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D. Coudert and D. SimplotRyl, 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
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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.

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 NiceSophia).
[WWW
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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
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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.

D. Coudert,
V. Issarny,
and N. Georgantas, editors.
1st International Workshop on Adhoc Ambient Computing (AdhocAmC),
Sophia Antipolis, France,
September 2008.
I3S, CNRS, Université de Nice Sophia, INRIA.
[WWW
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D. Coudert,
S. Krco,
and K. Wrona, editors.
PhD workshop (PhDNOW),
Sophia Antipolis, France,
September 2008.
I3S, CNRS, Université de Nice Sophia, INRIA.
[WWW
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D. Coudert,
D. SimplotRyl,
and I. Stojmenovic, editors.
7th International Conference on ADHOC Networks & Wireless (AdHocNOW),
volume 5198 of Lecture Notes in Computer Science,
September 2008.
Springer.
[WWW
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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.

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
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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: EnglishFrenchTurkish.
Prof. Tuncer Ören,
2006.

J. Hromkovic,
R. Klasing,
A. Pelc,
P. Ruzicka,
and W. Unger.
Dissemination of Information in Communication Networks: Broadcasting, Gossiping, Leader Election, and FaultTolerance,
Springer Monograph.
SpringerVerlag,
2005.

B. Reed and C. LinharesSales, editors.
Recent advances in algorithms and combinatorics,
CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 11.
SpringerVerlag,
New York,
2003.

H. Alt and A. Ferreira, editors.
Proceedings of STACS 2002,
volume 2285 of Lecture Notes in Computer Science.
SpringerVerlag,
2002.

M. Molloy and B. Reed.
Graph colouring and the probabilistic method,
volume 23 of Algorithms and Combinatorics.
SpringerVerlag,
Berlin,
2002.

O. Dalle,
S. Frénot,
and M. Riveill, editors.
Cinquième Ecole d'Hiver des Télécommunications,
Golfe Juan, France,
December 2002.
INRIA  CNRS  Univ. de Nice,
INRIA.

A. Ferreira and D. Krob, editors.
Mobile Networks & Applications (MONET)  Special Issue on Discrete Algorithms and Methods for Mobile Computing and Communications.
ACM/Baltzer,
2001.

A. Ferreira and H. Reichel, editors.
Proceedings of STACS 2001,
volume 2010 of Lecture Notes in Computer Science.
SpringerVerlag,
2001.

J. L. Ramìrez Alfonsìn and B. Reed, editors.
Perfect graphs,
WileyInterscience Series in Discrete Mathematics and Optimization.
John Wiley & Sons Ltd.,
Chichester,
2001.

A. Ferreira and G. Kindervater, editors.
Parallel Computing  Special Issue on High Performance Computing in Operations Research,
volume 26.
Elsevier Science B. V.,
2000.

E. Altman,
A. Ferreira,
and J. Galtier.
Les réseaux satellitaires de télécommunications.
Interéditions,
1999.

P. Berthomé and A. Ferreira, editors.
Optical Interconnects and Parallel Processing: Trends at the Interface.
Kluwer Academic Publisher,
Boston (USA),
1998.

A. Ferreira and J. Rolim, editors.
Journal of Parallel and Distributed Computing  Special Issue on Irregular Problems,
volume 50.
Academic Press,
April 1998.

A. Ferreira,
J. Rolim,
H. Simon,
and S. Teng, editors.
Solving Irregularly Structured Problems in Parallel  Irregular'98,
volume 1457 of Lecture Notes in Computer Science.
SpringerVerlag,
1998.

M. Habib,
C. McDiarmid,
J. RamirezAlfonsin,
and B. Reed, editors.
Probabilistic methods for algorithmic discrete mathematics,
volume 16 of Algorithms and Combinatorics.
SpringerVerlag,
Berlin,
1998.

G. Bilardi,
A. Ferreira,
R. Lüling,
and J. Rolim, editors.
Parallel Algorithms for Solving Irregularly Structured Problems  Irregular'97,
volume 1253 of Lecture Notes in Computer Science.
SpringerVerlag,
1997.

A. Ferreira and P. Pardalos, editors.
Solving Combinatorial Optimization Problems in Parallel: Methods and Techniques,
volume 1054 of LNCS StateoftheArt Surveys.
SpringerVerlag,
1996.

A. Ferreira and J. Rolim, editors.
Theoretical Computer Science  Special Issue on Irregularly Structured Problems.
NorthHolland,
1996.

A. Ferreira,
J. Rolim,
Y. Saad,
and T. Yang, editors.
Parallel Algorithms for Solving Irregularly Structured Problems  Irregular'96,
volume 1117 of Lecture Notes in Computer Science.
SpringerVerlag,
1996.

G. Authié,
JeanMarie Garcia,
A. Ferreira,
J.L. Roch,
G. Villard,
J. Roman,
C. Roucairol,
and B. Virot, editors.
Algorithmique parallèle et applications irrégulières.
Hermes,
Paris (F),
1995.

A. Ferreira and J. Rolim, editors.
Parallel Algorithms for Irregular Problems: State of the Art.
Kluwer Academic Publisher,
Boston (USA),
1995.

A. Ferreira and J. Rolim, editors.
Parallel Algorithms for Solving Irregularly Structured Problems  Irregular'95,
volume 980 of Lecture Notes in Computer Science.
SpringerVerlag,
1995.

S. Akl,
A. Ferreira,
P. Fraigniaud,
and D. Sotteau, editors.
Parallel Processing Letters  Special Issue on Algorithmic and Structural Aspects of Interconnection Networks.
World Publisher Co.,
1994.

G. Authié,
A. Ferreira,
J.L. Roch,
G. Villard,
J. Roman,
C. Roucairol,
and B. Virot, editors.
Algorithmes parallèles  analyse et conception.
Hermes,
Paris (F),
1994.

M. Cosnard,
A. Ferreira,
and J. Peters, editors.
Parallel and Distributed Computing  Theory and Practice,
volume 805 of Lecture Notes in Computer Science.
SpringerVerlag,
1994.

Jean de RUMEUR.
Communications dans les réseaux de processeurs.
Masson,
Paris,
1994.
Note: (including J.C. Bermond, E. Darrot ,D. Lafaye de Micheaux and M. Syska).

editor J.C. Bermond.
Interconnection Networks,
volume 37,38.
Discrete Applied Mathematics,
1992.
Note: (also appeared in Topics in Discrete Mathematics, Vol 5,1992, North Holland) 582 pp.

J. Araujo.
Graph Coloring and Graph Convexity.
PhD thesis,
University of NiceSophia Antipolis and Federal University of Ceará,
September 2012.
[PDF
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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 EdgeLabeling, 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. 

L. Sampaio.
Algorithmic aspects of graph colouring heuristics.
PhD thesis,
University of NiceSophia Antipolis,
November 2012.
[PDF
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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 wellknown NPhard
problem.
In this thesis we study the Grundy number and the bchromatic 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 NPhard, but it
is solvable in polynomial time for P5free bipartite graphs.
After, we show that the problem of determining the bchromatic number
of a chordal distancehereditary graph is
NPhard, and we give polynomialtime algorithms for some subclasses of
block graphs, complement of bipartite
graphs and P4sparse graphs.
We also consider the fixedparameter tractability of determining the
Grundy number and the bchromatic number,
and in particular we show that deciding if the Grundy number (or the
bchromatic 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 bchromatic number
and the Grundy number with various other related parameters of a graph. 

B. M. T. Worou.
Outils Algorithmiques pour la Détection des Communautés dans les Réseaux.
PhD thesis,
University of NiceSophia 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. 

N. Cohen.
Some results in graph theory and its applications.
PhD thesis,
Ecole doctorale STIC, Université de NiceSophia Antipolis,
October 2011.
[WWW
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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 noninduced 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 3uniform hypergraph can be
partitioned into $\lceil \frac {n(n1)} 6\rceil$ $\alpha$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. 

JC Maureira Bravo.
Internet on Rails.
THESE,
Ecole doctorale STIC, Université de Nice SophiaAntipolis,
January 2011.
[WWW
] [PDF
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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 twofold: 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 inmotion network (onboard 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 onboard trains, metros or urban buses. 

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 SophiaAntipolis,
November 2011.
[WWW
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Abstract: 
Nous nous intÃ©ressons dans cette thÃ¨se Ã diffÃ©rents types de rÃ©seaux
(optiques, sansfil, pairÃ pair) ayant chacun leurs spÃ©cificitÃ©s mais
partageant des problÃ©matiques communes : assurer la meilleure qualitÃ© de
services possible, garantir la stabilitÃ© du systÃ¨me, minimiser les
ressources et donc le coÃ»t de fonctionnement. Tout d'abord, nous
Ã©tudions le problÃ¨me de la reconfiguration du routage dans les rÃ©seaux
optiques consistant Ã rerouter les requÃªtes de connexion en minimisant
les perturbations pour les utilisateurs. Puis, nous nous intÃ©ressons au
problÃ¨me de la dÃ©termination de routages efficaces en Ã©nergie dans les
rÃ©seaux coeur. Pour ce faire, nous Ã©tudions le problÃ¨me de trouver des
routages minimisant le nombre d'Ã©quipements utilisÃ©s. Ensuite, nous nous
intÃ©ressons aux algorithmes d'ordonnancement des liens dans les rÃ©seaux
sansfil en prÃ©sence d'interfÃ©rence. Enfin, nous considÃ©rons le
problÃ¨me de stockage de donnÃ©es dans les rÃ©seaux pairÃ pair. Nous
Ã©tudions l'impact de diffÃ©rentes politiques de placement sur la durÃ©e de
vie des donnÃ©es et nous dÃ©terminons un choix de placement optimal. Pour
rÃ©soudre ces problÃ¨mes, nous utilisons les outils thÃ©oriques des
mathÃ©matiques discrÃ¨tes (graphes, configurations, optimisation
combinatoire), d'algorithmique (complexitÃ©, algorithmique distribuÃ©e) et
de probabilitÃ©s. 

J. Ribault.
Reuse and Scalability in Modeling and Simulation Software Engineering.
THESE,
Ecole doctorale STIC, Université de Nice SophiaAntipolis,
January 2011.
[WWW
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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, posttraitement 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. 

D. Coudert.
Algorithmique et optimisation dans les réseaux de télécommunications.
Habilitation à Diriger des Recherches,
Université de Nice SophiaAntipolis (UNS),
March 2010.
[WWW
] [PDF
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Julian Monteiro.
Modeling and Analysis of Reliable PeertoPeer Storage Systems.
PhD thesis,
Ecole doctorale STIC, Université de NiceSophia Antipolis,
November 2010.
[WWW
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Abstract: 
Large scale peertopeer 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 wellknown that erasure coding is a space efficient solution to obtain a high degree of faulttolerance 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 closedform 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 tradeoffs 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. 

