c} and J. Zhang (IEEE TPDS 13(9): 962-971, 2002). Furthermore, we prove that this algorithm is oblivious and translation invariant.

     
  34. L. Addario-Berry, O. Amini, J.-S. Sereni, and S. Thomassé. Guarding art galleries: the extra cost for sculptures is linear. In Proceedings of the Scandinavian Workshop on Algorithm Theory (SWAT 2008), volume 5124 of Lecture Notes in Computer Science, pages 41-52, July 2008. Springer.
     
  35. A. Aguiar, P.R. Pinheiro, A.L.V Coelho, N. Nepomuceno, A. Neto, and R. Cunha. Scalability Analysis of a Novel Integer Programming Model to Deal with Energy Consumption in Heterogeneous Wireless Sensor Networks. In Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO'08), volume 14 of Communications in Computer and Information Science, pages 11-20, 2008. Springer. [WWW ] [PDF ]
    Abstract:
    This paper presents a scalability analysis over a novel integer programming model devoted to optimize power consumption efficiency in heterogeneous wireless sensor networks. This model is based upon a schedule of sensor allocation plans in multiple time intervals subject to coverage and connectivity constraints. By turning off a specific set of redundant sensors in each time interval, it is possible to reduce the total energy consumption in the network and, at the same time, avoid partitioning the whole network by losing some strategic sensors too prematurely. Since the network is heterogeneous, sensors can sense different phenomena from different demand points, with different sample rates. As the problem instances grows the time spent to the execution turns impracticable.

     
  36. O. Amini, S. Griffiths, and F. Huc. 4-cycles in mixing digraphs. In Electronic Notes in Discrete MathematicsVolume 30, The IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07), volume 30, Puerto Varas, Chile, pages 63--68, February 2008. [PDF ]
    Abstract:
    It is known that every simple graph with $n^{3/2}$ edges contains a 4-cycle. A similar statement for digraphs is not possible since no condition on the number of edges can guarantee an (oriented) 4-cycle. We find a condition which does guarantee the presence of a 4-cycle and our result is tight. Our condition, which we call $f$-mixing, can be seen as a quasirandomness condition on the orientation of the graph. We also investigate the notion of mixing in the case of regular and almost regular digraphs. In particular we determine how mixing a random orientation of a random graph is.

     
  37. O. Amini, D. Peleg, S. Pérennes, I. Sau, and S. Saurabh. Degree-Constrained Subgraph Problems : Hardness and Approximation Results. In 6th International Workshop on Approximation and Online Algorithms (ALGO-WAOA 2008), volume 5426 of Lecture Notes in Computer Science, Karlsruhe, Germany, pages 29-42, September 2008. [PDF ]
    Abstract:
    A general instance of a \sc Degree-Constrained Subgraph problem consists of an edge-weighted or vertex-weighted graph $G$ and the objective is to find an optimal weighted subgraph, subject to certain degree constraints on the vertices of the subgraph. This class of combinatorial problems has been extensively studied due to its numerous applications in network design. If the input graph is bipartite, these problems are equivalent to classical transportation and assignment problems in operations research. This paper considers three natural \sc Degree-Constrained Subgraph problems and studies their behavior in terms of approximation algorithms. These problems take as input an undirected graph $G=(V,E)$, with $|V|=n$ and $|E|=m$. Our results, together with the definition of the three problems, are listed below. The Maximum Degree-Bounded Connected Subgraph (MDBCS$_d$) problem takes as input a weight function $\omega : E \rightarrow \mathbb R^+$ and an integer $d \geq 2$, and asks for a subset $E' \subseteq E$ such that the subgraph $G'=(V,E')$ is connected, has maximum degree at most $d$, and $\sum_e\in E' \omega(e)$ is maximized. This problem is one of the classical NP-hard problems listed by Garey and Johnson in (Computers and Intractability, W.H. Freeman, 1979), but there were no results in the literature except for $d=2$. We prove that MDBCS$_d$ is not in Apx for any $d\geq 2$ (this was known only for $d=2$) and we provide a $(\min m/ \log n,\ nd/(2 \log n))$-approximation algorithm for unweighted graphs, and a $(\min n/2,\ m/d)$-approximation algorithm for weighted graphs. We also prove that when $G$ accepts a low-degree spanning tree, in terms of $d$, then MDBCS$_d$ can be approximated within a small constant factor in unweighted graphs. The \sc Minimum Subgraph of Minimum Degree$_\geq d$ (MSMD$_d$) problem consists in finding a smallest subgraph of $G$ (in terms of number of vertices) with minimum degree at least $d$. We prove that MSMD$_d$ is not in Apx for any $d\geq 3$ and we provide an $\mathcal O(n/\log n)$-approximation algorithm for the classes of graphs excluding a fixed graph as a minor, using dynamic programming techniques and a known structural result on graph minors. In particular, this approximation algorithm applies to planar graphs and graphs of bounded genus. The \sc Dual Degree-Dense $k$-Subgraph (DDD$k$S) problem consists in finding a subgraph $H$ of $G$ such that $|V(H)| \leq k$ and $\delta_H$ is maximized, where $\delta_H$ is the minimum degree in $H$. We present a deterministic $\mathcal O(n^\delta)$-approximation algorithm in general graphs, for some universal constant $\delta < 1/3$.

     
  38. O. Amini, I. Sau, and S. Saurabh. Parameterized Complexity of the Smallest Degree-Constrained Subgraph Problem. In The International Workshop on Parameterized and Exact Computation (IWPEC 2008), volume 5008 of Lecture Notes in Computer Science, Victoria, Canada, pages 13-29, May 2008. [PDF ]
    Abstract:
    {In this paper we study the problem of finding an induced subgraph of size at most $k$ with minimum degree at least $d$ for a given graph $G$, from the parameterized complexity perspective. We call this problem {\sc Minimum Subgraph of Minimum Degree $_{\geq d}$ ({\sc MSMD}$_d$)}. For $d=2$ it corresponds to finding a shortest cycle of the graph. Our main motivation to study this problem is its strong relation to \textsc{Dense $k$-Subgraph} and \textsc{Traffic Grooming} problems. First, we show that {\sc MSMS}$_d$ is fixed-parameter intractable (provided $FPT\neq W[1]$) for $d\geq 3$ in general graphs, by showing it to be $W[1]$-hard using a reduction from {\sc Multi-Color Clique}. In the second part of the paper we provide {\em explicit} fixed-parameter tractable (FPT) algorithms for the problem in graphs with bounded local tree-width and graphs with excluded minors, {\em faster} than those coming from the meta-theorem of Frick and Grohe [FrickG01] about problems definable in first order logic over ``locally tree-decomposable structures". In particular, this implies faster fixed-parameter tractable algorithms in planar graphs, graphs of bounded genus, and graphs with bounded maximum degree.}, OPTx-editorial-board={yes}, OPTx-proceedings={yes}, OPTx-international-audience={yes}, sorte = "conf-int",

     
  39. M. Asté, F. Havet, and C. Linhares-Sales. Grundy number and lexicographic product of graphs. In Proceedings of International Conference on Relations, Orders and Graphs and their Interaction with Computer Science (ROGICS 2008), pages 9p, May 2008. [WWW ] [PDF ]
    Abstract:
    The {\em Grundy number} of a graph $G$, denoted by $\Gamma (G)$, is the largest $k$ such that $G$ has a {\em greedy} $k$-colouring, that is a colouring with $k$ colours obtained by applying the greedy algorithm according to some ordering of the vertices of $G$. In this paper, we study the Grundy number of the lexicographic product of two graphs in terms of the Grundy numbers of these graphs. We show that $\Gamma(G)\times\Gamma(H)\leq \Gamma(G[H])\leq 2^{\Gamma(G)-1}(\Gamma(H)-1)+\Gamma(G)-1$. In addition, we show that if $G$ is a tree or $\Gamma(G)=\Delta(G)+1$, then $\Gamma(G[H])=\Gamma(G)\times\Gamma(H)$. We then deduce that for every fixed $c\leq 1$, given a graph $G$, it is CoNP-Complete to decide if $\Gamma(G)\leq c\times \chi(G)$ and it is CoNP-Complete to decide if $\Gamma(G)\leq c\times \omega(G)$.

     
  40. J-C. Bermond, L. Gargano, and A.A. Rescigno. Gathering with minimum delay in tree sensor networks. In SIROCCO 2008, volume 5058 of Lecture Notes in Computer Science, Villars-sur-Ollon, Switzerland, pages 262-276, June 2008. Springer-Verlag. [PDF ]
    Abstract:
    Data gathering is a fundamental operation in wireless sensor networks in which data packets generated at sensor nodes are to be collected at a base station. In this paper we suppose that each sensor is equipped with an half--duplex interface; hence, a node cannot receive and transmit at the same time. Moreover, each node is equipped with omnidirectional antennas allowing the transmission over distance R. The network is a multi-hop wireless network and the time is slotted so that one--hop transmission of one data item consumes one time slot. We model the network with a graph where the vertices represent the nodes and two nodes are connected if they are in the transmission/interference range of each other. Due to interferences a collision happens at a node if two or more of its neighbors try to transmit at the same time. Furthermore we suppose that an intermediate node should forward a message as soon as it receives it. We give an optimal collision free gathering schedule for tree networks whenever each node has at least one data packet to send.

     
  41. J-C. Bermond and M-L. Yu. Optimal gathering algorithms in multi-hop radio tree networks with interferences. In Proceedings of the 7th international conference on Ad Hoc Networks and Wireless (AdHoc-Now), volume 5198 of Lecture Notes in Computer Science, pages 204-217, September 2008. Springer. [PDF ]
    Abstract:
    We study the problem of gathering information from the nodes of a multi-hop radio network into a pre-defined destination node under the interference constraints. In such a network, a message can only be properly received if there is no interference from another message being simultaneously transmitted. The network is modeled as a graph, where the vertices represent the nodes and the edges, the possible communications. The interference constraint is modeled by a fixed integer $d_I \geq 1$, which implies that nodes within distance $d_I$ in the graph from one sender cannot receive messages from another node. In this paper, we suppose that it takes one unit of time (slot) to transmit a unit-length message. A step (or round) consists of a set of non interfering (compatible) calls and uses one slot. We present optimal algorithms that give minimum number of steps (delay) for the gathering problem with buffering possibility, when the network is a tree, the root is the destination and $d_I =1$. In fact we study the equivalent personalized broadcasting problem instead.

     
  42. D. Coudert, F. Huc, and D. Mazauric. Algorithme générique pour les jeux de capture dans les arbres. In 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'08), Saint-Malo, pages 37--40, May 2008. [PDF ]
    Abstract:
    Nous pr\'esentons un algorithme distribu\'e simple calculant le process number des arbres en O(n.log(n)) \'etapes. De plus cet algorithme est facilement adaptable pour calculer d'autre param\`etres sur l'arbre, dont la pathwidth. Nous pr\'esentons \'egalement une condition n\'ecessaire et suffisante pour que la pathwidth d'un arbre soit \'egale \`a son process number.

     
  43. D. Coudert, F. Huc, and D. Mazauric. A distributed algorithm for computing and updating the process number of a forest (brief announcement). In G. Taubenfeld, editor, 22nd International Symposium on Distributed Computing (DISC), volume 5218 of Lecture Notes in Computer Science, Arcachon, France, pages 500-501, September 2008. Springer. [PDF ]
    Abstract:
    In this paper, we present a distributed algorithm to compute various parameters of a tree such as the process number, the edge search number or the node search number and so the pathwidth. This algorithm requires n steps, an overall computation time of O(n log(n)), and n messages of size log_3(n)+3. We then propose a distributed algorithm to update the process number (or the node search number, or the edge search number) of each component of a forest after adding or deleting an edge. This second algorithm requires O(D) steps, an overall computation time of O(D log(n)), and O(D) messages of size log_3(n)+3, where D is the diameter of the modified connected component. Finally, we show how to extend our algorithms to trees and forests of unknown size using messages of less than 2a+4+e bits, where a is the parameter to be determined and e=1 for updates algorithms.

     
  44. D. Coudert, F. Huc, and D. Mazauric. Computing and updating the process number in trees (short paper). In T. Baker and S. Tixeuil, editors, 12th International Conference On Principles Of DIstributed Systems (OPODIS), volume 5401 of Lecture Notes in Computer Science, Luxor, Egypt, pages 546-550, December 2008. Springer. [WWW ] [PDF ]
    Abstract:
    The process number is the number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the node search number, and thus to the pathwidth. However they are not always equal in general graphs. Determining these parameters is in general NP-complete. In this paper, we characterize the cases in which the process number and the node search number are equal in trees. We also present a distributed algorithm to compute these parameters as well as the edge search number. This algorithm can be executed in an asynchronous environment, requires $n$ steps, an overall computation time of $O(n\log{n})$, and $n$ messages of size $\log_3{n}+2$. We then propose a distributed algorithm to update the process number (or the node search number, or the edge search number) of each component of a forest after addition or deletion of any edge. This second algorithm requires $O(D)$ steps, an overall computation time of $O(D\log{n})$, and $O(D)$ messages of size $\log_3{n}+3$, where $D$ is the diameter of the modified connected component. Finally, we show how to extend our algorithms to trees and forests of unknown size using messages of less than $2\alpha+5$ bits, where $\alpha\leq\log_3{n}$ is the parameter to be determined.

     
  45. D. Coudert, F. Huc, F. Peix, and M.-E. Voge. Reliability of Connections in Multilayer Networks under Shared Risk Groups and Costs Constraints. In IEEE ICC, number ON01-6, Beijing, China, pages 5170 - 5174, May 2008. [WWW ] [PDF ]
    Abstract:
    The notion of Shared Risk Resource Groups (SRRG) has been introduced to capture survivability issues when a set of resources may fail simultaneously. Applied to Wavelength Division Multiplexing Network (WDM), it expresses that some links and nodes may fail simultaneously. The reliability of a connection therefore depends on the number of SRRGs through which it is routed. Consequently, this number has to be minimized. This problem has been proved NP-complete and hard to approximate in general, even when routing a single request. Some heuristics using shortest paths have already been designed, however the cost (the usual routing cost, not in term of SRRG) was not part of the objective. In this paper we study the problem of minimizing a linear combination of the average number of SRRG per paths and the cost of the routing. The main result of our work is a column generation formulation that allows to solve efficiently the problem of maximizing the reliability of a set of connection requests in MPLS/WDM mesh networks with SRRGs while keeping the cost of the routing low.

     
  46. O. Dalle, B.P. Zeigler, and G.A. Wainer. Extending DEVS to support multiple occurrence in component-based simulation. In S. J. Mason, R. R. Hill, L. Moench, and O. Rose, editors, Proceedings of the 2008 Winter Simulation Conference, pages 10p, December 2008. [PDF ]
    Abstract:
    This paper presents a new extension of the DEVS formalism that allowsmultiple occurrences of a given instance of a DEV Scomponent?. This paper is a follow-up to a previous short paper in which the issue of supporting a new construction called ashared component was raised, in the case of a DEVS model. In thispaper, we first demonstrate, formally, that the multi-occurrence extended definition,that includes the case of shared components, is valid because anymodel that is built using this extended definition accepts an equivalent modelbuilt using standard DEVS. Then we recall the benefits of sharingcomponents for modeling, and further extend this analysis to the simulation area, byinvestigating how shared components can help to design bettersimulation engines. Finally, we describe an existing implementation ofa simulation software that fully supports this shared componentfeature, both at the modeling and simulation levels.

     
  47. F. Giroire, J. Chandrashekar, G. Iannaccone, D. Papagiannaki, E. Schooler, and N. Taft. The Cubicle vs. The Coffee Shop: Behavioral Modes in Enterprise End-Users. In Proceeding of the Passive and Active Monitoring conference (PAM08), volume 4979 of Lecture Notes in Computer Science, pages 202-211, 2008. Springer. [PDF ]
    Abstract:
    Traditionally, user traffic profiling is performed by analyzing traffic traces collected on behalf of the user at aggregation points located in the middle of the network. However, the modern enterprise network has a highly mobile population that frequently moves in and out of its physical perimeter. Thus an in-the-network monitor is unlikely to capture full user activity traces when users move outside the enterprise perimeter. The distinct environments, such as the cubicle and the coffee shop (among others), that users visit, may each pose different constraints and lead to varied behavioral modes. It is thus important to ask: is the profile of a user constructed in one environment representative of the same user in another environment? In this paper, we answer in the negative for the mobile population of an enterprise. Using real corporate traces collected at nearly 400 end-hosts for approximately 5 weeks, we study how end-host usage differs across three environments: inside the enterprise, outside the enterprise but using a VPN, and entirely outside the enterprise network. Within these environments, we examine three types of features: (i) environment lifetimes, (ii) relative usage statistics of network services, and (iii) outlier detection thresholds as used for anomaly detection. We find significant diversity in end-host behavior across environments for many features, thus indicating that profiles computed for a user in one environment yield inaccurate representations of the same user in a different environment.