N. Nepomuceno.
Network optimization for wireless microwave backhaul.
PhD thesis,
Ecole doctorale STIC, Université de NiceSophia 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 costeffectively 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, chanceconstrained 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 

S. Pérennes.
Contribution à l'algorithmique des réseaux de télécommunications.
Habilitation à Diriger des Recherches,
Université de Nice SophiaAntipolis (UNS),
March 2010.
[WWW
]

C. Gomes.
Radio Mesh Networks and the Round Weighting Problem.
PhD thesis,
Université de NiceSophia Antipolis (UNS),
December 1st 2009.
[WWW
] [PDF
]
Keywords:
Radio Mesh Networks,
Multiobjective 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 multiobjective 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 nonuniform 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 singlehop around the gateway. It is due to the fact that the problem is convex under some conditions that are often met. 

C. Molle.
Optimisation de la capacité des réseaux radio maillés.
PhD thesis,
Ecole doctorale STIC, Université de NiceSophia Antipolis,
October 2009.
[WWW
] [PDF
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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 intercouche 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. 

G. Monaco.
Optimization and NonCooperative Issues in Communication Networks.
PhD thesis,
University of l'Aquila,
October 2009.
[WWW
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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 ondemandvideo, multimedia and data integrated networks, seamless and ubiquitous access to system resources in mobile environments, secure ondemand 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 noncooperative 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 noncooperative 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, NPcomplete results, approximation algorithms and inapproximability results; analysis of performances, convergence and existence of Nash equilibria in selfish scenarios. 

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 NiceSophia Antipolis,
August 2009.

P. Reyes.
Data Gathering in Radio Networks.
PhD thesis,
Ecole doctorale STIC, Université de NiceSophia Antipolis,
August 2009.
[WWW
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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. 

I. Sau.
Optimization in Graphs under Degree Constraints. Application to Telecommunication Networks.
PhD thesis,
Université de NiceSophia Antipolis (UNS) and Universitat Politècnica de Catalunya (UPC),
October 2009.
[PDF
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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 lowrate signals into higherspeed streams, in order to improve bandwidth utilization and reduce the network cost. The objective is to minimize the number of AddDrop Multiplexers (ADMs), which are devices that insert/extract lowrate traffic to/from a highspeed stream. In graphtheoretical 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 polynomialtime 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 alltoall 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 twoperiod 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 graphtheoretical 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 degreeconstrained problems, giving hardness results and polynomialtime approximation algorithms. We then study in Chapter~6 the parameterized complexity of finding degreeconstrained subgraphs, when the parameter is the size of the subgraphs. We prove hardness results in general graphs and provide explicit fixedparameter tractable algorithms for minorfree graphs. We obtain in Chapter~7 subexponential parameterized and exact algorithms for several families of degreeconstrained 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 surfaceembedded 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. 

J. Galtier.
L'adaptativité dans les télécommunications.
Habilitation à Diriger des Recherches,
Université de NiceSophia Antipolis,
February 2008.

F. Huc.
Conception de Réseaux Dynamiques Tolérants aux Pannes.
PhD thesis,
École doctorale STIC, Université de NiceSophia Antipolis,
November 2008.
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Abstract: 
Cette thÃ¨se aborde diffÃ©rents aspects de la conception d'un rÃ©seau de tÃ©lÃ©communications. Un tel rÃ©seau utilise des technologies hÃ©tÃ©rogÃ¨nes: liens antennessatellites, radio, fibres optiques ou bien encore rÃ©seaux embarquÃ©s dans un satellite. Les problÃ©matiques varient en fonction de la partie du rÃ©seau considÃ©rÃ©e, du type de requÃªtes et de l'objectif. Le cas des requÃªtes de type paquets est abordÃ© dans le cadre des rÃ©seaux en forme de grille, mais le thÃ¨me principal est le routage de requÃªtes de type connections (unicast et multicast). Les objectifs considÃ©rÃ©s sont : la conception d'un rÃ©seau embarquÃ© dans un satellite de tÃ©lÃ©communication, de taille minimum et tolÃ©rant des pannes de composants; le dimensionnement des liens d'un rÃ©seau afin qu'il supporte des pannes corrÃ©lÃ©es ou qu'il offre une bonne qualitÃ© de service, ou s'il autorise des connections multicast; le dimensionnement de la taille des buffers d'un rÃ©seau d'accÃ©s radio; et l'optimisation de l'utilisation des ressources d'un rÃ©seau dynamique orientÃ© connections. Dans tous ces cas la problÃ©matique du routage de connections est centrale.
Mon approche consiste Ã utiliser la complÃ©mentaritÃ© de techniques algorithmique et d'optimisation combinatoire ainsi que d'outils issus de la thÃ©orie des graphes tels la pathwidth et des notions reliÃ©es process number, jeux de captures et treewidth, diffÃ©rents types de coloration impropre et pondÃ©rÃ©e, proportionnelle, directed star colouring, les graphes d'expansion et des techniques de partitions telle la quasi partition. 

O. Amini.
Algorithmique des décompositions de graphes Applications aux réseaux de télécommunications.
PhD thesis,
École doctorale STIC, Université de NiceSophia 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 Ã 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. 

F. Havet.
Graph colouring and applications.
Habilitation à Diriger des Recherches,
Université de NiceSophia Antipolis,
December 12 2007.
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L. Hogie.
Mobile Ad Hoc Networks: Modelling, Simulation and Broadcastbased 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, WiFi or/ and Bluetoothenabled devices become of frequent use. More than allowing the connection to some access point (as they can be found in airport, train stations, citycenters, restaurants, etc), these interfaces permit also to interconnect directly with one another in a decentralized way and to hence selforganize 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 peertopeer 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, customertocustomer 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, endtoend 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 cityscale 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 bandwidthefficient broadcasting protocol called DFCN. 

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
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N. Morales.
Algorithmique des réseaux de communication radio modélisés par des graphes.
PhD thesis,
École doctorale STIC, Université de NiceSophia Antipolis,
26 Janvier 2007.
[PDF
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F. Giroire.
Réseaux, algorithmique et analyse combinatoire de grands ensembles.
PhD thesis,
Université Paris VI,
November 2006.
[WWW
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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 onboard 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. 

G. Huiban.
The reconfiguration problem in multifiber WDM networks.
PhD thesis,
University of Nice Sophia Antipolis & Federal University of Minas Gerais,
July 2006.
[WWW
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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 monoobjective 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 tradeoffs 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 tradeoffs. Giving a little flexibility with respect to a metric generally allows to significantly improve the solutions with respect to the other metrics. 

J.S. Sereni.
Colorations de graphes et applications.
PhD thesis,
École doctorale STIC, Université de NiceSophia Antipolis,
Juillet 2006.

ME. Voge.
Optimisation des réseaux de télécommunications: réseaux multicouches, tolérance aux pannes et surveillance de trafic.
PhD thesis,
École doctorale STIC, Université de NiceSophia Antipolis,
November 17 2006.
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A. Jarry.
Connexité dans les réseaux de télécommunications.
PhD thesis,
École doctorale STIC, Université de NiceSophia Antipolis,
March 2005.

J.F. Lalande.
Conception de réseaux de télécommunications : optimisation et expérimentations.
PhD thesis,
École doctorale STIC, Université de NiceSophia Antipolis,
Décembre 2004.
[PDF
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H. Rivano.
Algorithmique et télécommunications : coloration et multiflot approchés et applications aux réseaux d'infrastructure.
PhD thesis,
Université de NiceSophia Antipolis,
November 2003.
[WWW
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Abstract: 
Cette thèse s'intéresse aux problématiques fondamentales d'optimisation combinatoire qui se dégagent de la modélisation structurelle et algorithmique du dimensionnement des réseaux d'infrastructure de télécommunication. L'optimisation de ces réseaux est essentielle aux opérateurs de télécommunication, qui demandent la garantie d'une exploitation efficace des ressources déployées. Nous donnons une nouvelle modélisation des réseaux optiques WDM multifibres. En considérant un routage agrégé au niveau des câbles, nous optons pour une nouvelle lecture des contraintes d'affectation de longueurs d'onde fondée sur des conflits de groupe. Nous étudions aussi le problème de coloration de chemins, issu de l'affectation de longueurs d'onde dans les réseaux optiques monofibres. Nous développons, pour la relaxation linéaire de ce problème, un algorithme polynomial efficace dans les arbres de degré borné, puis, par extension, dans les graphes de largeur arborescente bornée. Nous majorons le coût d'une telle coloration dans les arbres binaires et donnons une (1+5/(3e)+o(1))approximation aléatoire pour la coloration entière dans les arbres de degré borné, ce qui améliore le meilleur algorithme connu pour ce cas. Nous présentons enfin des avancées algorithmiques pour les problèmes de multiflot entier et fractionnaire. Nous donnons un algorithme d'arrondi aléatoire incrémental pour l'approximation du multiflot entier. Motivés par le besoin d'un calcul rapide de multiflot fractionnaire pour l'algorithme précédent, nous nous intéressons aux approximations combinatoires de ce problème. En employant des techniques de calcul dynamique des plus courts chemins, nous améliorons l'un des meilleurs algorithme de la littérature. 

C. Touati.
Les principes d'équité appliqués aux réseaux de télécommunications.
PhD thesis,
Université de NiceSophia Antipolis,
September 2003.

S. Choplin.
Dimensionnement de réseaux virtuels de télécommunication.
PhD thesis,
Université de Nice  Sophia Antipolis,
November 2002.

L. Floriani.
Méthodes d'Analyse des Données Multivariables pour l'étude des Mécanismes des Heuristiques.
PhD thesis,
Université de NiceSophia Antipolis,
January 2002.

A. Laugier.
Cônes de Matrices et Programmation Mathématique : Quelques Applications.
PhD thesis,
Université de NiceSophia Antipolis,
March 2002.

D. Coudert.
Algorithmique et optimisation de réseaux de communications optiques.
PhD thesis,
Université de Nice SophiaAntipolis (UNSA),
Décembre 2001.
[POSTSCRIPT
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Abstract: 
This thesis deals with optical communication networks, especially free space optical networks and optical fiber networks.
First we address the design of free space optical networks using the Optical Transpose Interconnection System (OTIS) architecture defined in [MMHE93]. We give a model of these networks with H(p,q,d) digraphs which we characterize. We take a specific interest in isomorphisms between these digraphs and well known digraphs (de Bruijn, Kautz and other alphabet graphs). We develop a family of alphabet digraphs which includes a large number of digraphs isomorphic to the de Bruijn and use it to obtain an optimal design of the de Bruijn with OTIS, in terms of minimizing the number of lenses. Then, we study a family of networks modeled by directed hypergraphs and called stackKautz, for which we provide routing algorithms and control protocols.
In a second part we address the problem of WDM network survivability using protection. This problem consists in using precomputed and dedicated resources in order to ensure traffic continuity if a bundle of fibers breaks down. We describe numerous strategies for protecting the instance and the network. We go more deeply into subnetwork protection where protection resources are shared by sets of request describing a specific subnetwork (circuit). We give an optimal solution to this problem when the network is a cycle and the requests realize the AlltoAll pattern. 

B. Beauquier.
Communications dans les réseaux optiques par multiplexage en longueur d'onde.
PhD thesis,
université de NiceSophia Antipolis  STIC,
janvier 2000.
[POSTSCRIPT
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T. Jiménez.
Simulation de trafic routier: Étude des méthodologies de modélisation et parallélisation et mise en oe uvre.
PhD thesis,
université de NiceSophia Antipolis,
September 2000.

N. Marlin.
Communications Structurées dans les Réseaux.
PhD thesis,
université de NiceSophia Antipolis,
juin 2000.

O. Dalle.
Techniques et outils pour les communications et la répartition dynamique de charge dans les réseaux de stations de travail.
Thèse de Doctorat,
Université de Nice  Sophia Antipolis, École doctorale Sciences Pour l'Ingénieur,
Janvier 1999.

N. Furmento.
Schooner : Une Encapsulation Orintée Objet de Supports d'Exécution pour Applications Réparties.
PhD thesis,
Université de NiceSophia Antipolis,
France,
May 1999.

L. Liquori.
Type Assigment Systems for Lambda Calculi and for the Lambda Calculus of Objects.
Ph.D. Thesis, 193 pp.,
University of Turin,
October 1996.
[POSTSCRIPT
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A. Ferreira.
Structures de données et modélisation discrète pour l'algorithmique des systèmes massivement parallèles.
Habilitation à diriger des recherches,
Ecole Normale Supérieure de Lyon et Université Claude Bernard Lyon,
France,
February 1994.

A. Ferreira.
Contributions à la Recherche dans des Ensembles Ordonnés : du Séquentiel au Parallèle.
PhD thesis,
Institut National Polytechnique de Grenoble,
France,
Juanary 1990.

P. Mussi.
Modèles quantitatifs pour le Parallélisme.
PhD thesis,
Université de Paris V,
May 1990.

L. AddarioBerry,
F. Havet,
C. Linhares Sales,
B. Reed,
and S. Thomassé.
Oriented trees in digraphs.
Discrete Mathematics,
313(8):967974,
2013.
[WWW
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Abstract: 
"Let $f(k)$ be the smallest integer such that every $f(k)$chromatic digraph contains every oriented tree of order $k$. Burr proved $f(k)\leq (k1)^2$ in general, and he conjectured $f(k)=2k2$. Burr also proved that every $(8k7)$chromatic digraph contains every antidirected tree. We improve both of Burr's bounds. We show that $f(k)\leq k^2/2k/2+1$ and that every antidirected tree of order $k$ is contained in every $(5k9)$chromatic digraph.
We make a conjecture that explains why antidirected trees are easier to handle. It states that if $E(D) > (k2) V(D)$, then the digraph $D$ contains every antidirected tree of order $k$. This is a common strengthening of both Burr's conjecture for antidirected trees and the celebrated Erd\H{o}sS\'os Conjecture. The analogue of our conjecture for general trees is false, no matter what function $f(k)$ is used in place of $k2$. We prove our conjecture for antidirected trees of diameter 3 and present some other evidence for it.
Along the way, we show that every acyclic $k$chromatic digraph contains every oriented tree of order $k$ and suggest a number of approaches for making further progress on Burr's conjecture." 

J. Araujo,
V. Campos,
F. Giroire,
N. Nisse,
L. Sampaio,
and R. Soares.
On the hull number of some graph classes.
Theoretical Computer Science,
475:112,
2013.
[WWW
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Abstract: 
In this paper, we study the geodetic convexity of graphs focusing on the problem of the complexity to compute inclusionminimum 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 NPcomplete 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 NPhard 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 $(q,q4)$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 $1+\lceil \frac{3(n1)}{5}\rceil$ in general, at most $1+\lceil \frac{n1}{2}\rceil$ if $G$ is regular or has no triangle, and at most $1+\lceil \frac{n1}{3}\rceil$ if $G$ has girth at least $6$. 

JeanClaude Bermond,
Michel Cosnard,
and Stéphane Pérennes.
Directed acyclic graphs with the unique dipath property.
Theoretical Computer Science,
504:511,
September 2013.
[WWW
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Keywords:
DAG (Directed acyclic graphs),
load,
wavelengths,
dipaths,
good labelings,
conflict graphs,
intersection graphs,
chromatic number.
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 $\pi$(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 arcdisjoint. There exist DAGs such that the ratio between w(G, P) and $\pi$(G, P) cannot be bounded. An internal cycle is an oriented cycle such that all the vertices have at least one predecessor 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) = $\pi$(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 UPPDAGs. For these UPPDAGs 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 $\pi$(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. 

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):900926,
2013.
[PDF
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Abstract: 
Given a graph $G=(V,E)$ and a positive integer $k$, an edge modification problem for a graph property $\Pi$ consists in deciding whether there exists a set $F$ of pairs of $V$ of size at most $k$ such that the graph $H=(V,E\vartriangle F)$ satisfies the property $\Pi$. In the $\Pi$ \emph{edgecompletion problem}, the set $F$ is constrained to be disjoint from $E$; in the $\Pi$ \emph{edgedeletion problem}, $F$ is a subset of $E$; no constraint is imposed on $F$ in the $\Pi$ \emph{edgeediting problem}. A number of optimization problems can be expressed in terms of graph modification problems which have been extensively studied in the context of parameterized complexity. When parameterized by the size $k$ of the set $F$, it has been proved that if $\Pi$ is an hereditary property characterized by a finite set of forbidden induced subgraphs, then the three $\Pi$ edgemodification problems are FPT. It was then natural to ask whether these problems also admit a polynomial kernel. Using recent lower bound techniques, Kratsch and Wahlstr\"om answered this question negatively. However, the problem remains open on many natural graph classes characterized by forbidden induced subgraphs. Kratsch and Wahlstr\"om asked whether the result holds when the forbidden subgraphs are paths or cycles and pointed out that the problem is already open in the case of $P_4$free graphs (i.e. cographs). This paper provides positive and negative results in that line of research. We prove that \textsc{Parameterized cograph edgemodification} problems have cubic vertex kernels whereas polynomial kernels are unlikely to exist for the \textsc{$P_l$free edgedeletion} and the \textsc{$C_l$free edgedeletion} problems for $l\geq 7$ and $l\geq 4$ respectively. Indeed, if they exist, then $NP \subseteq coNP / poly$. 

F. Giroire,
D. Mazauric,
and J. Moulierac.
Energy Efficient Routing by SwitchingOff Network Interfaces,
chapter 10  EnergyAware Systems and Networking for Sustainable Initiatives,
pages 207236.
IGI Global,
june 2012.
[WWW
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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 polynomialtime constantfactor 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 mediumsized 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. 

O. Amini,
D. Peleg,
S. Pérennes,
I. Sau,
and S. Saurabh.
On the approximability of some degreeconstrained subgraph problems.
Discrete Applied Mathematics,
160(12):1661  1679,
2012.
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Abstract: 
In this article we provide hardness results and approximation algorithms for the following three natural degreeconstrained subgraph problems, which take as input an undirected graph G = ( V , E ) .
Let d â¥ 2 be a fixed integer.
The Maximum d â degreeboundedÂ Connected Subgraph ( MDBCS d ) problem takes as additional input a weight function Ï : E â R + , and asks for a subset E â² â E such that the subgraph induced by E â² is connected, has maximum degree at most d , and â e â E â² Ï ( e ) is maximized.
The Minimum Subgraph of Minimum Degree â¥ d ( MSMD d ) problem involves finding a smallest subgraph of G with minimum degree at least d .
Finally, the Dual Degreedense k Subgraph ( DDD k S ) problem consists in finding a subgraph H of G such that  V ( H )  â¤ k and the minimum degree in H is maximized. 

J. Araujo,
JC. Bermond,
F. Giroire,
F. Havet,
D. Mazauric,
and R. Modrzejewski.
Weighted improper colouring.
Journal of Discrete Algorithms,
16:5366,
2012.
Note: Selected papers from the 22nd International Workshop on Combinatorial Algorithms (IWOCA 2011).
[WWW
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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 endvertices.
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 NPhard 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 $t$. 

J. Araujo,
N. Cohen,
F. Giroire,
and F. Havet.
Good edgelabelling of graphs.
Discrete Applied Mathematics,
160(18):25012513,
2012.
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Abstract: 
{A {\it good edgelabelling} 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 nondecreasing 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 edgelabelling.
First, we exhibit infinite families of graphs for which no such edgelabelling can be found. We then show that deciding if a graph admits a good edgelabelling is NPcomplete.
Finally, we give
large classes of graphs admitting a good edgelabelling:
$C_3$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} 

J. Araujo and C. Linhares Sales.
On the Grundy number of graphs with few P4's.
Discrete Applied Mathematics,
160(18):25142522,
2012.
Note: V Latin American Algorithms, Graphs, and Optimization Symposium â Gramado, Brazil, 2009.
[WWW
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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 NPhard if $G$ is a $P_5$free graph. In this article, we define a new class of graphs, the fatextended $P_4$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 fatextended $P_4$laden class." 

J. BangJensen,
F. Havet,
and N. Trotignon.
Finding an induced subdivision of a digraph.
Theoretical Computer Science,
443:1024,
2012.
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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 2cycles.
We give a number of examples of polynomial instances as well as several NPcompleteness proofs. 

L. Barrière,
P. Flocchini,
F. Fomin,
P. Fraigniaud,
N. Nisse,
N. Santoro,
and D. Thilikos.
Connected Graph Searching.
Information and Computation,
219:116,
2012.
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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. nonaccessible 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 nonconnected one is $O(\log n)$ while for trees this ratio is always at most 2.
We also conjecture that this constantratio 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 forbiddengraph 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 HortonStralher number. 

S. Baruah,
V. Bonifaci,
G. D'Angelo,
H. Li,
A. MarchettiSpaccamela,
N. Megow,
and L. Stougie.
Scheduling Realtime Mixedcriticality Jobs.
IEEE Transactions on Computers,
61(8):11401152,
2012.
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Abstract: 
Many safetycritical 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 "mixedcriticality" 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 mixedcriticality 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, reservationbased scheduling and prioritybased scheduling, that are widely used in scheduling such mixedcriticality 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. 

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):447481,
2012.
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Abstract: 
We study a graphaugmentation 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 edgeminimal 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 ILPbased exact approaches and show how to stochastically evaluate a given shortcut assignment on graphs that are too large to do so exactly. 

JC. Bermond,
D. Coudert,
J. Moulierac,
S. Pérennes,
I. Sau,
and F. Solano Donado.
GMPLS Label Space Minimization through Hypergraph Layouts.
Theoretical Computer Science (TCS),
444:316,
July 2012.
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Abstract: 
{A}ll{O}ptical {L}abel {S}witching ({AOLS}) is a new technology that performs packet forwarding without any opticalelectricaloptical 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 napproximation, 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 polynomialtime dynamic programming algorithm for a fixed number k of sources running in {O}(n^{k+2}) time. 

JC. Bermond and J. Moulierac.
Internet et la théorie des graphes.
Revue TDC Textes et documents pour la Classe : la révolution Internet,
1042:3233,
2012.
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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 " petitmonde " Comment calculer un plus court chemin ? 