     
  48. C. Gomes, G. Huiban, and H. Rivano. A Branch-and-Price Approach to the Bandwidth Allocation Problem in Wireless Networks. In International Symposium on Combinatorial Optimization (CO), pages 1p, March 2008.
    Note: Abstract. [PDF ]
     
  49. C. Gomes, C. Molle, and P. Reyes. Optimal Design of Wireless Mesh Networks. In 9èmes Journées Doctorales en Informatique et Réseaux (JDIR 2008), Villeneuve d'Ascq, France, pages 10p, January 2008. [WWW ] [PDF ]
    Abstract:
    Wireless Mesh Networks (WMNs) are cost-effective and provide an appealing answer to connectivity issues of ubiquitous computing. Unfortunately, wireless networks are known for strong waste of capacity when their size in- creases. Thus, a key challenge for network operators is to provide guaranteed quality of service. Maximizing network capacity requires to optimize jointly the gateways placement, the routing and the link scheduling taking interferences into account. We present MILP models for computing an optimal 802.11a or 802.16 WMN design providing max-min bandwidth guarantee.

     
  50. C. Gomes, S. Pérennes, P. Reyes, and H. Rivano. Bandwidth Allocation in Radio Grid Networks. In 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'08), pages 4p, May 2008. [WWW ] [PDF ]
    Abstract:
    In this paper we give exact or almost exact bounds for the continuous gathering problem on grids. Under very general hypothesis on the traffic demand, we mainly prove that the throughput is determined by the bottleneck around the base station. We deal with two cases: the base station located in the center and in the corner. We use dual lower bounds and describe a protocol which is optimal when the traffic is uniform.

     
  51. C. Gomes, S. Pérennes, and H. Rivano. Bottleneck Analysis for Routing and Call Scheduling in Multi-hop Wireless Networks. In 4th IEEE Workshop on Broadband Wireless Access (BWA), New-Orleans, US, pages 6p, December 2008. [PDF ]
    Abstract:
    In this paper, we address the routing and call scheduling problem in which one has to find a minimum-length schedule of selected links in a TDMA (Time Division Multiple Access) based wireless network. As we deal with multi-hop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. We present a cross-layer formulation of the problem that computes joint routing and scheduling. We use a branch-and-price algorithm to solve optimally the problem. A column generation algorithm is used to cope with the exponential set of rounds. The branch-and-bound algorithm provides mono-routing. We run experiments on networks from the literature, with different number of gateways. Experimental results as well as theoretical insights let us conjecture that the bottleneck region analysis is enough to find the optimal solution. The Integer Round-Up Property (IRUP) seems to hold for our problem.

     
  52. F. Havet, B. Reed, and J.-S. Sereni. L(2,1)-labelling of graphs. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithm (SODA 2008), pages 621-630, January 2008. [WWW ] [PDF ]
    Abstract:
    An $L(2,1)$-labelling of a graph is a function $f$ from the vertex set to the positive integers such that $|f(x)-f(y)|\geq 2$ if $\dist(x,y)=1$ and $|f(x)-f(y)|\geq 1$ if $\dist(x,y)=2$, where $\dist(u,v)$ is the distance between the two vertices~$u$ and~$v$ in the graph $G$. The \emph{span} of an $L(2,1)$-labelling $f$ is the difference between the largest and the smallest labels used by $f$ plus $1$. In 1992, Griggs and Yeh conjectured that every graph with maximum degree $\Delta\geq 2$ has an $L(2,1)$-labelling with span at most $\D2+1$. We settle this conjecture for $\D$ sufficiently large.

     
  53. L. Hogie, G. Danoy, P. Bouvry, and F. Guinand. A Context-Aware Broadcast Protocol for DTNs. In Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO'08), volume 14 of Communications in Computer and Information Science, pages 507-519, September 2008. Springer. [PDF ]
    Abstract:
    Delay Tolerant Networks (DTNs) are a sub-class of mobile ad hoc networks (MANETs). They are mobile wireless networks that feature inherent connection disruption. In particular such net- works are generally non-connected. In this paper we focus on defining a broadcast service which operate on DTNs. A number of protocols solving the problem of broadcasting across DTNs have been proposed in the past, but all of them exhibit a static behavior, i.e. they provide no control parameter. However, at the application level, flexible broadcasting schemes are desirable. In particular, it is important that the user (the source of the broadcast message) can control the way the message gets spread across the network. This paper introduces a new broadcasting protocol dedicated to DTNs, called Context-Aware Broadcasting Protocol (CABP), which adapts its greediness according to the "urgency" (priority) of the broadcast message. A formal presentation of its strategy is proposed and through preliminary experi- ments, the cost-effectiveness of CABP is enlightened.

     
  54. C.-C. Huang, T. Kavitha, D. Michail, and M. Nasre. Bounded Unpopularity Matchings. In 11th Scandinavian Workshop on Algorithm Theory (SWAT)., volume 5124 of Lecture Notes in Computer Science, pages 127-137, July 2008.
    Abstract:
    We investigate the following problem: given a set of jobs and a set of people with preferences over the jobs, what is the optimal way of matching people to jobs? Here we consider the notion of popularity. A matching M is popular if there is no matching M' such that more people prefer M' to M than the other way around. Determining whether a given instance admits a popular matching and, if so, finding one, was studied in Abraham et al. . If there is no popular matching, a reasonable substitute is a matching whose unpopularity is bounded. We consider two measures of unpopularity - unpopularity factor denoted by u(M) and unpopularity margin denoted by g(M). McCutchen recently showed that computing a matching M with the minimum value of u(M) or g(M) is NP-hard, and that if G does not admit a popular matching, then we have Your browser may not support display of this image. for all matchings M in G. Here we show that a matching M that achieves u(M) = 2 can be computed in Your browser may not support display of this image.time (where m is the number of edges in G and n is the number of nodes) provided a certain graph H admits a matching that matches all people. We also describe a sequence of graphs: H = H2, H3,...,Hk such that if Hk admits a matching that matches all people, then we can compute in Your browser may not support display of this image.time a matching M such that Your browser may not support display of this image.and Your browser may not support display of this image.. Simulation results suggest that our algorithm finds a matching with low unpopularity.

     
  55. F. Huc, C. Linhares-Sales, and H. Rivano. The Proportional Colouring Problem: Optimizing Buffers in Radio Mesh Networks. In IV Latin-American Algorithms, Graphs, and Optimization Symposium (LAGOS 07), volume 30 of Electronic Notes in Discrete Mathematics, Puerto Varas, Chile, pages 141--146, February 2008. Elsevier. [PDF ]
    Abstract:
    In this paper, we consider a new edge colouring problem: the proportional edge-colouring. Given a graph $G$ with positive weights associated to its edges, we want to find a colouring which preserves the proportion given by the weights associated to each edge. If such colouring exists, we want to find one using a minimum number of colours. We proved that deciding if a weighted graph admits a proportional colouring is polynomial while determining its proportional chromatic index is NP-hard. In addition, we give a lower bound and an upper bound for this parameter that can be computed in polynomial time. We finally show a class of graphs and a class of weighted graphs for which we can exactly determine the proportional chromatic index.

     
  56. D. Ilcinkas, N. Nisse, and D. Soguet. Le cout de la monotonie dans les stratégies d'encerclement réparti. In 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'08), pages 4p, 2008. [WWW ] [PDF ]
    Abstract:
    L'encerclement dans les r\'eseaux vise \`a r\'ealiser le nettoyage, par une \'equipe d'agents mobiles, d'un r\'eseau contamin\'e. La strat\'egie d'encerclement est calcul\'ee en temps r\'eel, par les agents eux mêmes, et doit v\'erifier les trois propri\'et\'es suivantes: (1)~{\it connexit\'e} : la zone nettoy\'ee doit toujours être connexe de fa\c{c}on \`a assurer des communications s\'ecuris\'ees entre les agents, (2)~{\it monotonie} : la zone nettoy\'ee ne doit jamais être recontamin\'ee, ce qui permet un temps de nettoyage polynomial en la taille du r\'eseau, et (3)~{\it optimalit\'e} : le nombre d'agents utilis\'es doit être le plus petit possible afin de minimiser la taille des ressources utilis\'ees. Etant donn\'e un graphe $G$, le plus petit nombre d'agents n\'ecessaire pour nettoyer $G$ de façon monotone connexe dans un contexte centralis\'e est not\'e $\mcs(G)$. Plusieurs protocoles r\'epartis ont \'et\'e propos\'e pour r\'esoudre le probl\`eme de l'encerclement dans les r\'eseaux. Blin {\it et al.} ont propos\'e un algorithme distribu\'e permettant \`a $\mcs(G)$ agents de d\'eterminer et de r\'ealiser une strat\'egie d'encerclement dans tout graphe inconnu $G$ (inconnu signifie que les agents n'ont aucune connaissance {\it a priori} concernant le graphe) [AlgoTel'06]. Cependant, la strat\'egie r\'ealis\'ee n'est pas monotone et peut prendre un temps exponentiel. Nisse et Soguet ont prouv\'e que, pour r\'esoudre le probl\`eme de l'encerclement dans les r\'eseaux, il est n\'ecessaire et suffisant de fournir $\Theta(n \log n)$ bits d'information aux agents par le biais d'un \'etiquetage des sommets du graphe [AlgoTel'07]. Ainsi, pour nettoyer un graphe inconnu de fa\c{c}on monotone et connexe, il est necessaire d'utiliser plus d'agents que l'optimal. Dans cet article, nous \'etudions la proportion d'agents suppl\'ementaires qui sont n\'ecessaires et suffisants pour nettoyer de façon monotone connexe r\'eparti tout graphe inconnu. Nous montrons que la contrainte de monotonie implique une augmentation drastique de ce nombre d'agents. Nous prouvons que tout protocole distribu\'e ayant pour but de nettoyer tout graphe inconnu de $n$ sommets de façon monotone connexe r\'eparti a un ratio comp\'etitif de $\Theta(\frac{n}{\log n})$. Plus pr\'ecis\'ement, nous prouvons que pour tout protocole distribu\'e $\cal P$, il existe une constante $c$ tel que pour tout $n$ suffisamment grand, il existe un graphe $G$ de $n$ sommets tel que $\cal P$ requiert au moins $c\frac{n}{\log n}\, \mcs(G)$ agents pour nettoyer $G$. De plus, nous proposons un protocole distribu\'e qui permet \`a $O(\frac{n}{\log n})\, \mcs(G)$ agents de nettoyer tout graphe inconnu $G$ de $n$ sommets, de façon monotone connexe r\'eparti.

     
  57. K. Kawarabayashi and B. Reed. A nearly linear time algorithm for the half integral disjoint paths packing. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithm (SODA 2008), pages 446-454, 2008. [PDF ]
    Abstract:
    We consider the following problem, which is called the half integral k disjoint paths packing. Input: A graph G, k pair of vertices (s1, t1), (s2, t2),\cdots, (sk, tk) in G (which are sometimes called terminals). Output: Paths P1, \cdots, Pk in G such that Pi joins si and ti for i = 1,2,\cdots, k, and in addition, each vertex is on at most two of these paths. We present an O(n log n) time algorithm for this problem for fixed k. This improves a result by Kleinberg who gave an O(n3) algorithm for this problem. In fact, we also have algorithms running in O(n(1+\varepsilon)) time for any \varepsilon > 0 for these problems, if k is up to o((log log n)2/5) for general graphs, up to o((log n/(log log n))1/4) for planar graphs, and up to o((log n/g/(log log n/g))1/4) for graphs on the surface, where g is the Euler genus. Furthermore, if k is fixed, then we have linear time algorithms for the planar case and for the bounded genus case. We also obtain O(n log n) algorithms for several optimization problems related to the bounded unsplittable flow problem when the number of terminal pairs is bounded. These results can all carry over to problems involving edge capacities.

     
  58. Z. Li and B. Reed. Optimization and Recognition for ${K}_5$-minor Free Graphs in Linear Time. In Proceedings of LATIN, pages 206-215, 2008.
     
  59. C. Molle, F. Peix, S. Pérennes, and H. Rivano. Formulation en Coupe/Rounds pour le Routage dans les réseaux radio maillés. In 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'08), pages 4p, May 2008. [WWW ] [PDF ]
    Abstract:
    Un des probl\`emes au c\oe ur de l'optimisation des r\'eseaux radio maill\'es est le routage et l'ordonnancement d'appels. Dans cet article, nous \'etudions une relaxation classique de ce probl\`eme qui consiste \`a r\'epartir la capacit\'e entre les ensembles d'appels simultan\'es de mani\`ere \`a garantir un d\'ebit suffisant \`a chaque routeur du r\'eseau. Nous introduisons une nouvelle formulation s'affranchissant du routage pour se concentrer sur la capacit\'e de transport disponible sur les coupes du r\'eseau. Nous prouvons son \'equivalence avec les formulations existantes et pr\'esentons un processus efficace de r\'esolution par g\'en\'eration crois\'ee de lignes et de colonnes.

     
  60. C. Molle, F. Peix, S. Pérennes, and H. Rivano. Optimal Routing and Call Scheduling in Wireless Mesh Networks with Localized Information. In C. Kaklamanis and F. Nielson, editors, the fourth Symposium on Trustworthy Global Computing (TGC 2008), volume 5474 of Lecture Notes in Computer Science, Barcelona, Spain, pages 171-185, November 2008. [WWW ] [PDF ]
    Abstract:
    Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum per-flow throughput is computed. A classical relaxation of JRSP, denoted as the Round Weighting Problem (RWP), consists in assigning enough weight to sets of compatible simultaneous transmissions (rounds), while minimizing the sum of them, thus maximizing the relative weight of each round, which model the throughput. In this work, we present a new linear formulation of RWP focused on the transport capacity over the network cuts, thus eliminating the routing. We prove its equivalence with existing formulations with flows and formalize a primal-dual algorithm that quickly solves this problem using a cross line and column generations process. An asset of this formulation is to point out a bounded region, a "bottleneck" of the network, that is enough to optimize in order to get the optimal RWP of the whole network. The size and location of this area is experimentally made through simulations, highlighting a few hop distant neighborhood of the mesh gateways. One would then apply approximated methods outside this zone to route the traffic without degrading the achieved capacity.

     
  61. C. Molle, F. Peix, and H. Rivano. An optimization framework for the joint routing and scheduling in wireless mesh networks. In Proc. 19th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC'08), Cannes, France, September 2008. [WWW ] [PDF ]
    Abstract:
    In this paper, we address the problem of computing the transport capacity of Wireless Mesh Networks dedicated to Internet access. Routing and transmission scheduling have a major impact on the capacity provided to the clients. A cross- layer optimization of these problems allows the routing to take into account contentions due to radio interferences. We develop exact linear programs and provide an efficient column generation process computing a relaxation of the problem. It allows to work around the combinatoric of simultaneously achievable transmissions, hence computing solutions on large networks. Our approach is validated through extensive simulations. Evolution of the capacity of a mesh network with its parameters, as well as the algorithmic complexity are then discussed. We conjecture that the problem can be solved in polynomial time and that the gateway placement problem is only subject to localized constraints.

     
  62. C. Molle, F. Peix, and H. Rivano. Génération de colonnes pour le routage et l'ordonnancement dans les réseaux radio maillés. In Colloque francophone sur l'ingénierie des protocoles (CFIP 2008), pages 12p, March 2008.
    Note: Best student paper award. [WWW ] [PDF ]
    Abstract:
    Dans cet article, nous \'etudions la capacit\'e des r\'eseaux radio maill\'es d\'edi\'es à l'acc\`es à Internet. Nous nous pla\c ons dans l'hypoth\`ese d'un r\'eseau synchrone fonctionnant en r\'egime permanent o\`u les transmissions partagent un m\^eme canal radio. Le routage et l'ordonnancement des transmissions ont un impact majeur sur la capacit\'e fournie aux clients. Une optimisation jointe de ces deux probl\`emes permet de prendre en compte dans le routage les contentions dues aux interf\'erences radio. Nous en d\'eveloppons des formulations exactes en programmation lin\'eaire. Nous pr\'esentons ensuite un processus de g\'en\'eration de colonnes r\'esolvant une relaxation du probl\`eme. Ainsi, nous contournons l'\'ecueil de la combinatoire des transmissions r\'ealisables simultan\'ement pour permettre de calculer des solutions sur des r\'eseaux de grande taille. Des simulations sont effectu\'ees sur des topologies al\'eatoires. L'\'evolution de la capacit\'e d'un r\'eseau maill\'e avec ses param\`etres, ainsi que la complexit\'e algorithmique du probl\`eme sont discut\'ees.

     
  63. C. Molle and M.-E. Voge. Influence des acquittements sur la capacité des réseaux radio maillés. In 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'08), pages 4p, May 2008. [WWW ] [PDF ]
    Abstract:
    A la veille du d\'eploiement de l'informatique ubiquitaire, la performance des r\'eseaux radio est un enjeu \'economique majeur. Parmi les indicateurs de performance, la {\it capacit\'e}, ou volume maximal de trafic que peut \'ecouler le r\'eseau en un temps fix\'e, est essentielle. Dans cet article nous \'evaluons le gain en capacit\'e induit par la suppression des acquittements au niveau MAC en r\'esolvant un mod\`ele lin\'eaire par g\'en\'eration de colonnes.