JC. Bermond and J. Peters.
Optimal Gathering in Radio Grids with Interference.
Theoretical Computer Science,
457:1026,
October 2012.
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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 noninterfering
transmissions. In this paper, we determine the exact number of rounds
required to gather one piece of information from each node of a square
twodimensional grid into the central node. If $d_I = 2k1$ is odd,
then the number of rounds is $k(N1)c_k$ 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 $(k+\frac{1}{4})(N1)c'_k$ 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 nonshortest paths to establish the matching upper
bound. We then generalize our results to hexagonal grids. 

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):269275,
2012.
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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 routediscovery 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 NPComplete, and then propose an algorithm to build all rooted directed minimum spanning trees in already identified strongly connected components. 

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):7888,
2012.
[WWW
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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. 

Y. Chen,
E. Le Merrer,
Z. Li,
Y. Liu,
and G. Simon.
OAZE: A NetworkFriendly Distributed Zapping System for PeertoPeer IPTV.
Computer Networks,
56(1):365377,
2012.
[WWW
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Abstract: 
IPTV systems attracting millions of users are now commonly deployed on peertopeer (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 multicastbased IPTV. In order to speed up the switching process and to reduce the overall crossdomain 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 addon for existing P2P IPTV systems. 

D. Coudert,
F. Huc,
and D. Mazauric.
A Distributed Algorithm for Computing the Node Search Number in Trees.
Algorithmica,
63(12):158190,
2012.
[WWW
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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 treeedges 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). 

G. D'Angelo,
G. Di Stefano,
and A. Navarra.
Minimize the Maximum Duty in Multiinterface Networks.
Algorithmica,
63(12):274295,
2012.
[WWW
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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 multiinterface 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 NPhard 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 NPhard 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. 

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):767798,
2012.
[WWW
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Abstract: 
Lov{\'{a}}sz and Plummer conjectured in the 1970âs 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. 

A. Ferreira and A. Jarry.
MinimumEnergy Broadcast Routing in Dynamic Wireless Networks.
Journal of Green Engineering,
2(2):115123,
2012.
[PDF
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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 minimumenergy broadcast routing problem for a static network in the plane, which attracted a great deal of attention these past years.
The problem is NPhard 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 NPCompleteness result, namely that computing a Minimum Spanning Tree of a planar network in the presence of mobility is actually NPComplete.
This result implies that the above approximation solution cannot be used in dynamic wireless networks.
On the positive side, we give a polynomialtime algorithm to build a rooted spanning tree of an on/off network, that minimizes the maximum energy used. 

D. Gonçalves,
F. Havet,
A. Pinlou,
and S. Thomassé.
On spanning galaxies in digraphs.
Discrete Applied Mathematics,
160(6):744754,
2012.
[WWW
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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 vertexdisjoint 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 NPcomplete (even when restricted to acyclic digraphs), it becomes polynomialtime 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 polynomialtime 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 $D$. 

F. Havet,
C. Linhares Sales,
and L. Sampaio.
bcoloring of tight graphs.
Discrete Applied Mathematics,
160(18):27092715,
2012.
[WWW
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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):145168,
2012.
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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 $\Delta^2+C_p$. 

N. Nisse,
I. Rapaport,
and K. Suchan.
Distributed computing of efficient routing schemes in generalized chordal graphs.
Theoretical Computer Science,
444(27):1727,
2012.
[WWW
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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 kchordal 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 kchordal graphs, our routing scheme achieves an additive stretch of at most k1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k1.
In order to compute the routing tables of any nnode 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 3chordal graphs).
The routing scheme uses addresses of size log n bits and local memory of size 2(d1) log n bits in a node of degree d. 

JC. Bermond,
F. Ergincan,
and M. Syska.
Quisquater Festschrift,
volume 6805 of Lecture Notes in Computer Science,
chapter Line Directed Hypergraphs,
pages 2534.
SpringerVerlag,
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. 

G. A. Wainer,
K. AlZoubi,
O. Dalle,
R.C. Hill,
S. Mittal,
J. L. R. Martin,
H. Sarjoughian,
L. Touraille,
M. K. Traoré,
and B. P. Zeigler.
DiscreteEvent Modeling and Simulation: Theory and Applications,
chapter 18  Standardizing DEVS Simulation Middleware,
pages 459494.
Taylor and Francis,
2011.
[WWW
]

G . Wainer,
K. AlZoubi,
O. Dalle,
R. C. Hill,
S. Mittal,
J. L. R. Martin,
H. Sarjoughian,
L. Touraille,
M. K. Traoré,
and B. P. Zeigler.
DiscreteEvent Modeling and Simulation: Theory and Applications,
chapter 17  Standardizing DEVS model representation,
pages 427458.
Taylor and Francis,
2011.
[WWW
]

V. Andova,
N. Cohen,
and R. Skrekovski.
Graph Classes (Dis)satisfying the Zagreb Indices Inequality.
MATCH Commun. Math. Comput. Chem.,
65(3):647658,
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. 

M. Basavaraju,
L. S. Chandran,
N. Cohen,
F. Havet,
and T. Müller.
Acyclic edgecoloring of planar graphs.
SIAM Journal of Discrete Mathematics,
25(2):463478,
2011.
[PDF
]
Abstract: 
A proper edgecoloring with the property that every cycle contains edges of
at least three distinct colors is called an {\it acyclic
edgecoloring}. The {\it acyclic chromatic index} of a graph $G$,
denoted $\chi'_a(G)$ is the minimum $k$ such that $G$ admits an {\it
acyclic edgecoloring} 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. 

J. Beauquier,
J. Burman,
and S. Kutten.
A selfstabilizing Transformer for Population Protocols with Covering.
Theoretical Computer Science,
412(33):42474259,
2011.
[WWW
]
Abstract: 
Developing \emph{selfstabilizing} 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 selfstabilizing 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 resourcelimited 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 selfstabilizing algorithm for the same problem. The transformer is built using a \emph{reexecution approach} (the technique consisting of executing an algorithm repeatedly in order to obtain its selfstabilizing 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. 

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):600610,
2011.
[PDF
]
Abstract: 
The $\alpha$arboricity of the complete 3uniform
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. 

JC. Bermond,
X. Muñoz,
and I. Sau.
Traffic Grooming in Bidirectional WDM Ring Networks.
Networks,
58(1):2035,
2011.
[WWW
] [PDF
]
Abstract: 
We study the minimization of ADMs (AddDrop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and alltoall 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. 

V. Bilo,
M. Flammini,
G. Monaco,
and L. Moscardelli.
On the performances of Nash equilibria in isolation games.
Journal of Combinatorial Optimization,
22:378391,
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. 148â159, 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 playersâ utilities. Moreover, we prove that the convergence to Nash equilibria is not guaranteed in some of the not yet analyzed cases. 

B. Bresar,
F. Kardos,
J. Katrenic,
and G. Semanisin.
Minimum $k$path vertex cover.
Discrete Applied Mathematics,
159(12):11891195,
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 NPhard 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. 

C. Caillouet,
S. Pérennes,
and H. Rivano.
Framework for Optimizing the Capacity of Wireless Mesh Networks.
Computer Communications,
34(13):16451659,
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 crosslayer 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. 

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):333359,
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 copwin graphs as graphs admitting a dismantling scheme. In this
paper, we characterize in a similar way the copwin 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 copwin 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 copwin for any value of k. 

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):46754687,
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 APXhard, 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 NPcomplete. 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. 

N. Cohen and F. Havet.
Linear and 2Frugal Choosability of Graphs of Small Maximum Average Degree.
Graphs and Combinatorics,
27(6):831849,
2011.
[WWW
] [PDF
]
Abstract: 
A proper vertex colouring of a graph $G$ is {\it 2frugal} (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 2frugally} (resp. {\it linearly}) {\it $L$colourable} if for a given list assignment $L:V(G)\mapsto 2^{\mathbb N}$, there exists a 2frugal (resp. linear) colouring $c$ of $G$ such that $c(v)\in L(v)$ for all $v\in V(G)$. If $G$ is 2frugally (resp. linearly) $L$list colourable for any list assignment such that $L(v)\ge k$ for all $v\inV(G)$, then $G$ is {\it 2frugally} (resp. {\it linearly}) {\it $k$choosable}. In this paper, we improve some bounds on the 2frugal choosability and linear choosability of graphs with small maximum average degree. 

D. Coudert,
F. Giroire,
and I. Sau.
Circuits in graphs through a prescribed set of ordered vertices.
Journal of Interconnection Networks (JOIN),
11(34):121141,
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{edgesimple} 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 edgesimple 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 3vertexconnected. 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. 

D. Coudert and JS. Sereni.
Characterization of graphs and digraphs with small process number.
Discrete Applied Mathematics (DAM),
159(11):10941109,
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. 

J. Czap,
S. Jendrol',
and F. Kardos.
Facial parity edge colouring.
Ars Mathematica Contemporanea,
4(2):255269,
2011.
[PDF
]
Abstract: 
A \emph{facial parity edge colouring} of a connected bridgeless plane graph is such an edge colouring in which no two faceadjacent 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. 

J. Czap,
S. Jendrol',
and F. Kardos.
On the strong parity chromatic number.
Discussiones Mathematicae Graph Theory,
31:587600,
2011.
[PDF
]
Abstract: 
A vertex colouring of a 2connected 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) 512Â520] proved that every 2connected 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 

J. Czap,
S. Jendrol',
F. Kardos,
and J. Miskuf.
Looseness of Plane Graphs.
Graphs and Combinatorics,
27(1):7385,
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. 

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 NPhard 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. 

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 twopart 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 frontend, 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 ComponentBased 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. 

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 twopart 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 frontend, 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 ComponentBased 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. 

R. Erman,
F. Havet,
B. Lidicky,
and O. Pangrác.
5colouring graphs with 4 crossings.
SIAM Journal on Discrete Mathematics,
25(1):401422,
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 5colourable.
However, we show that every graph with crossing number at most 4 and
clique number at most 5 is 5colourable.
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. 

L. Esperet,
F. Kardos,
A. D. King,
D. Král',
and S. Norine.
Exponentially many perfect matchings in cubic graphs.
Advances in Mathematics,
227(4):16461664,
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. 

P. Giabbanelli and J. G. Peters.
Complex networks and epidemics.
Technique et Science Informatiques,
20(2):181212,
2011.
Abstract: 
The study of spreading processes, such as infectious diseases or
computer worms, is wellmotivated 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 "realworld" 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 scalefree
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. 

F. Havet,
S. Jendrol',
R. Soták,
and E. Skrabul'áková.
Facial nonrepetitive edgecolouring of plane graphs.
Journal of Graph Theory,
66(1):3848,
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 nonrepetitive} 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 nonrepetitive} if the sequence of colours of its edges is nonrepetitive. If $G$ is a plane graph, a {\em facial nonrepetitive edgecolouring} of $G$ is an edgecolouring such that any {\it facial trail} (i.e. trail of consecutive edges on the boundary walk of a face) is nonrepetitive. We denote $\pi'_f(G)$ the minimum number of colours of a facial nonrepetitive edgecolouring 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.


F. Havet,
M. Klazar,
J. Kratochvìl,
D. Kratsch,
and M. Liedloff.
Exact algorithms for L(2,1)labelling.
Algorithmica,
59(2):169194,
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 NPcomplete 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 NPcomplete 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
0x1.57ca7bff74688p895n $O(c^n)$ 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. 