     
  64. J. Monteiro. The use of Evolving Graph Combinatorial Model in Routing Protocols for Dynamic Networks. In Proceedings of the XV Concurso Latinoamericano de Tesis de Maestrìa (CLEI'08), Santa Fe, Argentina, pages 41--57, September 2008.
    Note: Third prize in the CLEI'08 Master's Thesis Contests. [PDF ]
    Abstract:
    The assessment of routing protocols for ad hoc networks is a difficult task, due to the networks’ highly dynamic behavior and the absence of benchmarks. Recently, a graph theoretic model – the evolving graphs – was proposed to help capture the network topology changes during time, with predictable dynamics at least. The algorithms and insights obtained through this model are theoretically very effcient and intriguing. However, there is no study about the use of such theoretical results into practical situations. We used the NS2 network simulator to first implement an evolving graph based routing protocol, and then used it as a benchmark when comparing four ma jor ad-hoc routing pro- tocols. Interestingly, our experiments showed that evolving graphs have the potential to be an effective and powerful tool. In order to make this model widely applicable, however, some practical issues still have to be addressed and incorporated into the model.

     
  65. X. Muñoz and I. Sau. Traffic Grooming in Unidirectional WDM Rings with Bounded-Degree Request Graph. In 34th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2008), volume 5344 of Lecture Notes in Computer Science, pages 300-311, June 2008. [PDF ]
    Abstract:
    Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely ADMs. We consider the case when the topology is a unidirectional ring. In graph-theoretical terms, the traffic grooming problem in this case consists in partitioning the edges of a request graph into subgraphs with a maximum number of edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded maximum degree $\Delta$, and our aim is to design a network being able to support any request graph satisfying the degree constraints. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and solve the cases $\Delta=2$ (for all values of $C$) and $\Delta = 3$ (except the case $C=4$). We also provide lower and upper bounds for the general case.

     
  66. N. Nisse and K. Suchan. Voleur véloce dans un réseau planaire. In 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'08), pages 4p, 2008. [WWW ] [PDF ]
    Abstract:
    D\'efini par Nowakowski et Winkler et, ind\'ependament, par Quilliot (1983), le jeu des gendarmes et du voleur impliquent deux joueurs qui jouent \`a tour de r\^ole dans un graphe. Le premier d\'eplace les gendarmes le long des ar\^etes du graphe, puis c'est au tour du second qui d\'eplace le voleur. Le but des gendarmes est d'attraper le voleur, tandis que ce dernier essaie d'\'eviter la capture ind\'efiniment. Le probl\`eme dans ce contexte est de minimiser le nombre de gendarmes n\'ecessaires pour capturer le voleur. Ce nombre s'appelle {\it l'indice d'\'evasion} du graphe ({\it cop-number} en anglais). Si les gendarmes et le voleur ont la m\^eme vitesse, Schr\"oder (2001) a prouv\'e que $3+\frac{3}{2}g$ gendarmes suffisent \`a capturer tout voleur dans un graphe de {\it genre} born\'e $g$. En particulier, cela signifie que la capture d'un voleur dans un graphe {\it planaire} est facile puisque $3$ gendarmes suffisent (en fait deux gendarmes sont suffisants dans toute grille). Dans ce travail, nous aidons le voleur en lui permettant de ce d\'eplacer plus vite que les gendarmes. Nous montrons que cela conduit \`a une augmentation drastique du nombre de gendarmes. Plus pr\'ecisement, nous prouvons que $\Omega(\sqrt{\log n})$ gendarmes sont n\'ecessaires pour capturer un voleur v\'eloce dans une grille carr\'ee de c\^ot\'e $n$. La preuve que nous proposons consiste en une \'el\'egante et simple strat\'egie d'\'evasion pour le voleur. Il est alors int\'eressant de savoir si le fait qu'un graphe planaire $H$ ait un indice d'\'evasion \'elev\'e est li\'e au fait que $H$ ``contient'' une large grille $G$. Nous montrons que ce n'est pas la cas lorsque la notion de contenance correspond \`a la notion de minoration topologique (c'est \`a dire si $G$ peut \^etre obtenu de $H$ en rempla\c{c}ant des chemins dont les sommets internes sont de degr\'e deux, par des ar\^etes). Cependant, nous prouvons que si $H$ planaire contient une large grille comme sous-graphe induit, alors son indice d'\'evasion est \'elev\'e. Notons que ce dernier r\'esultat n'est pas vrai dans le cas d'un graphe $H$ non planaire.

     
  67. N. Nisse and K. Suchan. Fast Robber in Planar Graphs. In Proceedings of the 34th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), volume 5344 of Lecture Notes in Computer Science, pages 33-44, 2008. [WWW ] [PDF ]
    Abstract:
    In the {\it cops and robber game}, two players play alternately by moving their tokens along the edges of a graph. The first one plays with the {\it cops} and the second one with one {\it robber}. The cops aim at capturing the robber, while the robber tries to infinitely evade the cops. The main problem consists in minimizing the number of cops used to capture the robber in a graph. This minimum number is called the {\it cop-number} of the graph. If the cops and the robber have the same velocity, $3+\frac{3}{2}g$ cops are sufficient to capture one robber in any graph with genus $g$ (Schr\"oder, 2001). In the particular case of a grid, $2$ cops are sufficient. We investigate the game in which the robber is slightly faster than the cops. In this setting, we prove that the cop-number of planar graphs becomes unbounded. More precisely, we prove that $\Omega(\sqrt{\log n})$ cops are necessary to capture a fast robber in the $n \times n$ square-grid. This proof consists in designing an elegant evasion-strategy for the robber. Then, it is interesting to ask whether a high value of the cop-number of a planar graph $H$ is related to a large grid $G$ somehow contained in $H$. We prove that it is not the case when the notion of containment is related to the classical transformations of edge removal, vertex removal, and edge contraction. For instance, we prove that there are graphs with cop-number at most $2$ and that are subdivisions of arbitrary large grid. On the positive side, we prove that, if $H$ planar contains a large grid as an induced subgraph, then $H$ has large cop-number. Note that, generally, the cop-number of a graph $H$ is not closed by taking induced subgraphs $G$, even if $H$ is planar and $G$ is an distance-hereditary induced-subgraph.

     
  68. J. Ribault and O. Dalle. Enabling advanced simulation scenarios with new software engineering techniques. In 20th European Modeling and Simulation Symposium (EMSS 2008), Briatico, Italy, pages 6p, 2008. [PDF ]
    Abstract:
    In this paper, we introduce new techniques in the field of simulationto help in the process of building advanced simulation scenarios usingpreexisting simulation components. The first technique consists in using the Aspect Oriented Programming? paradigm to capture some of the private data of anexisting model component. The second one is an Architecture Description Language (ADL) designed for the Fractal component model, that offers definition overloading and extension mechanisms similar to those found in traditional Object Oriented languages.The benefits of using both techniques are illustrated by simple usecases of network security studies.

     
  69. E. Altman, P. Nain, and J-C. Bermond. Distributed Storage Management of Evolving Files in Delay Tolerant Ad Hoc Networks. Research Report RR-6645, INRIA, September 2008. [WWW ] [PDF ]
    Abstract:
    This work focuses on a class of distributed storage systems whose content may evolve over time. Each component or node of the storage system is mobile and the set of all nodes forms a delay tolerant (ad hoc) network (DTN). The goal of the paper is to study efficient ways for distributing evolving files within DTNs and for managing dynamically their content. We specify to dynamic files where not only the latest version is useful but also previous ones; we restrict however to files where a file has no use if another more recent version is available. There are N+1 mobile nodes including a single source which at some points in time makes available a new version of a single file F. We consider both the cases when (a) nodes do not cooperate and (b) nodes cooperate. In case (a) only the source may transmit a copy of the latest version of F to a node that it meets, while in case (b) any node may transmit a copy of F to a node that it meets. A file management policy is a set of rules specifying when a node may send a copy of F to a node that it meets. The objective is to find file management policies which maximize some system utility functions under a constraint on the resource consumption. Both myopic (static) and state-dependent (dynamic) policies are considered, where the state of a node is the age of the copy of F it carries. Scenario (a) is studied under the assumption that the source updates F at discrete times t=0,1,\ldots. During a slot [t,t+1) the source meets any node with a fixed probability q. We find the optimal static (resp. dynamic) policy which maximizes a general utility function under a constraint on the number of transmissions within a slot. In particular, we show the existence of a threshold dynamic policy. In scenario (b) F is updated at random points in time, with the consequence that between two meetings with the source a node does not know the age evolution of the version of F it holds. Under Markovian assumptions regarding nodes mobility and update frequency of F, we study the stability of the system (aging of the nodes) and derive an (approximate) optimal static policy. We then revisit scenario (a) when the source does not know parameter N (node population) and q (node meeting probability) and derive a stochastic approximation algorithm which we show to converge to the optimal static policy found in the complete information setting. Numerical results illustrate the respective performance of optimal static and dynamic policies as well as the benefit of node cooperation.

     
  70. O. Amini, F. Huc, I. Sau, and J. Zerovnik. $(\ell,k)$-Routing on Plane Grids. Research Report 6480, INRIA, March 2008. [WWW ] [PDF ]
    Abstract:
    The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the $(\ell,k)$-routing problem, each node can send at most $\ell$ packets and receive at most $k$ packets. Permutation routing is the particular case $\ell=k=1$. In the $r$-central routing problem, all nodes at distance at most $r$ from a fixed node $v$ want to send a packet to $v$. In this article we study the permutation routing, the $r$-central routing and the general $(\ell,k)$-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the \emph{store-and-forward} $\Delta$-port model, and we consider both full and half-duplex networks. The main contributions are the following: \begin{itemize} \item[1.] Tight permutation routing algorithms on full-duplex hexagonal grids, and half duplex triangular and hexagonal grids. \item[2.] Tight $r$-central routing algorithms on triangular and hexagonal grids. \item[3.] Tight $(k,k)$-routing algorithms on square, triangular and hexagonal grids. \item[4.] Good approximation algorithms (in terms of running time) for $(\ell,k)$-routing on square, triangular and hexagonal grids, together with new lower bounds on the running time of any algorithm using shortest path routing. \end{itemize} \noindent All these algorithms are completely distributed, i.e. can be implemented independently at each node. Finally, we also formulate the $(\ell,k)$-routing problem as a \textsc{Weighted Edge Coloring} problem on bipartite graphs.

     
  71. O. Amini, D. Peleg, S. Pérennes, I. Sau, and S. Saurabh. Degree-Constrained Subgraph Problems: Hardness and Approximation Results. Research Report RR-6690, INRIA, October 2008. [WWW ] [PDF ]
    Abstract:
    A general instance of a Degree-Constrained Subgraph problem consists of an edge-weighted or vertex-weighted graph G and the objective is to find an optimal weighted subgraph, subject to certain degree constraints on the vertices of the subgraph. This paper considers three natural Degree-Constrained Subgraph problems and studies their behavior in terms of approximation algorithms. These problems take as input an undirected graph G=(V,E), with |V|=n and |E|=m. Our results, together with the definition of the three problems, are listed below. 1- The Maximum Degree-Bounded Connected Subgraph (MDBCS_d) problem takes as input a weight function w: E -> R+ and an integer d>1, and asks for a subset of edges E' such that the subgraph G'=(V,E') is connected, has maximum degree at most d, and the total edge-weight is maximized. We prove that MDBCS_d is not in APX for any d>1 (this was known only for d=2) and we provide a min{m/log n, nd/2log n}-approximation algorithm for unweighted graphs, and a min{n/2,m/d}-approximation algorithm for weighted graphs. 2- The Minimum Subgraph of Minimum Degree d (MSMD_d) problem consists in finding a smallest subgraph of G (in terms of number of vertices) with minimum degree at least d. For d=2 it corresponds to finding a shortest cycle of the graph. We prove that MSMD_d is not in APX for any d>2 and we provide an n/logn-approximation algorithm for the classes of graphs excluding a fixed graph as a minor, using dynamic programming techniques and a known structural result on graph minors. 3- The Dual Degree-Dense k-Subgraph (DDDkS) problem consists in finding a subgraph H of G such that |V(H)|

     
  72. M. Asté, F. Havet, and C. Linhares-Sales. Grundy number and products of graphs. Research Report RR-6672, INRIA, October 2008. [PDF ]
    Abstract:
    The {\em Grundy number} of a graph $G$, denoted by $\Gamma (G)$, is the largest $k$ such that $G$ has a {\em greedy} $k$-colouring, that is a colouring with $k$ colours obtained by applying the greedy algorithm according to some ordering of the vertices of $G$. In this paper, we study the Grundy number of the lexicographic, cartesian and direct products of two graphs in terms of the Grundy numbers of these graphs. Regarding the lexicographic product, we show that $\Gamma(G)\times\Gamma(H)\leq \Gamma(G[H])\leq 2^{\Gamma(G)-1}(\Gamma(H)-1)+\Gamma(G)-1$. In addition, we show that if $G$ is a tree or $\Gamma(G)=\Delta(G)+1$, then $\Gamma(G[H])=\Gamma(G)\times\Gamma(H)$. We then deduce that for every fixed $c\leq 1$, given a graph $G$, it is CoNP-Complete to decide if $\Gamma(G)\leq c\times \chi(G)$ and it is CoNP-Complete to decide if $\Gamma(G)\leq c\times \omega(G)$. Regarding the cartesian product, we show that there is no upper bound of $\Gamma(G\square H)$ as a function of $\Gamma(G)$ and $\Gamma(H)$. Nevertheless, we prove that for any fixed graph $G$, there is a function $h_G$ such that, for any graph $H$, $\Gamma(G\square H)\leq h_G(\Gamma(H))$. Regarding the direct product, we show that $\Gamma(G\times H)\geq \Gamma(G) +\Gamma(H)-2$ and construct for any $k$ some graph $G_k$ such that $\Gamma(G_k)=2k+1$ and $\Gamma(G_k\times K_2)=3k+1$.

     
  73. J-C. Bermond, I. Caragiannis, D. Coudert, F. Diedrich, L. Hogie, F. Huc, C. Molle, J. Monteiro, P. Leone, H. Rivano, and I. Sau. Algorithmic solutions for critical resource sharing: third year. Technical report Deliverable 2.2.3, IST FET AEOLUS, Integrated Project IST-015964, 2008. [PDF ]
     
  74. J-C. Bermond, R. Correa, and M-L. Yu. Optimal Gathering Protocols on Paths under Interference Constraints. Technical report inria-00168162, HAL, August 2008. [WWW ] [PDF ]
    Abstract:
    We study the problem of gathering information from the nodes of a multi-hop radio network into a predefined destination node under reachability and interference constraints. In such a network, a node is able to send messages to other nodes within reception distance, but doing so it might create interference with other communications. Thus, a message can only be properly received if the receiver is reachable from the sender and there is no interference from another message being simultaneously transmitted. The network is modeled as a graph, where the vertices represent the nodes of the network and the edges, the possible communications. The interference constraint is modeled by a fixed integer $d \geq 1$, which implies that nodes within distance $ d$ in the graph from one sender cannot receive messages from another node. In this paper, we suppose that each node has one unit-length message to transmit and, furthermore, we suppose that it takes one unit of time (slot) to transmit a unit-length message and during such a slot we can have only calls which do not interfere (called compatible calls). A set of compatible calls is referred to as a round. We give protocols and lower bounds on the minimum number of rounds for the gathering problem when the network is a path and the destination node is either at one end or at the center of the path. The protocols are shown to be optimal for any $d$ in the first case, and for $1 \leq d \leq 4$, in the second case.

     
  75. J-C. Bermond, D. Mazauric, V. Misra, and P. Nain. Distributed Call Scheduling in Wireless Networks. Technical report RR-6763, INRIA, December 2008. [WWW ] [PDF ]
    Abstract:
    This work investigates distributed transmission scheduling in wireless networks. Due to interference constraints, "neighboring links" cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We follow the model described by Bui, Sanghavi, and Srikant in SBS07,SBS09. We suppose that time is slotted and during each slot we have two phases: one control phase which determines what links will be activated and send data during the second phase. We assume random arrivals on each link during each slot, therefore a queue is associated to each link. Since nodes do not have a global knowledge of the network, our aim (like in SBS07,SBS09) is to design for the control phase, a distributed algorithm which determines a set of non interfering links. To be efficient the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead). In this article we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues); and it needs no knowledge. Indeed contrary to other existing algorithms, we do not need to know the values of the queues of the "neighboring links", which are difficult to obtain in a wireless network with interference. We prove that this algorithm gives a maximal set of active links (in each interference set, there is at least one active edge). We also give sufficient conditions for stability under Markovian assumptions. Finally the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.

     
  76. J-C. Bermond, V. Papadopoulou, and E. Pitoura. Subproject2: Resource Management Report on the activities of the third year. Technical report Deliverable 2.O.3, IST FET AEOLUS, Integrated Project IST-015964, 2008. [PDF ]
     
  77. P. Berthomé and N. Nisse. A unified FPT Algorithm for Width of Partition Functions. Research Report RR-6646, INRIA, September 2008. [WWW ] [PDF ]
    Abstract:
    During the last decades, several polynomial-time algorithms have been designed that decide if a graph has treewidth (resp., pathwidth, branchwidth, etc.) at most $k$, where $k$ is a fixed parameter. Amini {\it et al.} (to appear in SIAM J. Discrete Maths.) use the notions of partitioning-trees and partition functions as a generalized view of classical decompositions of graphs, namely tree-decomposition, path-decomposition, branch-decomposition, etc. In this paper, we propose a set of simple sufficient conditions on a partition function $\Phi$, that ensures the existence of a linear-time explicit algorithm deciding if a set $A$ has $\Phi$-width at most $k$ ($k$ fixed). In particular, the algorithm we propose unifies the existing algorithms for treewidth, pathwidth, linearwidth, branchwidth, carvingwidth and cutwidth. It also provides the first Fixed Parameter Tractable linear-time algorithm deciding if the $q$-branched treewidth, defined by Fomin {\it et al.} (Algo rithmica 2007), of a graph is at most $k$ ($k$ and $q$ are fixed). Our decision algorithm can be turned into a constructive one by following the ideas of Bodlaender and Kloks (J. of Alg. 1996).

     
  78. R. Correa, F. Havet, and J.-S. Sereni. About a Brooks-type theorem for improper colouring. Research Report RR-6432, INRIA, January 2008. [WWW ] [PDF ]
    Abstract:
    A graph is k-improperly -colourable if its vertices can be partitioned into parts such that each part induces a subgraph of maximum degree at most k. A result of Lovasz a states that for any graph G, such a partition exists if l is at least (Delta(G)+1)/(k+1) . When k = 0, this bound can be reduced by Brooks' Theorem, unless G is complete or an odd cycle. We study the following question, which can be seen as a generalisation of the celebrated Brooks' Theorem to improper colouring: does there exist a polynomial-time algorithm that decides whether a graph G of maximum degree has k-improper chromatic number at most (Delta+1)/(k+1) - 1? We show that the answer is no, unless P = N P , when Delta= (k + 1)l, k>0 and l+sqrt(l) < 2k + 4. We also show that, if G is planar, k = 1 or k = 2, Delta = 2k + 2, and l= 2, then the answer is still no, unless P = N P . These results answer some questions of Cowen et al. [Journal of Graph Theory 24(3):205-219, 1997].

     
  79. D. Coudert, F. Huc, D. Mazauric, N. Nisse, and J-S. Sereni. Routing Reconfiguration/Process Number: Coping wih Two Classes of Services. Research Report RR-6698, INRIA, October 2008. [WWW ]
    Abstract:
    In WDM backbone networks, the traffic pattern evolves constantly due to the nature of the demand itself or because of equipment failures leading to reroute affected connections. In this context, requests are routed greedily using available resources without changing the routing of pre-established connections. However, such a policy leads to a poor usage of resources and so higher blocking probability: new connection requests might be rejected while network resources are sufficient to serve all the traffic. Therefore, it is important to regularly reconfigure the network by rerouting established connections in order to optimize the usage of network resources. In this paper, we consider the network reconfiguration problem that consists in switching existing connections one after the other from the current routing to a new pre-computed routing. Due to cyclic dependencies between connections, some requests may have to be temporarily interrupted during this process. Clearly, the number of requests simultaneously interrupted has to be minimized. Furthermore, it might be impossible for the network operator to interrupt some connections because of the contract signed with the corresponding clients. In this setting, the network reconfiguration problem consists in going from a routing to another one given that some priority connections cannot be interrupted. The network reconfiguration problem without priority connections has previously been modeled as a cops-and-robber game in CPPS05,CoSe07. Here, we first extend this model to handle priority connections. Then we identify cases where no solution exists. Using a simple transformation, we prove that the reconfiguration problem with priority connections can be reduced to the problem without this constraint. Finally, we propose a new heuristic algorithm that improves upon previous proposals.

     
  80. D. Coudert, F. Huc, and D. Mazauric. A distributed algorithm for computing and updating the process number of a forest. Research Report RR-6560, INRIA, June 2008. [WWW ]
    Abstract:
    In this paper, we present a distributed algorithm to compute various parameters of a tree such as the process number, the edge search number or the node search number and so the pathwidth. This algorithm requires n steps, an overall computation time of O(n log(n)), and n messages of size log_3(n)+3. We then propose a distributed algorithm to update the process number (or the node search number, or the edge search number) of each component of a forest after adding or deleting an edge. This second algorithm requires O(D) steps, an overall computation time of O(D log(n)), and O(D) messages of size log_3(n)+3, where D is the diameter of the modified connected component. Finally, we show how to extend our algorithms to trees and forests of unknown size using messages of less than 2a+4+e bits, where a is the parameter to be determined and e=1 for updates algorithms.

     
  81. D. Coudert and D. Mazauric. Network Reconfiguration using Cops-and-Robber Games. Research Report RR-6694, INRIA, August 2008. [WWW ]
    Abstract:
    The process number is the number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the pathwidth. However they are not always equal in general graphs. Determining these parameters is in general NP-complete. In this paper, we propose a polynomial algorithm to compute an approximation of the process number of digraphs, improving the efficiency of the previous exponential algorithm.

     
  82. D. Coudert, N. Nepomuceno, and H. Rivano. Wireless Backhaul Networks: Minimizing Energy Consumption by Power Efficient Radio Links Configuration. Technical report RR-6752, INRIA, December 2008. [WWW ] [PDF ]
    Abstract:
    In this work, we investigate on minimizing the energy consumption of a wireless backhaul communication network through a joint optimization problem of data routing and radio configuration. The backhaul network is modeled by a digraph in which the nodes represent radio base stations and the arcs denote radio links. According to the scenario under consideration, a power efficient configuration can be characterized by a modulation constellation size and a transmission power level. Every link holds a set of power efficient configurations, each of them associating a capacity with its energy cost. The optimization problem involves deciding the network's configuration and flows which minimize the total energy expenditure, while handling all the traffic requirements simultaneously. An exact mathematical formulation of the problem is presented. It relies on a minimum cost multicommodity flow with stepwise cost functions which is very hard to optimize. We then introduce a linear relaxation of the problem, which exploits the convexity of the energy cost as a function of the throughput on a radio link. This yields lower bounds on the energy consumption, and eventually a heuristic algorithm based on the fractional optimum is presented. Our models are validated through extensive experiments which are reported and discussed. The results of the simulations testify the potentialities behind this novel approach. In particular, our algorithm takes a good advantage of the convexity of the cost function, inducing a quite small integrity gap in practice.

     
  83. O. Dalle, F. Giroire, J. Monteiro, and S. Pérennes. Analysis of Failure Correlation in Peer-to-Peer Storage Systems. Technical report RR-6761, INRIA, December 2008. [WWW ] [PDF ]
    Abstract:
    In this paper, we propose and study analytical models of self-repairing peer-to-peer storage systems subject to failures. The failures correspond to the simultaneous loss of multiple data blocks due to the definitive loss of a peer (or following a disk crash). In the system we consider that such failures happen continuously, hence the necessity of a self-repairing mechanism (data are written once for ever). We show that, whereas stochastic models of independent failures similar to those found in the literature give a correct approximation of the average behavior of real systems, they fail to capture their variations (e.g. in bandwidth needs). We propose to solve this problem using a new stochastic model based on a fluid approximation and we give a characterization of the behavior of the system according to this model (expectation and standard deviation). This new model is validated using comparisons between its theoretical behavior and computer simulations.

     
  84. J. Galtier. New algorithms to compute the strength of a graph. Research Report RR-6592, INRIA, July 2008.
     
  85. C. Gomes, S. Pérennes, and H. Rivano. Bottleneck Analysis for Routing and Call Scheduling in Multi-hop Wireless Networks. Technical report inria-00282200, INRIA, May 2008. [WWW ] [PDF ]
    Abstract:
    In this paper, we address the routing and call scheduling problem in which one has to find a minimum-length schedule of selected links in a TDMA (Time Division Multiple Access) based wireless network. As we deal with a multi-hop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. We present a cross-layer formulation of the problem that computes joint routing and scheduling. We use a branch-and-price algorithm to solve optimally the problem. A column generation algorithm is used to cope with the exponential set of rounds. The branch-and-bound algorithm provides mono-routing. We run experiments on networks from the literature, with different number of gateways. Experimental results as well as theoretical insights let us conjecture that the bottleneck region analysis is enough to find the optimal solution. The bottleneck is usually the gateway considering almost uniform traffic. The integer round-up property (IRUP) seems to hold for our problem.

     
  86. F. Havet, M. Klazar, J. Kratochvil, D. Kratsch, and M. Liedloff. Exact algorithms for $L(2,1)$-labelling. Research Report RR-6587, INRIA, 07 2008.
    Abstract:
    The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph $G=(V,E)$ into an interval of integers $0, \dots ,k$ is an $L(2,1)$-labeling of $G$ of span $k$ if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed $k\ge 4$, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive $O((k+1)^n)$ algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of $k=4$ -- here the running time of our algorithm is $O(1.3006^n)$. $O(1.3161^n)$. Furthermore we show that dynamic programming can be used to establish an $O(3.8730^n)$ algorithm to compute an optimal $L(2,1)$-labeling.

     
  87. F. Havet, D. Král, J.-S. Sereni, and R. Skrekovski. Facial coloring using Hall's Theorem. Research Report 383, ITI-series, 2008. [PDF ]
    Abstract:
    A vertex coloring of a plane graph is $\ell$-facial if every two distinct vertices joined by a facial walk of length at most $\ell$ receive distinct colors. It has been conjectured that every plane graph has an $\ell$-facial coloring with at most $3\ell+1$ colors. We improve the currently best known bound and show that every plane graph has an $\ell$-facial coloring with at most $\lfloor 7\ell/2\rfloor+6$ colors. Our proof uses the standard discharging technique, however, in the reduction part we have successfully applied Hall's Theorem, which seems to be quite an innovative approach in this area.

     
  88. F. Havet, B. Reed, and J.-S. Sereni. $L(p,1)$-labelling of graphs. Research Report RR-6673, INRIA, October 2008. [PDF ]
    Abstract:
    An $L(p,1)$-labelling of a graph is a function $f$ from the vertex set to the positive integers such that $|f(x)-f(y)|\geq p$ if $\dist(x,y)=1$ and $|f(x)-f(y)|\geq p$ if $\dist(x,y)=2$, where $\dist(x,y)$ is the distance between the two vertices~$x$ and~$y$ in the graph. The \emph{span} of an $L(p,1)$-labelling $f$ is the difference between the largest and the smallest labels used by $f$ plus $1$. In 1992, Griggs and Yeh conjectured that every graph with maximum degree $\Delta\geq 2$ has an $L(2,1)$-labelling with span at most $\D2+1$. We settle this conjecture for $\D$ sufficiently large. More generally, we show that for any positive integer $p$ there exists a constant $\Delta_p$ such that every graph with maximum degree $\Delta\geq \Delta_p$ has an $L(p,1)$-labelling with span at most $\D2+1$. This yields that, for each positive integer $p$, there is an integer $C_p$ such that every graph with maximum degree $\Delta$ has an $L(p,1)$-labelling with span at most $\Delta2+C_p$.

     
  89. F. Havet, J. van den Heuvel, C. McDiarmid, and B. Reed. List Colouring Squares of Planar Graphs. Research Report RR-6586, INRIA, July 2008.
    Abstract:
    In 1977, Wegner conjectured that the chromatic number of the square of every planar graph~$G$ with maximum degree $\Delta\ge8$ is at most $\bigl\lfloor\frac32\,\Delta\bigr\rfloor+1$. We show that it is at most $\frac32\,\Delta\,(1+o(1))$, and indeed this is true for the list chromatic number and for more general classes of graphs.

     
  90. X. Muñoz and I. Sau. Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph. Research Report RR-6481, INRIA, March 2008. [WWW ] [PDF ]
    Abstract:
    Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely ADMs. We consider the case when the topology is a unidirectional ring. In graph-theoretical terms, the traffic grooming problem in this case consists in partitioning the edges of a request graph into subgraphs with a maximum number of edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded maximum degree $\Delta$, and our aim is to design a network being able to support any request graph satisfying the degree constraints. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and solve the cases $\Delta=2$ (for all values of $C$) and $\Delta = 3$ (except the case $C=4$). We also provide lower and upper bounds for the general case.

     
  91. N. Nisse, K. Suchan, and I. Rapaport. Distributed computing of efficient routing schemes in generalized chordal graphs. Technical report CMM-B-08/10-220, CMM, October 2008. [PDF ]
    Abstract:
    We propose a simple interval routing scheme for a graph $G$, based on a Maximal Neighborhood BFS-tree $T$ of $G$. In our scheme a message simply follows the source-destination path in $T$ but, in at most one step, it may take a shortcut. This shortcut is taken when the current node has a neighbor in $G$ which is an ancestor in $T$ of the destination. In the class of $k$-chordal graphs, this gives an additive stretch of at most $k-1$, and at most $1$ in the class of chordal graphs. Our routing tables use $O(\Delta\log n)$ bits per node, where $\Delta$ is the maximum degree. We propose a simple distributed algorithm to compute such tables in time $O(D)$ in any $n$-node graph with diameter $D$.

     
  92. S. Pérennes and I. Sau. Sur la Conjecture des Jeux Uniques. Research Report RR-6691, INRIA, October 2008. [WWW ] [PDF ]
    Abstract:
    La plupart des problèmes d'optimisation combinatoire sont NP-difficiles, c'est-à -dire qu'ils ne peuvent être résolus en temps polynomial que si les classes P et NP sont identiques. Pour ces problèmes on peut espérer soit trouver des algorithmes d'approximation, soit prouver qu'ils ne peuvent pas être approximés de manière efficace. En 2002 S. Khot formula la Conjecture des Jeux Uniques (UGC), qui géneralise le théorème PCP et impliquerait d'importants résultats d'innaproximabilité pour plusieurs problèmes d'optimisation combinatoire (par exemple Max Cut ou Vertex Cover). Intuitivement, la UGC dit que, pour une certaine classe de jeux, appelés uniques, il est NP-dur de décider si l'on peut trouver une solution proche de l'optimale, ou si toutes les solutions sont loin de l'optimale. Cette conjecture est devenue un problème ouvert des plus importants dans la théorie de la complexité et de l'approximation. Dans cet article nous étudions un problème très relié à la UGC: Max-E$2$-Lin2 dans les graphes bipartis. Dans Max-E$2$-Lin2 on a un graphe $G$ ayant deux type d'arêtes, requérant soit la même soit différente couleur pour ses extrémités. Le but est de 2-colorer les sommets de $G$ en maximisant le nombre d'arêtes satisfaites. Nous prouvons que ce problème est APX-complet dans les graphes bipartis et, en utilisant le Théorème de Répétition Paralèlle, nous discutons les conséquences de ce résultat dans le cadre des jeux uniques et la UGC.

     
  93. N. Cohen. Coloration des graphes planaires, July 2008.
    Note: Internship report. [PDF ]
     
  94. M. Hadj Djilani. Interface MASCOPT pour CLP/CBC, September 2008.
    Note: Internship report. [PDF ]
     
  95. F. Giroire, J. Chandrashekar, N. Taft, E. Schooler, and K. Papagiannaki. Method and System for Detecting and Reducing Botnet Activity, December 2008.
    Note: Docket Number P28858 / 45631-207291.
     
  96. F. Giroire, A. Nucci, N. Taft, and C. Diot. Method and Systems for Identifying Optimal Mapping in a Network, November 2008.
    Note: Patent number US 7,453,824 B1. Filled in July 2003.
     
  97. F. Giroire, A. Nucci, N. Taft, and C. Diot. Method and Systems for Correlating Practical Constraints in a Network, July 2008.
    Note: Patent number US 7,394,760 B1. Filled in July 2003.
     
  98. S. Jafer, G. Wainer, J-C. Maureira Bravo, and O. Dalle. Event Behavior of Discrete Event Simulations in CD++ Vs. NS-2. 2008 Spring Simulation Multiconference (Spring Sim'08)- Poster Sessions (SCS-Poster sessions 2008), April 2008.
    Abstract:
    The study of events behavior through real simulations could contribute to develop or improve Future Event Set (FES) data structures in order to achieve better performance on large scale simulations. In this paper we have analyzed FES data structures of two discrete event simulators: CD++ and NS-2. We have run variety of simulations on each simulator to describe a real event behavior by observing event timestamps, life times into the FES and firing time (event execution time). The goal of this research is to present new ideas on how the FES data structures could be improved exploiting event behaviors.

     
  99. D. Mazauric. Conception et analyse d'algorithmes distribués d'ordonnancement des transmissions dans les réseaux sans-fil, September 2008.
    Note: Internship report. [PDF ]
     
  100. J. Monteiro and O. Dalle. CORRAL: Stackable Copy-on-Write Versioning Device using Linux Device-Mapper. USENIX Annual Technical Conference (USENIX'08), June 2008.
    Note: Poster.
     