F. Kardos,
J. Katrenic,
and I. Schiermeyer.
On computing the minimum 3path vertex cover and dissociation number of graphs.
Theoretical Computer Science,
412(50):70097017,
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. 

F. Kardos,
D. Král',
and J. Volec.
Fractional colorings of cubic graphs with large girth.
SIAM Journal on Discrete Mathematics,
25(3):14541476,
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. 

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
]

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
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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 6394.
Springer,
A. Koster and X. Muñoz edition,
2010.
[WWW
] [PDF
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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. 

L. AddarioBerry,
W.S. Kennedy,
A.D. King,
Z. Li,
and B. Reed.
Finding the maximumweight induced $k$partite subgraph of an $i$triangulated graph.
Discrete Applied Mathematics,
158(7):765770,
April 2010.
[WWW
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Abstract: 
An itriangulated graph is a graph in which every odd cycle has two noncrossing chords; itriangulated graphs form a subfamily of perfect graphs. A slightly more general family of perfect graphs are cliqueseparable graphs. A graph is cliqueseparable 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 maximumweight induced kpartite subgraph of an itriangulated graph, and show that the problem of finding a maximumsize bipartite induced subgraph in a cliqueseparable graph is View the MathML sourcecomplete. 

O. Amini,
F. Giroire,
F. Huc,
and S. Pérennes.
Minimal selectors and fault tolerant networks.
Networks,
55(4):326340,
July 2010.
[WWW
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Abstract: 
In this paper we study a combinatorial optimization problem issued from onboard 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 linkdisjoint. 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 $p$ edgedisjoint 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 $N\plk$. 

O. Amini,
F. Havet,
F. Huc,
and S. Thomassé.
WDM and directed star arboricity.
Combinatorics, Probability and Computing,
19:161182,
2010.
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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 $\lambda_n(m,k)$. 

M. Asté,
F. Havet,
and C. Linhares Sales.
Grundy number and products of graphs.
Discrete Mathematics,
310(9):14821490,
2010.
[PDF
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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 CoNPComplete to decide if $\Gamma(G)\leq c\times \chi(G)$ and it is CoNPComplete 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 $\Gamma(G\square H) \leq \Delta(G)\cdot 2^{\Gamma(H)1} + \Gamma(H)$. 

JC. Bermond,
C. J. Colbourn,
L. Gionfriddo,
G. Quattrocchi,
and I. Sau.
Drop Cost and Wavelength Optimal TwoPeriod Grooming with Ratio 4.
SIAM Journal on Discrete Mathematics,
24(2):400419,
2010.
[PDF
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Abstract: 
We study grooming for twoperiod optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the twoperiod grooming problem, during the first period of time there is alltoall uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is alltoall 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 twoperiod 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 twoperiod grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case. 

JC. Bermond,
L. Gargano,
and A. A. Rescigno.
Gathering with minimum completion time in sensor tree networks.
JOIN,
11(12):133,
2010.
Note: A preliminary version has been presented at Sirocco08.
[PDF
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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 halfâduplex 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 multihop wireless network and the time is slotted so that oneâhop 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. 

JC. Bermond,
F. Havet,
F. Huc,
and C. Linhares Sales.
Improper colouring of weighted grid and hexagonal graphs.
Discrete Mathematics, Algorithms and Applications,
2(3):395411,
2010.
[PDF
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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 2dimensional grid and the triangular lattice when the weights are all the same. 

JC. Bermond and ML. Yu.
Optimal gathering algorithms in multihop radio tree networks with interferences.
Ad Hoc and Sensor Wireless Networks,
9(12):109128,
2010.
[PDF
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Abstract: 
We study the problem of gathering information from the nodes of a multihop radio network into a predefined 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 unitlength 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. 

I. Caragiannis,
A. Ferreira,
C. Kaklamanis,
S. Pérennes,
and H. Rivano.
Fractional Path Coloring in Bounded Degree Trees with Applications.
Algorithmica,
58(2):516540,
2010.
[WWW
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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. 

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):683698,
2010.
[PDF
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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 $W(G) â¤ W(L(G))$. We prove that for every nonnegative 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 Melânikov \ [8] and encourages us to conjecture that the answer to a stronger form of their question is affirmative. 

N. Cohen,
F. V. Fomin,
G. Gutin,
E. Jung Kim,
S. Saurabh,
and A. Yeo.
Algorithm for finding kvertex outtrees and its application to kinternal outbranching problem.
Journal of Computer and System Sciences,
76(7):650  662,
2010.
[WWW
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Abstract: 
" An outtree T is an oriented tree with only one vertex of indegree zero. A vertex x of T is internal if its outdegree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given outtree 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 outtree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM'08)." 

N. Cohen and F. Havet.
Planar graphs with maximum degree $\Delta\geq 9$ are ($\Delta+1$)edgechoosable  short proof.
Discrete Mathematics,
310(21):30493051,
2010.
[PDF
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Keywords:
edgecolouring,
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 $(\{D}elta+1)$edgechoosable. 

D. Coudert,
N. Nepomuceno,
and H. Rivano.
PowerEfficient Radio Configuration in Fixed Broadband Wireless Networks.
Computer Communications, Special Section on Hot Topics in Mesh Networking,
33(8):898906,
May 2010.
[WWW
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Abstract: 
In this work, we investigate on determining feasible radio configurations in fixed broadband wireless networks, focusing on power efficiency. Under this scenario, a powerefficient configuration can be characterized by a modulation constellation size and a transmission power level. Every link holds a set of powerefficient 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 powerefficient 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. 

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):796823,
December 2010.
Note: EA DISSIMINET (Associated Team).
[WWW
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Abstract: 
Cellular automata were designed by John von Neumann in the 1940s, as a mathematical abstraction for modeling selfreplicating 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 (discreteevent systems specifications), which paved the way for componentbased modeling and simulation and related methodologies. The purpose of this article is to survey how cellular automata and its variant, called cellDEVS, 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 threedimensional model of a "virtual clay" that changes its shape when it is subject to pressure effects. 

N. Eggemann,
F. Havet,
and S. Noble.
kL(2,1)Labelling for Planar Graphs is NPComplete for $k\geq 4$.
Discrete Applied Mathematics,
158(16):17771788,
2010.
[WWW
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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 NPcomplete problem while it is polynomial for $k\leq 3$. For even $k\geq 8$, it remains NPcomplete when restricted to planar graphs. In this paper, we show that it remains NPcomplete for any $k \ge 4$ by reduction from Planar Cubic TwoColourable Perfect Matching. Schaefer stated without proof that Planar Cubic TwoColourable Perfect Matching is NPcomplete. In this paper we give a proof of this. 

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):267273,
November 2010.
[PDF
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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. 

A. Ferreira.
Uma estratégia face à Revolução Digital.
Teoria e Debate,
87:2023,
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 20072008 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\1074313560o 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}rioGeral 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 â governos, sociedade civil e as empresas do setor privado â 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 proponhome 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. 

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):627640,
2010.
[WWW
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Abstract: 
The assessment of routing protocols for mobile wireless networks is a difficult task, because of the networksÃ¢ÂÂ 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 modelÃ¢ÂÂthe evolving graphsÃ¢ÂÂwas 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. 

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(4042):35533562,
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 NPhard 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. 

F. V. Fomin,
P. A. Golovach,
J. Kratochvil,
N. Nisse,
and K. Suchan.
Pursuing a fast robber on a graph.
Theoretical Computer Science,
411(79):11671181,
2010.
[WWW
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Abstract: 
The Cops and Robbers game as originally defined independently by Quillot and by Nowakowski and Winkler in the 1980Ã¢??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 NPhard 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 NPhard 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. 

F. Havet,
D. Král,
J.S. Sereni,
and R. Skrekovski.
Facial coloring using Hall's theorems.
European Journal of Combinatorics,
31:10011019,
2010.
[WWW
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]
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. 

C. Molle.
Optimization of the Capacity of Wireless Mesh Networks.
4OR: A Quarterly Journal of Operations Research,
8(4):425428,
December 2010.
[WWW
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C. Molle and ME. Voge.
A quantitative analysis of the capacity of wireless mesh networks.
IEEE Communications Letters,
14(5):438440,
May 2010.
[WWW
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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(34):139162,
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 CSMACA 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 wellknown flat routing protocol OLSR against two main selforganized structure approaches, VSR and localized CDS. 

I. Sau and D. M. Thilikos.
Subexponential Parameterized Algorithms for Degreeconstrained Subgraph Problems on Planar Graphs.
Journal of Discrete Algorithms,
8(3):330338,
September 2010.
[WWW
] [PDF
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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. 

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 GameTheoretic Approaches to Optimization Problems in Communication Networks,
pages 241264.
Springer,
A. Koster and X. Muñoz edition,
November 2009.
[WWW
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Abstract: 
In this chapter we consider fundamental communication problems arising in networks with noncooperative users. The uncoordinated usersÃ¢ÂÂ 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. 

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 265279.
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{storeandforward} $\Delta$port model, and we consider both full and halfduplex networks. 

L. AddarioBerry,
N. Broutin,
and B. Reed.
Critical random graphs and the structure of a minimum spanning tree.
Random Structures and Algorithms,
35:323347,
2009.
[WWW
] [PDF
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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 Î(n13). This settles a question of Frieze and McDiarmid (Random Struct Algorithm 10 (1997), 5â42). The proofs are based on a precise analysis of the behavior of random graphs around the critical point. Â© 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009 

L. AddarioBerry and B. Reed.
Minima in branching random walks.
Annals of Probability,
37:10441079,
2009.
[WWW
] [PDF
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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) 89108], our results fully characterize the possible behavior of $\mathbf {E}M_n$ when the branching random walk has bounded branching and step size. 

O. Amini,
F. Huc,
and S. Pérennes.
On the pathwidth of planar graphs.
SIAM Journal of Discrete Mathematics,
23(3):13111316,
August 2009.
[WWW
] [PDF
]
Abstract: 
In this paper, we present a result concerning the relation between the pathwith of a planar graph and the pathwidth of its dual. More precisely, we prove that for a 3connected 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. 

O. Amini,
F. Mazoit,
N. Nisse,
and S. Thomassé.
Submodular partition functions.
Discrete Mathematics,
309(20):60006008,
2009.
[WWW
] [PDF
]
Abstract: 
Adapting the method introduced in Graph Minors X, we propose a new proof of the duality between the bramblenumber of a graph and its treewidth. 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 treewidth. One can also derive all known dual notions of other classical widthparameters from it. 

O. Amini,
S. Pérennes,
and I. Sau.
Hardness and Approximation of Traffic Grooming.
Theoretical Computer Science,
410(3840):37513760,
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 AddDrop 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, 44:194202, 2004 ). More precisely, we prove that Ring Traffic Grooming for fixed $g\leq 1$ and Path Traffic Grooming for fixed $g \leq 2$ are Apxcomplete. That is, they do not accept a PTAS unless P = NP. Both results rely on the fact that finding the maximum number of edgedisjoint triangles in a tripartite graph (and more generally cycles of length $2g + 1$ in a $(2g + 1)$partite graph of girth $2g + 1$) is Apxcomplete. On the other hand, we provide a polynomialtime 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. 