2007
  1. G. Chelius and D. Coudert, editors. Neuvièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'07), volume 9, Ile d'Oléron, France, May 2007. CNRS, LaBRI, Université Bordeaux I. [WWW ]
     
  2. O. Amini. Algorithmique des décompositions de graphes Applications aux réseaux de télécommunications. PhD thesis, École doctorale STIC, Université de Nice-Sophia Antipolis, November 28 2007.
    Abstract:
    La th\`ese comprend trois parties relativement ind\'ependantes. Le th\`eme central reliant ces parties est la d\'ecomposition de graphes: la premi\`ere partie traite de la d\'ecomposition arborescente; la deuxi\`eme, plus appliqu\'ee, se fonde sur les applications des d\'ecompositions d'ar\^etes ou de noeuds aux r\'eseaux de t\'el\'ecommunications, et la derni\`ere, plus th\'eorique, concerne la coloration de graphes. Les chapitres de la premi\`ere partie \'etudient la d\'ecomposition arborescente de graphes et ses applications à la conception d'algorithmes dits param\'etr\'es. La partie II regroupe des travaux sur les probl\`emes issus des r\'eseaux de t\'el\'ecommunications. Deux types de r\'eseaux sont \'etudi\'es: les r\'eseaux embarqu\'es dans les satellites et les r\'eseaux optiques WDM. La troisi\`eme partie, plus probabiliste, est essentiellement bas\'ee sur la coloration de graphes et l'existence des cycles orient\'es dans les digraphes.

     
  3. F. Havet. Graph colouring and applications. Habilitation à Diriger des Recherches, Université de Nice-Sophia Antipolis, December 12 2007. [WWW ]
     
  4. L. Hogie. Mobile Ad Hoc Networks: Modelling, Simulation and Broadcast-based Applications. PhD thesis, University of Le Havre, University of Luxembourg, April 2007.
    Abstract:
    Over the last few years, personal communication devices have invaded most developed countries and today, the majority of the population owns a mobile phone and most of them use personal digital assistants, mobile computers, etc. This tendency is reinforced and occurs at the same time with a new trend: most of these devices get equipped with one or several wireless networking interfaces. Practically, Wi-Fi or/ and Bluetooth-enabled devices become of frequent use. More than allowing the connection to some access point (as they can be found in airport, train stations, city-centers, restaurants, etc), these interfaces permit also to interconnect directly with one another in a decentralized way and to hence self-organize into ad hoc networks. A mobile ad hoc network (MANET) is a set of mobile nodes able to communicate with other nodes in their surroundings. These wireless communications happen in a peer-topeer manner, without relying on any predefined infrastructure. Today, MANETs are mainly used for sensing, gaming and military purposes. But the steadily wider adoption of wireless technologies in daily life let one foresee the next generation of MANETs applications: environmental and medical monitoring, groupware, customer-to-customer applications, risk management, entertainment, advertising, etc. In order to enable the development and spreading of these applications, a number of issues have to be solved. First, in such network, end-to-end connectivity cannot be guaranteed. Indeed MANETs may be partitioned and nodes may be sporadically present in the network. As such, MANETs can be considered as Delay Tolerant Networks (DTN). Second, the topology of the network changes over time because of the mobility of the stations. Then, the way the communication primitives were implemented in the context of wired networks is no longer applicable. It is hence necessary to propose new algorithms to enable those primitives, like broadcasting that serves as a basic pattern for the design of many MANETs applications. The design and implementation of such communication schemes, and more generally of MANETs application, can be achieved using two different ways: either by building a real network, or by resorting to modelling and simulation. In the context of this work, where city-scale environment were considered, simulation was hence unavoidable. The development of such a simulator took place at the crossroad of some projects in relation to complex system modelling, optimization and middleware design for MANETs, and conducted in several European countries. This diversity led to the design of a custom simulator called Madhoc. Madhoc captures the major characteristics of DTNs, by providing an extendable set of mobility models as well as a framework for the de_nition of new applications. Madhoc was primarily used for the investigation of the broadcasting issue. In this specific context, networks composed of thousands devices using a variety of wireless technologies were considered. These networks are partitioned and exhibit heterogeneous densities. This led to the design of a bandwidth-efficient broadcasting protocol called DFCN.

     
  5. L. Liquori. Peter, le langage qui n'existe pas... (Peter, the language that does not exists...). Habilitation à Diriger des Recherches, Institut National Polytechnique de Lorraine (INPL), 6 Juillet 2007. [PDF ]
     
  6. N. Morales. Algorithmique des réseaux de communication radio modélisés par des graphes. PhD thesis, École doctorale STIC, Université de Nice-Sophia Antipolis, 26 Janvier 2007. [PDF ]
     
  7. L. Addario-Berry, K. Dalal, C. McDiarmid, B. Reed, and A. Thomason. Vertex Colouring Edge Weightings. Combinatorica, 27:1-12, 2007.
     
  8. L. Addario-Berry, F. Havet, and S. Thomassé. Paths with two blocks in $n$-chromatic digraphs. Journal of Combinatorial Theory Ser. B, 97:620--626, 2007. [PDF ]
     
  9. E. Alba, B. Dorronsoro, F. Luna, A.J. Nebro, P. Bouvry, and L. Hogie. A cellular multi-objective genetic algorithm for optimal broadcasting strategy in metropolitan MANETs. Computer Communications, 30(4):685--697, August 2007. [WWW ]
    Abstract:
    Mobile Ad-hoc Networks (MANETs) are composed of a set of communicating devices which are able to spontaneously interconnect without any pre-existing infrastructure. In such scenario, broadcasting becomes an operation of capital importance for the own existence and operation of the network. Optimizing a broadcast strategy in MANETs is a multi-objective problem accounting for three goals: reaching as many stations as possible, minimizing the network utilization, and reducing the makespan. In this paper, we study the fine-tuning of broadcast strategies by using a cellular multi-objective genetic algorithm (cMOGA) that computes a Pareto front of the solutions to empower a human designer with the ability of choosing the preferred configuration for the network. We define two formulations of the problem, one with three objectives and another one with two objectives plus a constraint. Our experiments using a complex and realistic MANET simulator reveal that using cMOGA is a promising approach to solve the optimum broadcast problem.

     
  10. R. Bayon, N. Lygeros, and J.-S. Sereni. Orders with ten elements are circle orders. Applied Mathematics E-Notes, 7:16--22, 2007. [WWW ] [PDF ]
     
  11. J-C. Bermond, L. Braud, and D. Coudert. Traffic Grooming on the Path. Theoretical Computer Science, 384(2-3):139-151, October 2007. [WWW ] [PDF ]
    Abstract:
    In a WDM network, routing a request consists in assigning it a route in the physical network and a wavelength. If each request uses at most 1/C of the bandwidth of the wavelength, we will say that the grooming factor is C. That means that on a given edge of the network we can groom (group) at most C requests on the same wavelength. With this constraint the objective can be either to minimize the number of wavelengths (related to the transmission cost) or minimize the number of Add Drop Multiplexers (shortly ADM) used in the network (related to the cost of the nodes). We consider here the case where the network is a path on N nodes, P_N. Thus the routing is unique. For a given grooming factor C minimizing the number of wavelengths is an easy problem, well known and related to the load problem. But minimizing the number of ADM's is NP-complete for a general set of requests and no results are known. Here we show how to model the problem as a graph partition problem and using tools of design theory we completely solve the case where C=2 and where we have a static uniform all-to-all traffic (one request for each pair of vertices).

     
  12. J-C. Bermond, A. Ferreira, S. Pérennes, and J. Peters. Neighbourhood Broadcasting in Hypercubes. SIAM Journal on Discrete Mathematics, 21(4):823-843, 2007. [PDF ]
    Abstract:
    In the broadcasting problem, one node needs to broadcast a message to all other nodes in a network. If nodes can only communicate with one neighbor at a time, broadcasting takes at least $\lceil \log_2 N \rceil$ rounds in a network of $N$ nodes. In the neighborhood broadcasting problem, the node that is broadcasting needs to inform only its neighbors. In a binary hypercube with $N$ nodes, each node has $\log_2 N$ neighbors, so neighborhood broadcasting takes at least $\lceil \log_2 \log_2 (N+1) \rceil$ rounds. In this paper, we present asymptotically optimal neighborhood broadcast protocols for binary hypercubes.

     
  13. J-C. Bermond and M-L. Yu. Vertex disjoint routings of cycles over tori. Networks, 49(3):217-225, 2007. [PDF ]
     
  14. E. Birmelé, J. A. Bondy, and B. Reed. The Erdos-Posa property for long circuits. Combinatorica, 27:135-145, 2007.
     
  15. P. Charbit, S. Thomassé, and A. Yeo. The minimum feedback arc set problem is NP-hard for tournament. Combinatorics, Probability and Computing, 16:1--4, 2007.
     
  16. A. Ciaffaglione, L. Liquori, and M. Miculan. Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts. JAR, Journal of Automated Reasoning, 39:1--47, 2007. [PDF ]
     
  17. D. Coudert, P. Datta, S. Perennes, H. Rivano, and M-E. Voge. Shared Risk Resource Group: Complexity and Approximability issues. Parallel Processing Letters, 17(2):169-184, June 2007. [PDF ]
    Abstract:
    This article investigates complexity and approximability properties of combinatorial optimization problems yielded by the notion of Shared Risk Resource Group (SRRG). SRRG has been introduced in order to capture network survivability issues where a failure may break a whole set of resources, and has been formalized as colored graphs, where a set of resources is represented by a set of edges with same color. We consider here the analogous of classical problems such as determining paths or cuts with the minimum numbers of colors or color disjoint paths. These optimization problems are much more difficult than their counterparts in classical graph theory. In particular standard relationship such as the Max Flow - Min Cut equality do not hold any longer. In this article we identify cases where these problems are polynomial, for example when the edges of a given color form a connected subgraph, and otherwise give hardness and non approximability results for these problems.

     
  18. D. Coudert, F. Huc, and J.-S. Sereni. Pathwidth of outerplanar graphs. Journal of Graph Theory, 55(1):27-41, May 2007. [PDF ]
    Abstract:
    We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin, after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected outerplanar graph is at most c plus the pathwidth of its dual. They also conjectured that this was actually true with c being one for every biconnected planar graph. Fomin proved that the second conjecture is true for all planar triangulations. First, we construct for each p>=1 a biconnected outerplanar graph of pathwidth 2p 1 whose (geometric) dual has pathwidth p 1, thereby disproving both conjectures. Next, we also disprove two other conjectures (one of Bodlaender and Fomin, implied by one of Fomin). Finally we prove, in an algorithmic way, that the pathwidth of every biconnected outerplanar graph is at most twice the pathwidth of its (geometric) dual minus one. A tight interval for the studied relation is therefore obtained, and we show that all cases in the interval happen.

     
  19. S. Fiorini, N. Hardy, B. Reed, and A. Vetta. Approximate min-max relations for odd cycles in planar graphs. Mathematical Programming Ser. B, 110(1):71--91, 2007.
     
  20. M. Flammini, R. Klasing, A. Navarra, and S. Pérennes. Improved approximation results for the Minimum Energy Broadcasting problem. Algorithmica, 49(4):318-336, 2007. [WWW ]
    Abstract:
    In this paper we present new results on the performance of the Minimum Spanning Tree heuristic for the Minimum Energy Broadcast Routing (MEBR) problem. We first prove that, for any number of dimensions d≥2, the approximation ratio of the heuristic does not increase when the power attenuation coefficient α, that is the exponent to which the coverage distance must be raised to give the emission power, grows. Moreover, we show that, for any fixed instance, as a limit for α going to infinity, the ratio tends to the lower bound of Clementi et al., Wan et al. given by the d-dimensional kissing number, thus closing the existing gap between the upper and the lower bound. We then introduce a new analysis allowing to establish a 7.45-approximation ratio for the 2-dimensional case, thus significantly decreasing the previously known 12 upper bound (actually corrected to 12.15 in Klasing et al.). Finally, we extend our analysis to any number of dimensions d≥2 and any α≥d, obtaining a general approximation ratio of 3 d −1, again independent of α. The improvements of the approximation ratios are specifically significant in comparison with the lower bounds given by the kissing numbers, as these grow at least exponentially with respect to d.

     
  21. N. Fountoulakis and B. Reed. Faster Mixing and Small Bottlenecks. Probability Theory and Related Fields, 137:475-486, 2007.
     
  22. J. Galtier and A. Laugier. Flow on data network and a positive semidefinite representable delay function. Journal of Interconnection Networks, 8(1):29--43, March 2007. [PDF ]
    Abstract:
    Data networks are subject to congestion, thereby the delay to go across the network may be large enough in order to dishearten customers to keep on using such a network. In this paper we address the problem of determining in a given network a routing which minimizes the delay or keeps it under a certain bound. This problem was already shown as complete. Our main contribution is to study it in the special context of the positive semidefinite programming and we present a column generation approach to solve the underlying problem.

     
  23. L. Grigori, M. Cosnard, and E. G. Ng. On the row merge for sparse LU factorization with partial pivoting. BIT Numerical Mathematics, 47(1):45--76, March 2007. [PDF ]
    Abstract:
    We consider the problem of structure prediction for sparse LU factorization with partial pivoting. In this context, it is well known that the column elimination tree plays an important role for matrices satisfying an irreducibility condition, called the strong Hall property. Our primary goal in this paper is to address the structure prediction problem for matrices satisfying a weaker assumption, which is the Hall property. For this we consider the row merge matrix, an upper bound that contains the nonzeros in L and U for all possible row permutations that can be performed during the numerical factorization with partial pivoting. We discuss the row merge tree, a structure that represents information obtained from the row merge matrix; that is, information on the dependencies among the columns in Gaussian elimination with partial pivoting and on structural upper bounds of the factors L and U. We present new theoretical results that show that the nonzero structure of the row merge matrix can be described in terms of branches and subtrees of the row merge tree. These results lead to an efficient algorithm for the computation of the row merge tree, that uses as input the structure of A, and has a time complexity almost linear in the number of nonzeros in A. We also investigate experimentally the usage of the row merge tree for structure prediction purposes on a set of matrices that satisfy only the Hall property. We analyze in particular the size of upper bounds of the structure of L and U, the reordering of the matrix based on a postorder traversal and its impact on the factorization runtime. We show experimentally that for some matrices, the row merge tree is a preferred alternative to the column elimination tree.

     
  24. F. Honsell, M. Lenisa, and L. Liquori. A Framework for Defining Logical Frameworks. Electronic Notes in Theoretical Computer Science, 172:399 - 436, 2007.
    Note: Computation, Meaning, and Logic: Articles dedicated to Gordon Plotkin. [WWW ] [PDF ]
    Abstract:
    " In this paper, we introduce a General Logical Framework, called GLF, for defining Logical Frameworks, based on dependent types, in the style of the well known Edinburgh Logical Framework LF. The framework GLF features a generalized form of lambda abstraction where [beta]-reductions fire provided the argument satisfies a logical predicate and may produce an n-ary substitution. The type system keeps track of when reductions have yet to fire. The framework GLF subsumes, by simple instantiation, LF as well as a large class of generalized constrained-based lambda calculi, ranging from well known restricted lambda calculi, such as Plotkin's call-by-value lambda calculus, to lambda calculi with patterns. But it suggests also a wide spectrum of new calculi which have intriguing potential as Logical Frameworks. We investigate the metatheoretical properties of the calculus underpinning GLF and illustrate its expressive power. In particular, we focus on two interesting instantiations of GLF. The first is the Pattern Logical Framework (PLF), where applications fire via pattern-matching in the style of Cirstea, Kirchner, and Liquori. The second is the Closed Logical Framework (CLF) which features, besides standard [beta]-reduction, also a reduction which fires only if the argument is a closed term. For both these instantiations of GLF we discuss standard metaproperties, such as subject reduction, confluence and strong normalization. The GLF framework is particularly suitable, as a metalanguage, for encoding rewriting logics and logical systems, where rules require proof terms to have special syntactic constraints, e.g. logics with rules of proof, in addition to rules of derivations, such as, e.g., modal logic, and call-by-value lambda calculus."

     
  25. L. Liquori and S. Ronchi Della Rocca. Intersection Typed System it à la Church. IC, Journal of Information and Computation, 205(9):1371--1386, September 2007. [WWW ] [PDF ]
     
  26. O. Amini, S. Pérennes, and I. Sau. Hardness of Approximating the Traffic Grooming. In Neuvièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'07), Ile d'Oléron, France, pages 45-48, May 2007. [WWW ] [PDF ]
    Abstract:
    Le groupage est un problème central dans l'étude des réseaux optiques. Dans cet article, on propose le premier résultat d'inapproximabilité pour le problème du groupage, en affirmant la conjecture de Chow et Lin (2004, Networks, 44, 194-202), selon laquelle le groupage est APX-complet. On étudie aussi une version amortie du problème de sous-graphe le plus dense dans un graphe donné: trouver le sous-graphe de taille minimum ayant le degré minimum au moins d, d>=3. On démontre que ce dernier n'a pas d'approximation à un facteur constant.

     
  27. O. Amini, S. Pérennes, and I. Sau. Hardness and Approximation of Traffic Grooming. In The 18th International Symposium on Algorithms and Computation (ISAAC 2007), volume 4835 of Lecture Notes in Computer Science, Sendai, Japan, pages 561-573, December 2007. Springer-Verlag. [WWW ] [PDF ]
    Abstract:
    Traffic grooming is a central problem in optical networks. It refers to pack low rate signals into higher speed streams, in order to improve bandwidth utilization and reduce network cost. In WDM networks, the most accepted criterion is to minimize the number of electronic terminations, namely the number of SONET Add-Drop Multiplexers (ADMs). In this article we focus on ring and path topologies. On the one hand, we provide the first inapproximability result for \textsc{Traffic Grooming} for fixed values of the grooming factor $g$, answering affirmatively the conjecture of Chow and Lin (\emph{Networks, 44:194-202, 2004}). More precisely, we prove that \textsc{Ring Traffic Grooming} for fixed $g\geq 1$ and \textsc{Path Traffic Grooming} for fixed $g\geq 2$ are \textsc{APX}-complete. That is, they do not accept a PTAS unless $\textsc{P}=\textsc{NP}$. Both results rely on the fact that finding the maximum number of edge-disjoint triangles in a graph (and more generally cycles of length $2g+1$ in a graph of girth $2g+1$) is \textsc{APX}-complete. On the other hand, we provide a polynomial-time approximation algorithm for \textsc{Ring} and \textsc{Path Traffic Grooming}, based on a greedy cover algorithm, with an approximation ratio independent of $g$. Namely, the approximation guarantee is $\mathcal{O}(n^{1/3} \log2 n)$ for any $g \geq 1$, $n$ being the size of the network. This is useful in practical applications, since in backbone networks the grooming factor is usually greater than the network size. As far as we know, this is the first approximation algorithm with this property. Finally, we improve this approximation ratio under some extra assumptions about the request graph.

     
  28. O. Amini and B. Reed. List Colouring Constants of Triangle Free Graphs. In IV Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 07), Puerto Varas, Chile, pages 6p, November 2007. [WWW ] [PDF ]
    Abstract:
    In this paper we prove a result about vertex list colourings which in particular shows that a conjecture of the second author (1999, Journal of Graph Theory 31, 149-153) is true for triangle free graphs of large maximum degree. There exists a constant K such that the following holds: Given a graph G and a list assignment L to vertices of G, assigning a list of available colours L(v) to each vertex $v\in V(G)$, such that $|L(v)| = K\Delta/\log(\Delta)$ , then there exists a proper list colouring of vertices of G provided that for each colour c, the graph induced by all vertices v with c ∈ L(v) is triangle free and has maximum degree at most \Delta.

     
  29. J. Araujo and C. Linhares Sales. Teorema de Hajós para Coloração Ponderada. In XXXIX Simpósio Brasileiro de Pesquisa Operacional, Fortaleza, Brazil, pages 5p, August 2007. [PDF ]
    Abstract:
    The vertex coloring problem is one of the most investigated problems in graph theory because of it models several important practical problems and because of its inherent difficulty: it is NP-hard to determine the chromatic number of a graph. The Theorem of Haj´os [Haj´os, 1961] shows a necessary and sufficient condition to a graph have chromatic number at least k: the graph must contain a k-constructible subgraph. A graph is k-constructible if it can be obtained from a complete graph by successively applying a set of well-defined operations. In this article, we prove that the weighted coloring problem [Guan and Zhu, 1997] admits a version of the Haj´os’ Theorem and so we show a necessary and sufficient condition to a weighted graph G have weighted chromatic number at least k, for any integer k.

     
  30. N. Ben Ali, J. Moulierac, B. Belghith, and M. Molnár. mQMA: multi-constrained QoS Multicast Aggregation. In IEEE Global Telecommunications Conference (IEEE GLOBECOM 2007), Washington DC, USA, pages 5p, November 2007. [PDF ]
    Abstract:
    Traditional IP Multicast has been proposed in order to manage group communications over the Internet in a bandwidth efficient manner. Although this proposition has been well studied, there are still some problems for its deployment. In this paper, we propose a new algorithm mQMA that deals with two important problems of traditional IP multicast, i.e., multicast forwarding state scalability and multi-constrained QoS routing. The algorithm mQMA builds few trees and maintains few forwarding states for the groups thanks to the technique of multicast tree aggregation, which allows several groups to share the same delivery tree. Moreover, the algorithm mQMA builds trees satisfying multiple QoS constraints. We show, trough extensive simulations, that mQMA leverages the same QoS performances as Mamcra which is the main multi-constrained multicast routing algorithm. Moreover, mQMA reduces dramatically the number of trees to be maintained.

     
  31. J-C. Bermond and M. Cosnard. Minimum number of wavelengths equals load in a DAG without internal cycle. In Parallel and Distributed Processing Symposium, 2007. IPDPS 2007. IEEE International, Long Beach, CA, U.S.A., pages 1-10, March 2007. [PDF ]
     
  32. J-C. Bermond, F. Giroire, and S. Pérennes. Design of Minimal Fault Tolerant On-Board Networks : Practical constructions. In 14th International Colloquium on Structural Information and Communication Complexity (SIROCCO 07), volume 4474 of Lecture Notes in Computer Sciences, Castiglioncello, Italy, pages 261-273, June 2007. [PDF ]
     
  33. J-C. Bermond, F. Havet, F. Huc, and C. Linhares-Sales. Allocation de fréquences et coloration impropre des graphes hexagonaux pondérés. In Neuvièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'07), Ile d'Oléron, France, pages 53-56, May 2007. [WWW ] [PDF ]
    Abstract:
    Motiv\'es par un probl\`eme d'allocation de fr\'equences, nous \'etudions la coloration impropre des graphes pond\'er\'es et plus particuli\`erement des graphes hexagonaux pond\'er\'es. Nous donnons des algorithmes d'approximation pour trouver de telles colorations.

     
  34. S. Bessy, N. Lichiardopol, and J.-S. Sereni. Two proofs of Bermond-Thomassen conjecture for regular tournaments. In Proceedings of the sixth Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, volume 28 of Electronic Notes in Discrete Mathematics, pages 47--53, 2007. Elsevier. [WWW ] [PDF ]
     
  35. E. Birmele, J. A. Bondy, and B. Reed. Brambles, Prisms and Grids. In Proceedings of a Conference in Memory of Claude Berge, Graph Theory in Paris, Basel, pages 37-44, 2007. Birkhauser.
     
  36. R. Chand, L. Liquori, and M. Cosnard. Improving Resource Discovery in the Arigatoni Overlay Network. In 20th International Conference on Architecture of Computing Systems (ARCS 2007), volume 4415 of Lecture Notes in Computer Science, Zurich, Switzerland, pages 98--111, 2007. Springer. [PDF ]
     
  37. A. Chattopadhyay and B. Reed. Properly 2-Colouring Linear Hypergraphs. In 11th Intl. Workshop on Randomization and Computation (RANDOM 2007), volume 4627 of Lecture Notes in Computer Science, Princeton University, NJ, USA, pages 395-408, 2007. Springer. [PDF ]
     
  38. M. Cosnard, L. Liquori, and R. Chand. Virtual Organizations in Arigatoni. In DCM, International Workshop on Developpment in Computational Models, volume 171 of Electronique Notes in Theoretical Computer Science, pages 55--75, 2007. [WWW ] [PDF ]
     
  39. A. da Silva, A. da Silva, and C. Linhares-Sales. Largura em Árvore de Grafos Planares Livres de Ciclos Pares Induzidos. In XXXIX Congresso da Sociedade Brasileira de Pesquisa Operacional (SBPO 2007), Fortaleza, Brazil, August 2007. [WWW ]
     
  40. O. Dalle. The OSA Project: an Example of Component Based Software Engineering Techniques Applied to Simulation. In Proc. of the Summer Computer Simulation Conference (SCSC'07), San Diego, CA, USA, pages 1155--1162, July 2007.
    Note: Invited paper. [PDF ]
     
  41. O. Dalle and C. Mrabet. An Instrumentation Framework for component-based simulations based on the Separation of Concerns paradigm. In Proc. of 6th EUROSIM Congress (EUROSIM'2007), Ljubljana, Slovenia, pages 10p, September 2007. [PDF ]
     
  42. O. Dalle and G. Wainer. An Open Issue on Applying Sharing Modeling Patterns in DEVS. In Proc. of the DEVS Workshop of the Summer Computer Simulation Conference (SCSC'07), San Diego, CA, July 2007.
    Note: Short paper. [PDF ]
     
  43. O. Dalle. Component-based Discrete Event Simulation Using the Fractal Component Model. In AI, Simulation and Planning in High Autonomy Systems (AIS)-Conceptual Modeling and Simulation (CMS) Joint Conference, Buenos Aires, AR, pages 213--218, February 2007. [PDF ]
     
  44. G. Danoy, P. Bouvry, and L. Hogie. Coevolutionary Genetic Algorithms for Ad Hoc Injection Networks Design Optimization. In Proceedings of the IEEE Congress on Evolutionary Computation - CEC, Singapore, pages 8p, September 2007. IEEE. [WWW ] [PDF ]
    Abstract:
    When considering realistic mobility patterns, nodes in mobile ad hoc networks move in such a way that the networks most often get divided in a set of disjoint partitions. This presence of partitions is an obstacle to communication within these networks. Ad hoc networks are generally based on technologies allowing nodes in a geographical neighborhood to communicate for free, in a P2P manner. These technologies include IEEE802.11 (Wi-Fi), Bluetooth, etc. In most cases a communication infrastructure is available. It can be a set of access point as well as GMS/UMTS network. The use of such an infrastructure is billed, but it permits distant nodes to get in communication, through what we call "bypass links". The objective of our work is to improve the network connectivity by defining a set of long distance connections. To do this we consider the number of bypass links, as well as the two properties that build on the "small-world" graph theory: the clustering coefficient, and the characteristic path length. A fitness function, used for genetic optimization, is processed out of these three metrics. In this paper we investigate the use of two Coevolutionary Genetic Algorithms (LCGA and CCGA) and compare their performance to a generational and a steadystate genetic algorithm (genGA and ssGA) for optimizing one instance of this topology control problem and present evidence of their capacity to solve it.

     
  45. A. Ferreira, A. Goldman, and J. Monteiro. On the evaluation of shortest journeys in dynamic networks. In Proceedings of the 6th IEEE International Symposium on Network Computing and Applications, Cambridge, MA, USA, pages 3--10, July 2007.
    Note: Invited Paper. [PDF ]
    Abstract:
    The assessment of routing protocols for wireless networks is a difficult task, because of the networks’ highly dynamic behavior and the absence of benchmarks. However, some of these networks, such as intermittent wireless sensors networks, periodic or cyclic networks, and low earth orbit (LEO) satellites systems, have more predictable dynamics, as the temporal variations in the network topology are somehow deterministic, which may make them easier to study. The graph theoretic model – the evolving graphs – was proposed to help capture the dynamic behavior of these networks, in view of the construction of least cost routing and other algorithms. Our recent experiments showed that evolving graphs have all the potentials to be an effective and powerful tool in the development of routing protocols for dynamic networks. In this paper, we evaluated the shortest journey evolving graph algorithm when used in a routing protocol for MANETs. We use the NS2 network simulator to compare this first implementation to the four well known protocols, namely AODV, DSR, DSDV, and OLSR. In this paper we present simulation results on the energy consumption of the nodes. We also included other EG protocol, namely EGForemost , in the experiments.

     
  46. A. Ferreira, A. Goldman, and J. Monteiro. Using Evolving Graphs Foremost Journey to Evaluate Ad-Hoc Routing Protocols. In Proceedings of 25th Brazilian Symposium on Computer Networks (SBRC'07), Belem, Brazil, pages 17--30, June 2007. [PDF ]
    Abstract:
    The performance evaluation of routing protocols for ad hoc networks is a difficult task. However, a graph theoretic model – the evolving graphs – was recently proposed to help capture the behavior of dynamic networks with fixed-schedule behavior. Our recent experiments showed that evolving graphs have all the potentials to be an effective and powerful tool in the development of routing protocols for dynamic networks. In this paper, we design a new con- gestion avoidance mechanism and a modified end-to-end delay metric in order to improve the evolving graph based routing protocol proposed previously. We use the NS2 network simulator to compare this new version to the three proto- cols provided by NS2, namely AODV, DSR and DSDV, and to OLSR, which is included in the experiments for the first time.

     
  47. E. Fusy and F. Giroire. Estimating the number of active flows in a data stream over a sliding window. In David Appelgate, editor, Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments and the Fourth Workshop on Analytic Algorithmics and Combinatorics, pages 223-231, 2007. SIAM Press.
    Note: Proceedings of the New Orleans Conference. [PDF ]
    Abstract:
    A new algorithm is introduced to estimate the number of distinct flows (or connections) in a data stream. The algorithm maintains an accurate estimate of the number of distinct flows over a sliding window. It is simple to implement, parallelizes optimally, and has a very good trade-off between auxiliary memory and accuracy of the estimate: a relative accuracy of order $1/\sqrt{m}$ requires essentially a memory of order $m\ln(n/m)$ words, where $n$ is an upper bound on the number of flows to be seen over the sliding window. For instance, a memory of only $64 kB$ is sufficient to maintain an estimate with accuracy of order $4$ percents for a stream with several million flows. The algorithm has been validated both by simulations and experimentations on real traffic. It proves very efficient to monitor traffic and detect attacks.

     
  48. J. Galtier. Analysis and optimization of MAC with constant size congestion window for WLAN. In The Second International Conference on Systems and Networks Communications (ICSNC'07), Cap Esterel, French Riviera, France, pages 6p, August 2007. [PDF ]
     
  49. C. Gomes and G. Huiban. Multiobjective Analysis in Wireless Mesh Networks. In International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS), pages 103--108, October 2007. Bogazici University, Istanbul, Turkey, IEEE. [WWW ] [PDF ]
    Abstract:
    Wireless Mesh Networks is a scalable and cost-effective solution for next-generation wireless networking. In the present work, we consider the Round Weighting Problem (RWP). It solves a joint routing and scheduling problem to attend a given demand subjected to the multiaccess interferences. We proposed a multiobjective approach that deal with two objective functions. The first one is to minimize the load over the routers, it increases the security in case of failure and minimizes the cost with memory in each node. The second objective is to minimize the time of the communication. We aim to identify the Pareto frontier of the problem. The Column generation method was used to solve efficiently the test instances. We make experiments with some networks with different number of sinks. Our approach captures the trade-off generated by using these two conflicting objective functions. This relationship corresponds to a convex piecewise linear function.

     
  50. C. Gomes, C. Molle, P. Reyes, and H. Rivano. Models for Optimal Wireless Mesh Network Design. In The 22nd European Conference on Operational Research (EURO XXII), Prague, pages 1p, July 2007.
    Abstract:
    Wireless Mesh Networks (WMNs) are cost-effective and provide an appealing answer to connectivity issues of ubiquituous computing. Unfortunately, wireless networks are known for strong waste of capacity when their size increase. Thus, a key challenges for network operators is to provide guaranteed quality of service. Maximizing network capacity requires to optimize jointly the Access Points (AP) placement, the routing and the link scheduling taking interferences into account. We present MILP models for computing an optimal 802.11a or 802.16 WMN design providing max-min bandwidth guaranty.

     
  51. C. Gomes, C. Molle, P. Reyes, and H. Rivano. Placement Optimal de points d'accès dans les réseaux radio maillés. In Neuvièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'07), Ile d'Oléron, France, pages 117-120, May 2007. [WWW ] [PDF ]
    Abstract:
    Cet article pr\'esente un mod\`ele lin\'eaire permettant de placer un nombre minimum de points d'acc\`es dans un r\'eseau radio maill\'e ({\em Wireless Mesh Network}). Connaissant la topologie du r\'eseau, le probl\`eme est de d\'eterminer le nombre minimum de points d'acc\`es reli\'es \`a Internet n\'ecessaires pour que la demande de chaque routeur soit satisfaite. Afin de prendre en compte les interf\'erences spatiales d\^ues \`a la technologie radio, le temps est d\'ecoup\'e en intervalles r\'eguliers au cours desquels un ensemble de liens n'interf\'erant pas deux \`a deux est d\'etermin\'e, ce qui engendre une limitation de la capacit\'e des liens en fonction de leur activation dans le temps. Le placement se fait ensuite de mani\`ere \`a assurer \`a chaque n\oe{}ud le d\'ebit d\'esir\'e en r\'egime permanent.

     
  52. F. Havet, J. van den Heuvel, C. McDiarmid, and B. Reed. List colouring squares of planar graphs. In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2007), volume 29 of Electronic Notes in Discrete Mathematics, Sevilla, Spain, pages 515-519, September 2007. [PDF ]
     
  53. G. Huiban and P. Datta. Multi-Metrics Reconfiguration in Core WDM Networks. In International Workshop on the Design of Reliable Communication Networks (DRCN), La Rochelle, France, pages 8p, October 2007. SEE. [WWW ] [PDF ]
    Abstract:
    We consider the reconfiguration problem in multifiber WDM optical networks. In a network with evolving traffic, the virtual topology may not remain optimal, leading to degradation of network performance. However, adapting the virtual topology to the changing traffic may lead to service disruption. This optimization problem hence captures the trade-off between network performance and number of reconfigurations applied to the virtual topology. This trade-off is considered via a multi-metrics approach. The above problem is solved through a Mixed Integer Linear Programming (MILP) formulation with a multivariate objective function. However the problem is NP-hard and such an approach is unable to solve large problem instances in a reasonable time. Therefore we propose a simulated annealing (SA) based heuristic approach for solving problems of higher complexity. We compare the performance and the computation time of solving the MILP model and the heuristic approach considering different test instances. We can find near optimal solutions for instances of medium complexity using the MILP model. The SA scheme can be used as a heuristic to arrive at near optimal solutions when the run-time of the MILP becomes practically infeasible. It also appears that the trade-off's involved in the reconfiguration problem cannot be left aside, as a little flexibility with respect to one metric allows to drastically improve the quality of the solution with respect to other metrics.