JC. Bermond,
R. Correa,
and M.L. Yu.
Optimal Gathering Protocols on Paths under Interference Constraints.
Discrete Mathematics,
309(18):55745587,
September 2009.
Note: A preliminary version has been presented at CIAC06.
[WWW
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Abstract: 
We study the problem of gathering information from the nodes of a multihop 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 unitlength message to transmit and, furthermore, we suppose that it takes one unit of time (slot) to transmit a unitlength 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. 

E. Birmelé,
J. A. Bondy,
and B. Reed.
Treewidth of graphs without a 3 by 3 grid minor.
Discrete Applied Mathematics,
157:25772598,
2009.
[WWW
] [PDF
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Abstract: 
We show that graphs with no minor isomorphic to the 3x3 grid have treewidth at most 7. 

R. Correa,
F. Havet,
and JS. Sereni.
About a Brookstype theorem for improper colouring.
Australasian Journal of Combinatorics,
43:219230,
2009.
[PDF
]
Abstract: 
A graph is $k$improperly \lcolourable 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 polynomialtime 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):205219, 1997]. 

F. V. Fomin,
P. Fraigniaud,
and N. Nisse.
Nondeterministic Graph Searching: From Pathwidth to Treewidth.
Algorithmica,
53(3):358373,
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 gametheoretic 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 qbranched tree decompositions. The equivalence between nondeterministic graph searching and qbranched tree decomposition enables us to design an exact (exponential time) algorithm computing qbranched 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. 

J. Galtier.
Realtime resource allocation for LEO satellite constellations.
Wireless Networks,
15(6):791803,
August 2009.
[WWW
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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 callaccesscontrol 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 callaccesscontrol and optimization of the use of the spectrum is identified. Some experimental results are presented. 

J. Geelen,
B. Gerards,
B. Reed,
P. Seymour,
and A. Vetta.
On the oddminor variant of Hadwiger's conjecture.
Journal of Combinatorial Theory Ser. B,
99:2029,
2009.
[WWW
] [PDF
]
Abstract: 
A Klexpansion consists of l vertexdisjoint trees, every two of which are joined by an edge. We call such an expansion odd if its vertices can be twocoloured 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 Klexpansion then its chromatic number is View the MathML source. In doing so, we obtain a characterization of graphs which contain no odd Klexpansion which is of independent interest. We also prove that given a graph and a subset S of its vertex set, either there are k vertexdisjoint odd paths with endpoints in S, or there is a set X of at most 2kâ2 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. 

F. Giroire.
Order statistics and estimating cardinalities of massive data sets.
Discrete Applied Mathematics,
157(2):406427,
2009.
[WWW
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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. 

F. Havet.
Choosability of the square of planar subcubic graphs with large girth.
Discrete Mathematics,
309:35533563,
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 $5$. 

F. Havet,
R. Kang,
T. Müller,
and J.S. Sereni.
Circular choosability.
Journal of Graph Theory,
61(4):241334,
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. 

F. Havet,
R. Kang,
and J.S. Sereni.
Improper Colouring of Unit Disk Graphs.
Networks,
54(3):150164,
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 NPcompleteness 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. 

F. Havet and S. Thomassé.
Complexity of $(p,1)$total labelling.
Dicrete Applied Mathematics,
157:28592870,
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 NPhard to compute even for cubic bipartite graphs~\cite{MDSA94}. In this paper we assume $p\geq 2$. It is easy to show that $\lambda_p(G)\geq \Delta +p1$, 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 $\Delta +p1$ or to $\Delta +p$ when $G$ is bipartite. This is trivial when $\Delta \leq p$, polynomial when $\Delta =3$ and $p=2$, and NPcomplete in the remaining cases. 

F. Huc,
I. Sau,
and J. Zerovnik.
$(\ell,k)$Routing on Plane Grids.
Journal of Interconnection Networks,
10(12):2757,
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{storeandforward} $\Delta$port model, and we consider both full and halfduplex networks. The main contributions are the following: \begin{itemize} \item[1.] Tight permutation routing algorithms on fullduplex 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. 

D. Ilcinkas,
N. Nisse,
and D. Soguet.
The Cost of Monotonicity in Distributed Graph Searching.
Distributed Computing,
22(2):117127,
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 nnode 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. 

A. Jarry and S. Pérennes.
Disjoint Path in symmetric Graphs.
Discrete Applied Mathematics,
157(1):9097,
2009.

K. Kawarabayashi,
O. Lee,
and B. Reed.
Removable cycles in nonbipartite graphs.
Journal of Combinatorial Theory Ser. B,
99:3038,
2009.
[WWW
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Abstract: 
In this paper we prove the following result. Suppose that s and t are vertices of a 3connected graph G such that Gst is not bipartite and there is no cutset X of size three in G for which some component U of GX is disjoint from {s,t}. Then either (1) G contains an induced path P from s to t such that GV(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 GV(P) is connected, while if G is 5connected then (1) must hold and P can be chosen so that GV(P) is 2connected. 

K. Kawarabayashi and B. Reed.
Highly parity linked graphs.
Combinatorica,
29:215225,
2009.
[WWW
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Abstract: 
A graph G is klinked if G has at least 2k vertices, and for any 2k vertices x 1,x 2, â¦, x k ,y 1,y 2, â¦, y k , G contains k pairwise disjoint paths P 1, â¦, P k such that P i joins x i and y i for i = 1,2, â¦, k. We say that G is parityklinked if G is klinked and, in addition, the paths P 1, â¦, 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 parityklinked if the deletion of any 4k3 vertices leaves a nonbipartite graph.
In this paper, we will show that the above statement is still valid for 50kconnected graphs. This is the first result that connectivity which is a linear function of k guarantees the ErdÅsPÃ³sa type result for parityklinked graphs. 

R. Klasing,
Z. Lotker,
A. Navarra,
and S. Pérennes.
From Balls and Bins to Points and Vertices.
Algorithmic Operations Research (AlgOR),
4(2):133143,
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 polynomialsize family of witness cuts while for trees we provide a 2approximation algorithm. Many applications concern the variation in which $m = (1 â q)n for some 0 < q < 1$. We provide several bounds for the maximum relocation distance according to different graph topologies. 

B. Lévêque,
F. Maffray,
B. Reed,
and N. Trotignon.
Coloring Artemis graphs.
Theoretical Computer Science,
410:22342240,
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). 

G. B. Mertzios,
I. Sau,
and S. Zaks.
A New Intersection Model and Improved Algorithms for Tolerance Graphs.
SIAM Journal on Discrete Mathematics,
23:18001813,
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 constraintbased temporal reasoning, resource allocation, and scheduling problems, among others. In this article we propose the first nontrivial intersection model for general tolerance graphs, given by threedimensional 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 

N. Nisse.
Connected graph searching in chordal graphs.
Discrete Applied Mathematics,
157(12):26032610,
2009.
[WWW
] [PDF
]
Abstract: 
Graph searching was introduced by Parson [T. Parson, Pursuitevasion in a graph, in: Theory and Applications of Graphs, in: Lecture Notes in Mathematics, SpringerVerlag, 1976, pp. 426441]: 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 polynomialtime 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 treedecomposition. 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 treedecomposition of G. 

N. Nisse and D. Soguet.
Graph Searching with Advice.
Theoretical Computer Science,
410(14):13071318,
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, SpringerVerlag, 2006, pp. 7084] 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. 

L. AddarioBerry and B. Reed.
Horizons of Combinatorics,
volume 17 of Bolyai Society Mathematical Studies,
chapter Ballot Theorems, Old and New,
pages 935.
Springer,
2008.

N. Nepomuceno,
P.R. Pinheiro,
and A.L.V. Coelho.
A Hybrid Optimization Framework for Cutting and Packing Problems: Case Study on Constrained 2D Nonguillotine Cutting.
In Recent Advances in Evolutionary Computation for Combinatorial Optimization,
volume 153 of Studies in Computational Intelligence,
chapter 6,
pages 8799.
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 twodimensional nonguillotine cutting problem. Computational experiments performed over standard benchmark problems are reported and discussed here, evidencing the effectiveness of the novel approach. 

L. AddarioBerry,
M. Chudnovsky,
F. Havet,
B. Reed,
and P. Seymour.
Bisimplicial vertices in evenholefree graphs.
Journal of Combinatorial Theory Ser. B,
98(6):11191164,
2008.
[PDF
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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 evenholefree 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 evenholefree graph has a bisimplicial vertex, which was originally conjectured by Reed. 

L. AddarioBerry,
K. Dalal,
and B. Reed.
DegreeConstrained Subgraphs.
Discrete Applied Mathematics,
156:11681174,
2008.

N. Ben Ali,
B. Belghith,
J. Moulierac,
and M. Molnár.
QoS multicast aggregation under multiple additive constraints.
Computer Communications,
31(15):35643578,
September 2008.
[PDF
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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 multiconstrained 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 multiconstrained multicast routing algorithm. 

JC. Bermond,
D. Coudert,
and B. Lévêque.
Approximations for Alltoall Uniform Traffic Grooming on Unidirectional Ring.
Journal of Interconnection Networks (JOIN),
9(4):471486,
December 2008.
[WWW
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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 adddrop 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 alltoall 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. 

L. Blin,
P. Fraigniaud,
N. Nisse,
and S. Vial.
Distributed chasing of network intruders.
Theoretical Computer Science,
399(12):1237,
2008.
[WWW
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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. 

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,
156:22702278,
2008.

R. Chand,
M. Cosnard,
and L. Liquori.
Powerful resource discovery for Arigatoni overlay network.
Future Generation Computer Systems,
24:3138,
2008.
[WWW
] [PDF
]

S. Fiorini,
N. Hardy,
B. Reed,
and A. Vetta.
Planar graph bipartization in linear time.
Discrete Applied Mathematics,
156:11751180,
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. 

M. Flammini,
R. Klasing,
A. Navarra,
and S. Pérennes.
Tightening the Upper Bound for the Minimum Energy Broadcasting problem.
Wireless Networks,
14(5):659669,
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
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M. Flammini,
L. Moscardelli,
A. Navarra,
and S. Pérennes.
Asymptotically Optimal Solutions for Small World Graphs.
Theory of Computing Systems,
42(4):632650,
May 2008.
[WWW
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Abstract: 
We consider the problem of determining constructions with an asymptotically optimal oblivious diameter in small world graphs under the Kleinbergâs 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 Î©(logâ2 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 ddimensional grids for any fixed value of d. 

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,
33:6886,
2008.

P. Fraigniaud and N. Nisse.
Monotony Properties of Connected Visible Graph Searching.
Information and Computation,
206(12):13831393,
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 nonconnected 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.unitrier.de/~ley/db/conf/wg/wg2006.php}, pdf = {http://wwwsop.inria.fr/members/Nicolas.Nisse/publications/WG06_nisse.ps}, OPTxeditorialboard={yes}, OPTxproceedings={yes}, OPTxinternationalaudience={yes}, sorte = "revint", 

F. Havet,
J.S. Sereni,
and R. Skrekovski.
3facial colouring of plane graphs.
SIAM Journal on Discrete Mathematics,
22(1):231247,
2008.
[WWW
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Abstract: 
A plane graph is \lfacially $k$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 facesize 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. 

F. Havet,
S. Thomassé,
and A. Yeo.
HoangReed conjecture for tournaments.
Discrete Mathematics,
308(15):34123415,
August 2008.
[PDF
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Abstract: 
Ho\`angReed 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 forestlike structure. Formally, $V(C_i)\cap (V(C_1)\cup \dots \cup V(C_{i1}))\leq 1$, for all $i=2,\dots ,\delta^+$. We verify this conjecture for the class of tournaments. 

F. Havet and M.L. Yu.
$(p,1)$total labelling of graphs.
Discrete Mathematics,
308(4):496513,
February 2008.
[PDF
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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 $[p+5, 6p210p+4]$ for which we show that $\lambda_p^T(K_n) \in n+2p3, n+2p2$. 

R. J. Kang,
T. Müller,
and J.S. Sereni.
Improper colouring of (random) unit disk graphs.
Discrete Mathematics,
308:14381454,
April 2008.
Note: The Special Issue devoted to EuroComb 2005.
[PDF
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K. Kawarabayashi,
O. Lee,
B. Reed,
and P. Wollan.
A weaker version of Lovasz' path removable conjecture.
Journal of Combinatorial Theory (Series B),
98:972979,
2008.

K. Kawarabayashi and B. Reed.
Fractional coloring and the odd Hadwiger's conjecture.
European Journal of Combinatorics,
29(2):411417,
2008.
Abstract: 
Gerards and Seymour (see [T.R. Jensen, B. Toft, Graph Coloring Problems, WileyInterscience, 1995], page 115) conjectured that if a graph has no odd complete minor of order p, then it is (p1)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"kminors (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"pminor 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) 147152] who proved that the fractional chromatic number of a graph with no K"p"+"1minor is at most 2p. 

R. Klasing,
N. Morales,
and S. Pérennes.
On the Complexity of Bandwidth Allocation in Radio Networks.
Theoretical Computer Science,
406(3):225239,
October 2008.
[WWW
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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 noninterfering transmissions. We provide a formal specification of the problem that we call round weighting. By modeling noninterfering 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 n1âÎµ (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)." 

C. LinharesSales,
F. Maffray,
and B. Reed.
On Planar QuasiParity Graphs.
SIAM Journal of Discrete Mathematics,
22:329347,
2008.

F. Mazoit and N. Nisse.
Monotonicity of nondeterministic graph searching.
Theoretical Computer Science,
399(3):169178,
2008.
[WWW
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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. 364375] introduced an important graph searching variant, called nondeterministic 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 nondeterministic graph searching was however left open.
In this paper, we prove that nondeterministic 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 nondeterministic graph searching belongs to NP. Moreover, the exact algorithms designed by Fomin et al. do compute optimal nondeterministic search strategies. 

C. McDiarmid and B. Reed.
On the maximum degree of a random planar graph.
Combinatorics, Probability and Computing,
17:591601,
2008.

C. Meagher and B. Reed.
Fractionally total colouring ${G}_{n,p}$.
Discrete Applied Mathematics,
156:11121124,
2008.

B. Reed.
Skew Partitions in Perfect Graphs.
Discrete Applied Mathematics,
156:11501156,
2008.

I. Sau and J. Zerovnik.
An Optimal Permutation Routing Algorithm on FullDuplex Hexagonal Networks.
Discrete Mathematics and Theoretical Computer Science,
10(3):4962,
2008.
[PDF
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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 fullduplex hexagonal networks, using the addressing scheme described by F.G. Nocetti, I. Stojmenovi\'{c} and J. Zhang (IEEE TPDS 13(9): 962971, 2002). Furthermore, we prove that this algorithm is oblivious and translation invariant. 

L. AddarioBerry,
K. Dalal,
C. McDiarmid,
B. Reed,
and A. Thomason.
Vertex Colouring Edge Weightings.
Combinatorica,
27:112,
2007.

L. AddarioBerry,
F. Havet,
and S. Thomassé.
Paths with two blocks in $n$chromatic digraphs.
Journal of Combinatorial Theory Ser. B,
97:620626,
2007.
[PDF
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E. Alba,
B. Dorronsoro,
F. Luna,
A.J. Nebro,
P. Bouvry,
and L. Hogie.
A cellular multiobjective genetic algorithm for optimal broadcasting strategy in metropolitan MANETs.
Computer Communications,
30(4):685697,
August 2007.
[WWW
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Abstract: 
Mobile Adhoc Networks (MANETs) are composed of a set of communicating devices which are able to spontaneously interconnect without any preexisting 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 multiobjective 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 finetuning of broadcast strategies by using a cellular multiobjective 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. 

R. Bayon,
N. Lygeros,
and J.S. Sereni.
Orders with ten elements are circle orders.
Applied Mathematics ENotes,
7:1622,
2007.
[WWW
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]

JC. Bermond,
L. Braud,
and D. Coudert.
Traffic Grooming on the Path.
Theoretical Computer Science,
384(23):139151,
October 2007.
[WWW
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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 NPcomplete 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 alltoall traffic (one request for each pair of vertices). 

JC. Bermond,
A. Ferreira,
S. Pérennes,
and J. Peters.
Neighbourhood Broadcasting in Hypercubes.
SIAM Journal on Discrete Mathematics,
21(4):823843,
2007.
[PDF
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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. 

JC. Bermond and M.L. Yu.
Vertex disjoint routings of cycles over tori.
Networks,
49(3):217225,
2007.
[PDF
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E. Birmelé,
J. A. Bondy,
and B. Reed.
The ErdosPosa property for long circuits.
Combinatorica,
27:135145,
2007.

P. Charbit,
S. Thomassé,
and A. Yeo.
The minimum feedback arc set problem is NPhard for tournament.
Combinatorics, Probability and Computing,
16:14,
2007.

A. Ciaffaglione,
L. Liquori,
and M. Miculan.
Reasoning about Objectbased Calculi in (Co)Inductive Type Theory and the Theory of Contexts.
JAR, Journal of Automated Reasoning,
39:147,
2007.
[PDF
]

D. Coudert,
P. Datta,
S. Perennes,
H. Rivano,
and ME. Voge.
Shared Risk Resource Group: Complexity and Approximability issues.
Parallel Processing Letters,
17(2):169184,
June 2007.
[PDF
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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. 

D. Coudert,
F. Huc,
and J.S. Sereni.
Pathwidth of outerplanar graphs.
Journal of Graph Theory,
55(1):2741,
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. 

S. Fiorini,
N. Hardy,
B. Reed,
and A. Vetta.
Approximate minmax relations for odd cycles in planar graphs.
Mathematical Programming Ser. B,
110(1):7191,
2007.

M. Flammini,
R. Klasing,
A. Navarra,
and S. Pérennes.
Improved approximation results for the Minimum Energy Broadcasting problem.
Algorithmica,
49(4):318336,
2007.
[WWW
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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 dâ¥2, the approximation ratio of the heuristic does not increase when the power attenuation coefficient Î±, 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 Î± going to infinity, the ratio tends to the lower bound of Clementi et al., Wan et al. given by the ddimensional kissing number, thus closing the existing gap between the upper and the lower bound. We then introduce a new analysis allowing to establish a 7.45approximation ratio for the 2dimensional 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 dâ¥2 and any Î±â¥d, obtaining a general approximation ratio of 3 d â1, again independent of Î±. 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. 

N. Fountoulakis and B. Reed.
Faster Mixing and Small Bottlenecks.
Probability Theory and Related Fields,
137:475486,
2007.

J. Galtier and A. Laugier.
Flow on data network and a positive semidefinite representable delay function.
Journal of Interconnection Networks,
8(1):2943,
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. 

L. Grigori,
M. Cosnard,
and E. G. Ng.
On the row merge for sparse LU factorization with partial pivoting.
BIT Numerical Mathematics,
47(1):4576,
March 2007.
[PDF
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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. 

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
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]
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 nary 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 constrainedbased lambda calculi, ranging from well known restricted lambda calculi, such as Plotkin's callbyvalue 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 patternmatching 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 callbyvalue lambda calculus." 

L. Liquori and S. Ronchi Della Rocca.
Intersection Typed System à la Church.
IC, Journal of Information and Computation,
205(9):13711386,
September 2007.
[WWW
] [PDF
]

J. BangJensen,
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 613627.
Springer,
Berlin,
M. Klazar, J. Kratochvil, M. Loebl, J. Matousek, R. Thomas and P. Valtr edition,
2006.

JC. Bermond and D. Coudert.
Handbook of Combinatorial Designs (2nd edition),
volume 42 of Discrete mathematics and Applications,
chapter VI.27, Grooming,
pages 494496.
Chapman & Hall CRC Press, editors C.J. Colbourn and J.H. Dinitz,
November 2006.
[WWW
] [PDF
]
Abstract: 
Stateoftheart on traffic grooming with a design theory approach 

S. Alouf,
E. Altman,
J. Galtier,
J.F. Lalande,
and C. Touati.
QuasiOptimal Resource Allocation in MultiSpot MFTDMA Satellite Networks.
In M. Cheng,
Y. Li,
and D.Z. Du, editors,Combinatorial Optimization in Communication Networks,
chapter 12,
pages 325366.
Kluwer Academic Publishers,
2006.
[PDF
]

D. Bartha,
P. Berthomé,
M. Diallo,
and A. Ferreira.
Revisiting parametric multiterminal problems: Maximum flows, minimum cuts and cuttree computations.
Discrete Optimization,
3(3):195205,
September 2006.

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):116121,
2006.
[PDF
]

JC. Bermond,
J. Galtier,
R. Klasing,
N. Morales,
and S. Pérennes.
Hardness and approximation of Gathering in static radio networks.
Parallel Processing Letters,
16(2):165183,
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 timesteps in each of which a round (set of noninterfering 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{NPhard}, 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. 

JC. Bermond,
F. Havet,
and D. Tóth.
Fault tolerant on board networks with priorities.
Networks,
47(1):925,
2006.
[PDF
]
Abstract: 
We consider onboard 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 linkdisjoint. 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 $p$ bestquality amplifiers. Let $R(n,p,f)$ be the minimum number of switches of such a network. We prove here that $R(n,p,f)\leq \frac{n+f}{2} \lceil \log_2 p \rceil +\frac{5}{2}(np) +g(f)$ with $g$ a function depending only on $f$. We then compute $R(n,p,f)$ exactly for a few small values of $p$ and $f$. 

S. Bessy,
E. Birmelé,
and F. Havet.
Arcchromatic number of digraphs in which each vertex has bounded outdegree or bounded indegree.
Journal of Graph Theory,
53(4):315332,
2006.
[WWW
] [PDF
]

A. Bondy,
J. Shen,
S. Thomassé,
and C. Thomassen.
Density conditions for triangles in multipartite graphs.
Combinatorica,
26(2):121131,
2006.