     
  54. D. Ilcinkas, N. Nisse, and D. Soguet. The Cost of Monotonicity in Distributed Graph Searching. In OPODIS, volume 4878 of Lecture Notes in Computer Science, Guadeloupe, France, pages 415-428, December 2007. Springer. [WWW ] [PDF ]
    Abstract:
    Blin {\it et al.} (2006) proposed a distributed protocol that ena\-bles the smallest number of searchers to clear any unknown asynchronous graph in a decentralized manner. {\it Unknown} means that the searchers are provided no {\it a priori} information about the graph. However, the strategy that is actually performed lacks of an important property, namely the monotonicity. That is, the clear part of the graph can decrease at some steps of the execution of the protocol. As a consequence, the protocol of Blin {\it et al.} is executed in exponential time. Nisse and Soguet (2007) proved that, in order to ensure the smallest number of searchers to clear any $n$-node graph in a monotone way, it is necessary and sufficient to provide $\Theta(n \log n)$ bits of information to the searchers. This paper deals with the smallest number of searchers that are necessary and sufficient to monotoneously clear any unknown graph in a decentralized manner. The distributed graph searching problem considers a team of searchers that is aiming at clearing any connected contaminated graph. The clearing of the graph is required to be {\it connected}, i.e., the clear part of the graph must remain permanently connected, and {\it monotone}, i.e., the clear part of the graph only grows. The {\it search number} $\mcs(G)$ of a graph $G$ is the smallest number of searchers necessary to clear $G$ in a monotone connected way in centralized settings. We prove that $\Theta(\frac{n}{\log n}\, \mcs(G))$ searchers are necessary and sufficient to clear any unknown $n$-node graph $G$ in a monotone connected way, in decentralized settings. More precisely, we prove that, no distributed protocol using less than $\Omega(\frac{n}{\log n}\, \mcs(G))$ searchers can clear any unknown synchronous $n$-node graph $G$ in a monotone connected way. Moreover, we propose a distributed protocol that allows $O(\frac{n}{\log n}\, \mcs(G))$ searchers to clear any unknown asynchronous $n$-node graph $G$ in a monotone connected way.

     
  55. K. Kawarabayashi and B. Reed. Computing crossing number in linear time.. In 39th ACM Symposium on Theory of Computing (STOC 2007), San Diego, CA, USA, pages 382-390, June 2007.
     
  56. A. King and B. Reed. Asymptotics of the chromatic number for quasi-line graphs. In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2007), volume 29 of Electronic Notes in Discrete Mathematics, Sevilla, Spain, pages 327-331, September 2007.
     
  57. L. Liquori and M. Cosnard. Weaving Arigatoni with a Graph Topology. In International Conference on Advanced Engineering Computing and Applications in Sciences (ADVCOMP 2007), Papeete, French Polynesia, pages 8p, November 2007. IEEE Computer Society Press. [PDF ]
     
  58. L. Liquori and M. Cosnard. Logical Networks: Towards Foundations for Programmable Overlay Networks and Overlay Computing Systems. In 3rd Symposium on Trustworthy Global Computing (TGC 2007), volume 4912 of Lecture Notes in Computer Science, Sophia Antipolis, France, pages 90-107, November 2007. Springer. [PDF ]
     
  59. F. Mazoit and N. Nisse. Monotonicity of Non-deterministic Graph Searching. In Proceedings of the 33rd International Workshop on Graph-Theoretic Concepts in Computer Science (WG), volume 4769 of Lecture Notes in Computer Science, Dornburg, Germany, pages 33-44, June 2007. Springer. [WWW ] [PDF ]
    Abstract:
    In graph searching, a team of searchers is aiming at capturing a fugitive moving in a graph. In the initial variant, called \emph{invisible graph searching}, the searchers do not know the position of the fugitive until they catch it. In another variant, the searchers permanently know the position of the fugitive, i.e. the fugitive is visible. This latter variant is called \emph{visible graph searching}. A search strategy that catches any fugitive in such a way that, the part of the graph reachable by the fugitive never grows is called \emph{monotone}. {\it A priori}, monotone strategies may require more searchers than general strategies to catch any fugitive. This is however not the case for visible and invisible graph searching. Two important consequences of the monotonicity of visible and invisible graph searching are: (1) the decision problem corresponding to the computation of the smallest number of searchers required to clear a graph is in NP, and (2) computing optimal search strategies is simplified by taking into account that there exist some that never backtrack. Fomin \emph{et al.} (2005) introduced an important graph searching variant, called \emph{non-determi\-nistic graph searching}, that unifies visible and invisible graph searching. In this variant, the fugitive is invisible, and the searchers can query an oracle that permanently knows the current position of the fugitive. The question of the monotonicity of non-deterministic graph searching is however left open. In this paper, we prove that non-deterministic graph searching is monotone. In particular, this result is a unified proof of monotonicity for visible and invisible graph searching. As a consequence, the decision problem corresponding to non-determinisitic graph searching belongs to NP. Moreover, the exact algorithms designed by Fomin \emph{et al.} do compute optimal non-deterministic search strategies.

     
  60. N. Nepomuceno, P. R. Pinheiro, and A. L. V. Coelho. Tackling the Container Loading Problem: A Hybrid Approach Based on Integer Linear Programming and Genetic Algorithms. In 7th European Conference on Evolutionary Computation in Combinatorial Optimization (EvoCOP), Valencia, Spain, pages 154-165, 2007. [WWW ] [PDF ]
     
  61. N. Nepomuceno, P. R. Pinheiro, and A. L. V. Coelho. Combining Metaheuristics and Integer Linear Programming: A Hybrid Methodology Applied to the Container Loading Problem. In XX Concurso de Teses e Dissertações (CTD), Rio de Janeiro, Brazil, pages 2028-2032, 2007. [PDF ]
     
  62. N. Nisse and D. Soguet. Graph Searching with Advice. In Proceedings of the 14th International Colloquium on Structural Information and Communication Complexity (SIROCCO), volume 4474 of Lecture Notes in Computer Science, Castiglioncello, Italy, pages 51-65, June 2007. Springer. [WWW ] [PDF ]
    Abstract:
    Fraigniaud {\it et al.} (2006) introduced a new measure of difficulty for a distributed task in a network. The smallest {\it number of bits of advice} of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to capture an invisible and arbitrarily fast fugitive in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. We show that the minimum number of bits of advice permitting the monotone connected clearing of a network in a distributed setting is $O (n \log n)$, where $n$ is the number of nodes of the network, and this bound is tight. More precisely, we first provide a labelling of the vertices of any graph $G$, using a total of $O(n \log n)$ bits, and a protocol using this labelling that enables clearing $G$ in a monotone connected distributed way. Then, we show that this number of bits of advice is almost optimal: no protocol using an oracle providing $o(n \log n)$ bits of advice permits the monotone connected clearing of a network using the smallest number of searchers.

     
  63. N. Nisse and D. Soguet. Stratégies d'encerclement avec information. In 9èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), pages 49-52, 2007. [WWW ] [PDF ]
    Abstract:
    Dans le cadre de l'algorithmique r\'eparti dans les r\'eseaux, l'efficacit\'e d'un algorithme d\'epend tr\`es fortement de la connaissance du r\'eseau, disponible {\it a priori}. Tr\`es souvent, cette connaissance {\it a priori} est de nature qualitative (taille du r\'eseau, son diam\`etre, etc.). Fraigniaud {\it et al.} (2006) ont introduit une mesure quantitative de la complexit\'e d'une tâche r\'epartie dans un r\'eseau. Etant donn\'e un probl\`eme r\'eparti, cette mesure, {\it la taille d'oracle}, consiste en le plus petit nombre de bits d'information dont doit disposer l'algorithme pour r\'esoudre le probl\`eme efficacement. Nous nous int\'eressons \`a la taille d'oracle permettant de r\'esoudre efficacement {\it l'encerclement} dans les graphes. L'encerclement dans les r\'eseaux vise \`a r\'ealiser la capture d'un fugitif invisible, arbitrairement rapide et omniscient, par une \'equipe d'agents mobiles, dans un r\'eseau. La strat\'egie d'encerclement est calcul\'ee en temps r\'eel, par les agents eux mêmes, et doit v\'erifier les trois propri\'et\'es suivantes: (1)~{\it connexit\'e} : la zone nettoy\'ee doit toujours être connexe, (2)~{\it monotonie} : la zone nettoy\'ee ne doit jamais être recontamin\'ee, et (3)~{\it optimalit\'e} : le nombre d'agents utilis\'es doit être le plus petit possible. Les deux premi\`eres contraintes assurent des communications s\'ecuris\'ees entre les agents, ainsi qu'un temps de nettoyage polynomial en la taille du r\'eseau. La troisi\`eme propri\'et\'e assure une taille minimum des ressources utilis\'ees. La seule connaissance, concernant le r\'eseau, dont les agents disposent {\it a priori}, est mod\'elis\'ee par un {\it oracle} qui r\'epartit sur les n{\oe}uds du r\'eseau une chaîne de bits d'information. Nous prouvons que la taille d'oracle pour r\'esoudre l'encerclement est $O(n \log n)$ bits, avec $n$ la taille du r\'eseau, et que cette borne est optimale. Plus pr\'ecis\'ement, nous proposons un \'etiquetage des sommets, de taille $O(n \log n)$ bits, et un protocole r\'eparti utilisant cet \'etiquetage. Ce protocole permet \`a une \'equipe d'agents, dont la m\'emoire est de taille $O(\log n)$ bits, de nettoyer le r\'eseau de façon optimale monotone et connexe. Ce protocole am\'eliore le protocole propos\'e par Blin {\it et al.} (2006) qui ne dispose d'aucune information {\it a priori} et, de ce fait, n\'ecessite un temps de nettoyage exponentiel. De plus, nous prouvons qu'il n'existe pas de protocole r\'eparti utilisant un oracle de taille $o(n \log n)$ bits qui permette de nettoyer tous les r\'eseaux de façon optimale monotone et connexe.

     
  64. I. Sau and J. Zerovnik. Optimal Permutation Routing on Mesh Networks. In Proc. of International Network Optimization Conference (INOC 2007), Spa, Belgium, pages 6p, April 2007. [PDF ]
    Abstract:
    Permutation routing is used as one of the standard tests of routing algorithms. In the permutation routing problem, each processor is the origin of at most one packet and the destination of no more than one packet. The goal is to minimize the number of time steps required to route all packets to their respective destinations. Wireless mesh networks are based on plane tessellations that divide the area into cells and give rise to triangular, square, and hexagonal grids. In this paper we study permutation routing algorithms that work on finite convex subgraphs of basic grids, under the store-and-forward $\Delta$-port model. We consider algorithms implemented independently at each node, without assuming any global knowledge about the network. I.e., distributed algorithms. We describe optimal distributed permutation routing algorithms for subgraphs of triangular and square grids that need $\ell_{max}$ (the maximum over the length of the shortest path of all packets) routing steps, and show that there is no such algorithm on the hexagonal grids. Furthermore, we show that these algorithms are oblivious and translation invariant.

     
  65. O. Amini, D. Coudert, and N. Nisse. Some Results on Non-deterministic Graph Searching in Trees. Research Report INRIA-00174965, INRIA, September 2007. [WWW ] [PDF ]
    Abstract:
    Pathwidth and treewidth of graphs have been extensively studied for their important structural and algorithmic aspects. Determining these parameters is NP-complete in general, however it becomes linear time solvable when restricted to some special classes of graphs. In particular, many algorithms have been proposed to compute efficiently the pathwidth of trees. Skodinis (2000) proposes a linear time algorithm for this task. Pathwidth and treewidth have also been studied for their nice game-theoretical interpretation, namely graph searching games. Roughly speaking, graph searching problems look for the smallest number of searchers that are sufficient to capture a fugitive in a graph. Fomin et al. (2005) define the non-deterministic graph searching that provides an unified approach for the pathwidth and the treewidth of a graph. Given q>=0, the q-limited search number, denotes by s_q(G), of a graph G is the smallest number of searchers required to capture an invisib le fugitive in G, such that the searchers are allowed to know the position of the fugitive at most q times. Roughly, s_0(G) corresponds to the pathwidth of a graph G, and s_\infty(G) corresponds to its treewidth. Fomin et al. proved that computing s_q(G) is NP-complete in general, and left open the complexity of the problem restricted to the class of trees. This paper studies this latter problem. On one hand, we give tight upper bounds on the number of queries required to search a tree when the number of searchers is fixed. We also prove that this number can be computed in linear time when two searchers are used. On the other hand, our main result consists in the design of a simple polynomial time algorithm that computes a 2-approximation of s_q(T), for any tree T and any q>=0. This algorithm becomes exact if q=0 or 1, which proves that the decision problem associated to s_1 is polynomial in the class of trees.

     
  66. O. Amini, L. Esperet, and J. van den Heuvel. Frugal Colouring of Graphs. Research Report 6178, INRIA, May 2007. [WWW ] [PDF ]
    Abstract:
    A $k$-frugal colouring of a graph~$G$ is a proper colouring of the vertices of~$G$ such that no colour appears more than~$k$ times in the neighbourhood of a vertex. This type of colouring was introduced by Hind, Molloy and Reed in 1997. In this paper, we study the frugal chromatic number of planar graphs, planar graphs with large girth, and outerplanar graphs, and relate this parameter with several well-studied colourings, such as colouring of the square, cyclic colouring, and $L(p,q)$-labelling. We also study frugal edge-colourings of multigraphs.

     
  67. O. Amini, F. Havet, F. Huc, and S. Thomassé. WDM and Directed Star Arboricity. Research Report 6179, INRIA, January 2007. [WWW ] [PDF ]
    Abstract:
    Motivated by wavelength assignment for multicast in star networks, introduced by Brandt and Gonzalez [BrGo05], we study the directed star arboricity (dst) of digraphs in terms of their degree. Among other results we prove that every digraph $D$ with maximum indegree $k$ satisfies $dst(D)\leq 2k+1$, which is one short of the lower bound $2k$. Significant improvements of the bounds proposed in~\cite{BrGo05} are given.

     
  68. O. Amini, F. Mazoit, N. Nisse, and S. Thomassé. Submodular partition functions. Technical report RR-1427-07, LABRI, Univ. Bordeaux, April 2007.
    Note: Submitted in SIAM J. discrete Maths. [PDF ]
    Abstract:
    we propose a new proof of the duality between the bramble-number of a graph and its tree-width. This proof is based on a new definition of submodularity on partition functions which naturally extends the usual one on set functions. The technique simplifies the proof of bramble/tree-width duality. The proof does not rely on Menger's theorem, and thus simplifies the proof of the bramble/tree-width duality. It provides a dual for matroid tree-width and one can also derive all known dual notions of other classical width-parameters from it.

     
  69. O. Amini, S. Pérennes, and I. Sau. Hardness and Approximation of Traffic Grooming. Research Report 6236, INRIA, June 2007. [WWW ] [PDF ]
    Abstract:
    Traffic grooming is a central problem in optical networks. It refers to pack low rate signals into higher speed streams, in order to improve bandwidth utilization and reduce network cost. In WDM networks, the most accepted criterion is to minimize the number of electronic terminations, namely the number of SONET Add-Drop Multiplexers (ADMs). In this article we focus on ring and path topologies. On the one hand, we provide the first inapproximability result for \textsc{Traffic Grooming} for fixed values of the grooming factor $g$, answering affirmatively the conjecture of Chow and Lin (\emph{Networks, 44:194-202, 2004}). More precisely, we prove that \textsc{Ring Traffic Grooming} for fixed $g\geq 1$ and \textsc{Path Traffic Grooming} for fixed $g\geq 2$ are \textsc{APX}-complete. That is, they do not accept a PTAS unless $\textsc{P}=\textsc{NP}$. Both results rely on the fact that finding the maximum number of edge-disjoint triangles in a graph (and more generally cycles of length $2g+1$ in a graph of girth $2g+1$) is \textsc{APX}-complete. On the other hand, we provide a polynomial-time approximation algorithm for \textsc{Ring} and \textsc{Path Traffic Grooming}, based on a greedy cover algorithm, with an approximation ratio independent of $g$. Namely, the approximation guarantee is $\mathcal{O}(n^{1/3} \log^2 n)$ for any $g \geq 1$, $n$ being the size of the network. This is useful in practical applications, since in backbone networks the grooming factor is usually greater than the network size. As far as we know, this is the first approximation algorithm with this property. Finally, we improve this approximation ratio under some extra assumptions about the request graph.

     
  70. O. Amini, I. Sau, and S. Saurabh. Parameterized Complexity of the Smallest Degree-Constrained Subgraph Problem. Research Report 6237, INRIA, June 2007. [WWW ] [PDF ]
    Abstract:
    In this paper we initiate the study of finding an induced subgraph of size at most $k$ with minimum degree at least $d$. We call this problem \sc Minimum Subgraph of Minimum Degree $_{\geq d}$ (MSMD$_d$). For $d=2$, it corresponds to finding a shortest cycle of the graph. The problem is strongly related to the \textsc{Dense $k$-Subgraph} problem and is of interest in practical applications. We show that the {\sc MSMS}$_d$ is fixed parameter intractable for $d\geq 3$ in general graphs by showing it to be W[1]-hard by a reduction from {\sc Multi-Color Clique}. On the algorithmic side, we show that the problem is fixed parameter tractable in graphs which excluded minors and graphs with bounded local tree-width. In particular, this implies that the problem is fixed parameter tractable in planar graphs, graphs of bounded genus and graphs with bounded maximum degree.

     
  71. J-C. Bermond, I. Caragiannis, D. Coudert, C. Gomes, I. Guerin-Lassous, G. Huiban, C. Molle, and I. Sau. Algorithmic solutions for critical resource sharing: second year. Technical report Deliverable 2.2.2, IST FET AEOLUS, Integrated Project IST-015964, 2007. [PDF ]
     
  72. J-C. Bermond, D. Coudert, and B. Leveque. Approximations for All-to-all Uniform Traffic Grooming on Unidirectional Ring. Technical report inria-00175795, hal, October 2007. [WWW ] [PDF ]
    Abstract:
    Traffic grooming in a WDM network consists of assigning to each request (lightpath) a wavelength with the constraint that a given wavelength can carry at most C requests or equivalently a request uses at most 1/C of the bandwidth. C is known as the grooming ratio. A request (lightpath) need two SONET add-drop multiplexers (ADMs) at each end node~; using grooming different requests can share the same ADM. The so called traffic grooming problem consists of minimizing the total number of ADMs to be used (in order to reduce the overall cost of the network). Here we consider the traffic grooming problem in WDM unidirectional rings with all-to-all uniform unitary traffic. This problem has been optimally solved for specific values of the grooming ratio, namely C=2,3,4,5,6. In this paper we present various simple constructions for the grooming problem providing good approximation of the total number of ADMs. For that we use the fact that the problem corresponds to a partition of the edges of the complete graph into subgraphs, where each subgraph has at most C edges and where the total number of vertices has to be minimized.

     
  73. J-C. Bermond, V. Papadopoulou, and E. Pitoura. Subproject2: Resource Management Report on the activities of the second year. Technical report Deliverable 2.O.2, IST FET AEOLUS, Integrated Project IST-015964, 2007. [PDF ]
     
  74. D. Coudert, F. Huc, F. Peix, and M-E. Voge. On Minimizing the Average Reliability of Connections in Multilayer Networks under Shared Risk Groups and Costs Constraints. Technical report inria-00175813, hal, October 2007. [WWW ] [PDF ]
    Abstract:
    The notion of Shared Risk Resource Groups (SRRG) has been introduced to capture survivability issues when a set of resources may fail simultaneously. Applied to Wavelength Division Multiplexing Network (WDM), it expresses that some links and nodes may fail simultaneously. The reliability of a connection therefore depends on the number of SRRGs through which it is routed. Consequently, this number has to be minimized. This problem has been proved NP-complete and hard to approximate in general, even when routing a single request. Some heuristics using shortest paths have already been designed, however the cost (the usual routing cost, not in term of SRRG) was not part of the objective. In this paper we study the problem of minimizing a linear combination of the average number of SRRG per paths and the cost of the routing. The main result of our work is a column generation formulation that allows to solve the problem of maximizing the reliability of a set of connection requests in MPLS/WDM mesh networks with SRRGs while keeping the cost of the routing low.

     
  75. D. Coudert, S. Perennes, H. Rivano, and M-E. Voge. Shared Risk Resource Groups and Colored Graph: Polynomial Cases and Transformation Issues. Technical report inria-00175143, HAL, September 2007. [WWW ] [PDF ]
    Abstract:
    In this paper, we characterize polynomial cases for several combinatorial optimization problems in the context of multilayer networks with shared risk resource groups.

     
  76. D. Coudert and J-S. Sereni. Characterization of graphs and digraphs with small process number. Research Report 6285, INRIA, September 2007. [WWW ] [PDF ]
    Abstract:
    The process number of a digraph has been introduced as a tool to study rerouting issues in WDM networks. We consider the recognition and the characterization of (di)graphs with process number at most two.

     
  77. J. Galtier. Tournament MAC with constant size congestion window for WLAN. Technical report RR-6396, INRIA, December 2007. [WWW ] [PDF ]
    Abstract:
    In the context of radio distributed networks, we present a generalized approach for the Medium Access Control (MAC) with fixed congestion window. Our protocol is quite simple to analyze and can be used in a lot of different situations. We give mathematical evidence showing that our performance is tight, in the sense that no protocol with fixed congestion window can do better. We also place ourselves in the WiFi/WiMAX framework, and show experimental results enlightening collision reduction of 14{\%} to 21{\%} compared to the best known other methods. We show channel capacity improvement, and fairness considerations.

     
  78. F. Giroire, J. Chendrashekar, G. Iannaccone, T. Karagiannis, K. Papagiannaki, E. Schooler, and N. Taft. Inside the Forbidden City: A look at End-Host Traffic inside a Modern Enterprise. Technical Report, Intel Research, 2007. [PDF ]
     
  79. F. Giroire, J. Chendrashekar, N. Taft, G. Iannaccone, T. Karagiannis, K. Papagiannaki, and E. Schooler. The Case For Personalizing End-Host Detectors.. Technical Report, Intel Research, 2007. [PDF ]
     
  80. C. Gomes and H. Rivano. Fair Joint Routing and Scheduling Problem in Wireless Mesh Networks. Research Report 6198, INRIA, May 2007. [WWW ] [PDF ]
    Abstract:
    There is an increasing interest in using Wireless Mesh Networks (WMNs) as broadband backbone for next-generation wireless networking. WMNs is a scalable and cost-effective solution. Industrial standards groups are revisiting the existing protocols and they work enhanced specifications for WMNs. Wireless Mesh Networks (WMNs) are cost-effective and provide an appealing answer to connectivity issues of ubiquituous computing. One of the key challenges of WMNs is to provide guaranteed quality of service that network operator could claim. In this paper, we address the Fair Round Weighting Problem (F_RWP) and present mixed integer linear programming models for computing an optimal routing and link scheduling. We have considered two kind of transmissions scenarios, burst transmission and permanent regime, and their specific settings.

     
  81. F. Havet, R. Kang, and J.-S. Sereni. Improper colouring of unit disk graphs. Research Report 6206, INRIA, May 2007. [WWW ] [PDF ]
    Abstract:
    Motivated by a satellite communications problem, we consider a generalised colouring problem on unit disk graphs. A colouring is k -improper if no vertex receives the same colour as k +1 of its neighbours. The k -improper chromatic number chi_k (G) is the least number of colours needed in a k -improper colouring of a graph G. The main sub ject of this work is analysing the complexity of computing chi_k for the class of unit disk graph and some related classes, e.g. hexagonal graphs and interval graphs. We show NP-completeness in many restricted cases and also provide both positive and negative approximability results. Due to the challenging nature of this topic, many seemingly simple questions remain: for example, it remains open to determine the complexity of computing k for unit interval graphs.

     
  82. F. Havet and S. Thomasse. Complexity of $(p,1)$-total labelling. Research Report 6305, INRIA, September 2007. [WWW ] [PDF ]
    Abstract:
    A \it $(p,1)$-total labelling of a graph $G=(V,E)$ is a total coloring $L$ from $V\cup E$ into $0,\dots ,l$ such that $|L(v)-L(e)|\geq p$ whenever an edge $e$ is incident to a vertex $v$. The minimum $l$ for which $G$ admits a $(p,1)$-total labelling is denoted by $\lambda_p(G)$. The case $p=1$ corresponds to the usual notion of total colouring, which is NP-hard to calculate even for cubic bipartite graphs [MDSA94]. We assume $p\geq 2$ in this paper. It is easy to show that $\lambda_p(G)\geq \Delta +p-1$, where $\Delta$ is the maximum degree of $G$. Moreover, when $G$ is bipartite, $\Delta +p$ is an upper bound for $\lambda_p(G)$, leaving only two possible values. In this paper, we completely settle the computational complexity of deciding whether $\lambda_p(G)$ is equal to $\Delta +p-1$ or to $\Delta +p$ when $G$ is bipartite. This is trivial when $\Delta \leq p$, polynomial when $\Delta =3$ and $p=2$, and NP-complete in the remaining cases.

     
  83. R. Klasing, Z. Lotker, A. Navarra, and S. Pérennes. From Balls and Bins to Points and Vertices. Technical Report RR-1437-07, LaBRI, October 2007.
     
  84. L. Liquori, D. Borsetti, C. Casetti, and C. Chiasserini. Overlay Networks for Vehicular Networks. Research Report, Politecnico di Torino, 2007.
     
  85. C. Molle, F. Peix, and H. Rivano. Cross-Layer Design for Wireless Mesh Networks Using Column Generation. Technical report 6448, INRIA, December 2007. [WWW ] [PDF ]
    Abstract:
    Wireless Mesh Networks (WMNs) have become an interesting answer for broadband wireless networking. Cross-layer optimization problems for WMNs deployment and management are necessary and challenging. In this paper we focus on jointly optimizing routing and link scheduling in a single-channel wireless mesh network, in order to maximize fair network throughput or equivalently minimize time period. Our approach is based on a path/configuration linear formulation of the joint routing and scheduling problem, which is solved by column generation with two auxiliary programs to generate new paths and configurations. The method is validated on small topologies from an optimal node/arc formulation, and simulations are then done on random and grid topologies.

     
  86. P. Nain, C. Casetti, and L. Liquori. A Stochastic Model of an Arigatoni Overlay Computer. Research Report to be given, Politecnico di Torino, 2007.
     
  87. S. Teigen. Distributing OSA Simulations using FractalRMI. Technical Report, INRIA, 2007.
    Note: Unpublished, internal document.
     
  88. C. Gomes and G. Huiban. Multiobjective Analysis in Wireless Mesh Networks using a Column Generation Approach. Ecole ResCom 2007 Reseaux Autonomes et Internet du Futur, 2007.
    Note: Poster. [PDF ]
     
2006
  1. T. Ören, L. Torres, F. Amblard, J.-P. Belaud, J. Caussanel, O. Dalle, R. Duboz, A. Ferrarini, C. Frydman, E.-A. M. Hamri, D. Hill, A. Naamane, P. Siron, E. Tranvouez, and G. Zacharewicz. Modeling and Simulation Dictionary: English-French-Turkish. Prof. Tuncer Ören, 2006.
     
  2. F. Giroire. Réseaux, algorithmique et analyse combinatoire de grands ensembles. PhD thesis, Université Paris VI, November 2006. [WWW ] [PDF ]
    Abstract:
    Two classes of algorithmic problems motivated by network thematics are studied in this thesis. The first problem is to estimate the number of distinct elements or cardinality of very large multisets while using a very small amount of auxiliary memory. The number of applications of this very simple question is surprisingly important. In particular, we may mention the detection of some kinds of attack against networks. We proposed new families of algorithms to answer this problem. They are validated by mathematical analysis as well as by simulations with real traffic. The second problem is the design of efficient on-board networks in satellites. On one hand these networks must be able to tolerate a given number of mechanical failures of their components. On the other hand they should be of small sizes because of their extremely high cost. We introduced a new class of networks and proposed minimal constructions in lots of cases.

     
  3. G. Huiban. The reconfiguration problem in multifiber WDM networks. PhD thesis, University of Nice Sophia Antipolis & Federal University of Minas Gerais, July 2006. [WWW ] [PDF ]
    Abstract:
    An optical telecommunication network is configured to transmit a given traffic in order to meet a given objective. However the demand changes with time and infrastructure development. The reconfiguration problem stands in this context. It consists in being able to alter the configuration of the network to adjust it to the new traffic. It is generally necessary to interrupt partially or totally the traffic to reconfigure a network. Considering the amount of data flowing on it, it may not be possible to regularly stop the network, even for a short amount of time. Many parameters have to be taken into account to find out a good solution, and many metrics can be used in order to measure the quality of a solution. In a first part, we focus on the reconfiguration problem as a mono-objective optimization problem. We propose a mathematical model representing the reconfiguration problem. However solving exactly the proposed model may require a high computational time. We also propose a greedy and a simulated annealing heuristics. Depending on the metric optimized, the solutions have different characteristics. The greedy algorithm is fast and provides decent solutions whereas the simulated annealing algorithm provides solutions competing with the optimal ones. In a second part, we focus on the multiobjective aspect of the reconfiguration problem. We consider at the same time different metrics and search for a set of solutions representing different interesting trade-offs instead of a unique solution. We propose an algorithm based on our mathematical formulation. We also adapt an evolutionary algorithm. The proposed methods succeed in finding different interesting trade-offs. Giving a little flexibility with respect to a metric generally allows to significantly improve the solutions with respect to the other metrics.

     
  4. J.-S. Sereni. Colorations de graphes et applications. PhD thesis, École doctorale STIC, Université de Nice-Sophia Antipolis, Juillet 2006.
     
  5. M-E. Voge. Optimisation des réseaux de télécommunications: réseaux multicouches, tolérance aux pannes et surveillance de trafic. PhD thesis, École doctorale STIC, Université de Nice-Sophia Antipolis, November 17 2006. [PDF ]
     
  6. J. Bang-Jensen, B. Reed, M. Schacht, R. Sámal, B. Toft, and U. Wagner. Topics in Discrete Mathematics, Dedicated to Jarik Nesetril on the Occasion of his 60th birthday, volume 26 of Algorithms and Combinatorics, chapter On six problems posed by Jarik Nesetril, pages 613--627. Springer, Berlin, M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas and P. Valtr edition, 2006.
     
  7. J-C. Bermond and D. Coudert. Handbook of Combinatorial Designs (2nd edition), volume 42 of Discrete mathematics and Applications, chapter VI.27, Grooming, pages 494-496. Chapman & Hall- CRC Press, editors C.J. Colbourn and J.H. Dinitz, November 2006. [WWW ] [PDF ]
    Abstract:
    State-of-the-art on traffic grooming with a design theory approach

     
  8. S. Alouf, E. Altman, J. Galtier, J.-F. Lalande, and C. Touati. Quasi-Optimal Resource Allocation in Multi-Spot MFTDMA Satellite Networks. In M. Cheng, Y. Li, and D.-Z. Du, editors,Combinatorial Optimization in Communication Networks, chapter 12, pages 325-366. Kluwer Academic Publishers, 2006. [PDF ]
     
  9. D. Bartha, P. Berthomé, M. Diallo, and A. Ferreira. Revisiting parametric multi-terminal problems: Maximum flows, minimum cuts and cut-tree computations. Discrete Optimization, 3(3):195--205, September 2006.
     
  10. J. Becker, Z. Csizmadia, J. Galtier, A. Laugier, J. Szabó, and L. Szego. An integer programming approach to routing in Daisy networks. Networks, 47(2):116--121, 2006. [PDF ]
     
  11. J-C. Bermond, J. Galtier, R. Klasing, N. Morales, and S. Pérennes. Hardness and approximation of Gathering in static radio networks. Parallel Processing Letters, 16(2):165--183, 2006. [PDF ]
    Abstract:
    In this paper, we address the problem of gathering information in a specific node (or \emph{sink}) of a radio network, where interference constraints are present. We take into account the fact that, when a node transmits, it produces interference in an area bigger than the area in which its message can actually be received. The network is modeled by a graph; a node is able to transmit one unit of information to the set of vertices at distance at most $\dt$ in the graph, but when doing so it generates interference that does not allow nodes at distance up to $\di$ ($\di \ge \dt$) to listen to other transmissions. Time is synchronous and divided into time-steps in each of which a round (set of non-interfering radio transmissions) is performed. We give general lower bounds on the number of rounds required to gather into a sink of a general graph, and present an algorithm working on any graph, with an approximation factor of 4. We also show that the problem of finding an optimal strategy for gathering is \textsc{NP-hard}, for any values of $\di$ and $\dt$. If $\di>\dt$, we show that the problem remains hard when restricted to the uniform case where each vertex in the network has exactly one piece of information to communicate to the sink.

     
  12. J-C. Bermond, F. Havet, and D. Tóth. Fault tolerant on board networks with priorities. Networks, 47(1):9--25, 2006. [PDF ]
    Abstract:
    We consider on-board networks in satellites interconnecting entering signals (inputs) to amplifiers (outputs). The connections are made via expensive switches, each of which has four available links. The paths connecting inputs to outputs should be link-disjoint. Some of the input signals, called priorities, must be connected to the amplifiers which provide the best quality of service (that is to some specific outputs). In practice, amplifiers are prone to fail and the faults cannot be repaired. Therefore, extra outputs have to be built into the network to ensure that every input can be routed to operational outputs. Given three integers, $n$, $p$, and $f$, we would like to design a low cost network (where the network cost is proportional to the total number of switches) such that it is possible to route all $n$ inputs to $n$ operational amplifiers, and to route the $p$ priorities to the $p$ best quality amplifiers for any set of $f$ faulty and $p$ be