D. J. Dougherty,
P. Lescanne,
and L. Liquori.
Addressed Term Rewriting Systems: Application to a Typed Object Calculus.
Journal of Mathematical Structures in Computer Science,
16(4):667709,
2006.
[PDF
]

M. Flammini,
A. Navarra,
and S. Pérennes.
The Real Approximation Factor of the MST heuristic for the Minimum Energy Broadcasting.
ACM Journal of Experimental Algorithmics,
11:113,
2006.
Note: (Special Issue associated to the 4th International Workshop on Efficient and Experimental Algorithms (WEA 2005)).

F. Havet.
Repartitors, selectors and superselectors.
Journal of Interconnection Networks,
7(3):391415,
2006.
[PDF
]

F. Havet and J.S. Sereni.
Improper choosability of graphs and maximum average degree.
Journal of Graph Theory,
52(3):181199,
2006.
[PDF
]

C. McDiarmid and B. Reed.
Concentration for selfbounding functions and an inequality of talagrand.
Random Structures and Algorithms,
29:549557,
2006.

J. Moulierac,
A. Guitton,
and M. Molnár.
Hierarchical Aggregation of Multicast Trees in Large Domains.
Journal of Communications (JCM),
6(1):3344,
September 2006.
[PDF
]
Abstract: 
Multicast tree aggregation is a technique that reduces the control overhead and the number of states induced by multicast. The main idea of this protocol is to route several groups to the same distribution tree in order to reduce the total number of multicast forwarding states. In this article, we show that this technique cannot be applied to large domains. Indeed, when the number of border routers is large, actual tree aggregation protocols are unable to find similar groups to aggregate to the same tree. However, by dividing the domain into several smaller subdomains, we prove that it is possible to achieve important savings. A hierarchical protocol is designed to interconnect the trees of the subdomains together. While previous protocols cannot cope with more than 25 border routers, our protocol still shows significant benefits for domains with 200 border routers. 

C. Touati,
E. Altman,
and J. Galtier.
Generalized Nash Bargaining Solution for bandwidth allocation.
Computer Networks,
50:32423263,
2006.
[PDF
]

L. AddarioBerry,
R. E. L. Aldred,
K. Dalal,
and B. Reed.
Vertex colouring edge partitions.
J. Combin. Theory Ser. B,
94(2):237244,
2005.

D. Avis,
C. De Simone,
and B. Reed.
On the fractional chromatic index of a graph and its complement.
Oper. Res. Lett.,
33(4):385388,
2005.

R. Bayon,
N. Lygeros,
and J.S. Sereni.
New progress in enumeration of mixed models.
Applied Mathematics ENotes,
5:6065,
2005.
[WWW
] [PDF
]

JC. Bermond,
C. Colbourn,
D. Coudert,
G. Ge,
A. Ling,
and X. Muñoz.
Traffic Grooming in Unidirectional WDM Rings With Grooming Ratio C=6.
SIAM Journal on Discrete Mathematics,
19(2):523542,
2005.
[PDF
]
Abstract: 
SONET/WDM networks using wavelength adddrop multiplexing can be constructed using certain graph decompositions used to form a grooming, consisting of unions of primitive rings. The cost of such a decomposition is the sum, over all graphs in the decompositio n, of the number of vertices of nonzero degree in the graph. The existence of such decompositions with minimum cost, when every pair of sites employs no mo re than $\frac{1}{6}$~of the wavelength capacity, is determined with a finite number of possible exceptions. Indeed, when the number $N$ of sites satisfies $N \equiv 1 \pmod{3}$, the determination is complete, and when $N \equiv 2 \pmod{3}$, the only value le ft undetermined is $N = 17$. When $N \equiv 0 \pmod{3}$, a finite number of values of $N$ remain, the largest being $N = 2580$. The techniques developed rely heavily on tools from combinatorial design theory. 

S. Choplin,
A. Jarry,
and S. Pérennes.
Virtual network embedding in the cycle.
Discrete Applied Mathematics,
145(3):368375,
2005.

C. Cooper,
R. Klasing,
and M. Zito.
Lower Bounds and Algorithms for Dominating Sets in Web Graphs.
Internet Mathematics,
2(3):275300,
2005.

D. J. Dougherty,
P. Lescanne,
L. Liquori,
and F. Lang.
Addressed Term Rewriting Systems: Syntax, Semantics, and Pragmatics: Extended Abstract.
TERMGRAPH: International Workshop on Computing with Terms and Graphs. Electr. Notes Theor. Comput. Sci.,
127(5):5782,
2005.
[POSTSCRIPT
]

H. Everett,
C. M. H. de Figueiredo,
S. Klein,
and B. Reed.
The perfection and recognition of bullreducible Berge graphs.
Theor. Inform. Appl.,
39(1):145160,
2005.

B. Farzad,
M. Molloy,
and B. Reed.
$(\Deltak)$critical graphs.
J. Combin. Theory Ser. B,
93(2):173185,
2005.

M. Flammini and S. Pérennes.
Lower bounds on systolic gossip.
Information and Computation,
196(2):7194,
2005.

L. Liquori and S. Ronchi Della Rocca.
Towards an Intersection Typed System à la Church.
ITRS: Workshop on Intersection Types and Related Systems. Electr. Notes Theor. Comput. Sci.,
136:4356,
2005.
[POSTSCRIPT
]

L. Liquori and B. Wack.
The Polymorphic Rewritingcalculus: [Type Checking vs. Type Inference].
WRLA: International Workshop on Rewriting Logic and its Applications. Electr. Notes Theor. Comput. Sci.,
117:89111,
2005.
[POSTSCRIPT
]

B. Reed and B. Sudakov.
List colouring when the chromatic number is close to the order of the graph.
Combinatorica,
25(1):117123,
2005.

J.C. Bermond,
C.J. Colbourn,
A. Ling,
and M.L. Yu.
Grooming in unidirectional rings : $K_4 e$ designs.
Discrete Mathematics, Lindner's Volume,
284(13):5762,
2004.
[PDF
]

H.J. Böckenhauer,
D. Bongartz,
J. Hromkovic,
R. Klasing,
G. Proietti,
S. Seibert,
and W. Unger.
On the hardness of constructing minimal 2connected spanning subgraphs in complete graphs with sharpened triangle inequality.
Theoretical Computer Science,
326(13):137153,
2004.

I. Caragiannis,
A. Ferreira,
C. Kaklamanis,
S. Pérennes,
P. Persiano,
and H. Rivano.
Approximate Constrained Bipartite Edge Coloring.
Discrete Applied Mathematics,
143(13):5461,
September 2004.
[PDF
] [POSTSCRIPT
]
Abstract: 
We study the following Constrained Bipartite Edge Coloring (CBEC) problem: We are given a bipartite graph G(U,V,E) of maximum degree l with n vertices, in which some of the edges have been legally colored with c colors. We wish to complete the coloring of the edges of G minimizing the total number of colors used. The problem has been proved to be NPhard event for bipartite graphs of maximum degree three. 

M. Cosnard,
E. Jeannot,
and T. Yang.
Compact Dag Representation and its Symbolic Scheduling.
Journal of Parallel and Distributed Computing,
64(8):921935,
August 2004.

S. Céroi and F. Havet.
Trees with three leaves are $(n+1)$unavoidable.
Discrete Applied Mathematics,
141:1939,
2004.
[PDF
]

S. Dantas,
C. M. H. de Figueiredo,
S. Klein,
S. Gravier,
and B. Reed.
Stable skew partition problem.
Discrete Appl. Math.,
143(13):1722,
2004.

M. DeVos,
G. Ding,
B. Oporowski,
D. P. Sanders,
B. Reed,
P. Seymour,
and D. Vertigan.
Excluding any graph as a minor allows a low treewidth 2coloring.
J. Combin. Theory Ser. B,
91(1):2541,
2004.

A. Ferreira.
Building a reference combinatorial model for MANETs.
IEEE Network,
18(5):2429,
2004.

G. Fertin,
A. Raspaud,
and B. Reed.
Star coloring of graphs.
J. Graph Theory,
47(3):163182,
2004.

M. Flammini and S. Pérennes.
Lower Bounds on the Broadcasting and Gossiping Time of Restricted Protocols.
SIAM Journal on Discrete Mathematics,
17(4):521540,
2004.
[PDF
]

C. Gavoille,
D. Peleg,
S. Pérennes,
and R. Raz.
Distance labeling in Graphs.
Journal of Algorithms,
53(1):85112,
2004.
[PDF
]

F. Havet.
Pancyclic arcs and connectivity in tournaments.
Journal of Graph Theory,
47(2):87110,
2004.
[PDF
]

F. Havet.
Stable set meeting every longest path.
Discrete Mathematics,
289(13):169173,
2004.
[PDF
]

F. Havet and M. Wennink.
The Push Tree Problem.
Networks,
44(4):281291,
2004.
[PDF
]

C. T. Hoàng and B. Reed.
On the co$P\sb 3$structure of perfect graphs.
SIAM J. Discrete Math.,
18(3):571576 (electronic),
2004/05.

R. Klasing and C. Laforest.
Hardness results and approximation algorithms of $k$tuple domination in graphs.
Information Processing Letters,
89(2):7583,
2004.
[WWW
]

B. Reed and P. Seymour.
Hadwiger's conjecture for line graphs.
European J. Combin.,
25(6):873876,
2004.

B. Reed,
K. Smith,
and A. Vetta.
Finding odd cycle transversals.
Oper. Res. Lett.,
32(4):299301,
2004.

B. Reed,
S. W. Song,
and J. L. Szwarcfiter.
Preface [Brazilian Symposium on Graphs, Algorithms and Combinatorics].
Discrete Appl. Math.,
141(13):1,
2004.
Note: Held in Fortaleza, 2001.

D. Coudert and X. Muñoz.
Recent Research Developments in Optics, 3,
chapter 37, Graph Theory and Traffic Grooming in WDM Rings,
pages 759778.
Research Signpost. Kerala, India,
2003.
Note: ISBN: 8127100285.
[PDF
] [POSTSCRIPT
]
Abstract: 
This paper has a double purpose. In the first part of the paper we give an overview of different aspects of graph theory which can be applied in communication engineering, not trying to present immediate results to be applied neither a complete survey of results, but to give a flavor of how graph theory can help research in optical networks. The second part of this paper is a detailed example of the usage of graph theory, but it is also a complete survey of recent results in minimization of the number of adddrop multiplexers (ADMs) required in a WDM ring with traffic grooming. 

B. Reed.
Algorithmic aspects of tree width.
In Recent advances in algorithms and combinatorics,
volume 11 of CMS Books Math./Ouvrages Math. SMC,
pages 85107.
Springer,
New York,
2003.

R. Balakhrishnan,
J.C. Bermond,
P. Paulraja,
and M.L. Yu.
On Hamilton cycle decompositions of the tensor product of complete graphs.
Discrete Mathematics,
268:4958,
2003.
[PDF
]

O. Barrientos,
R. Correa,
P. Reyes,
and A. Valdebenito.
A Branch and Bound Method for Solving Integer Separable Concave Problems.
Comput. Optim. Appl.,
26(2):155171,
2003.
[WWW
] [PDF
]
Abstract: 
A branch and bound algorithm is proposed for solving integer separable concave problems. The method uses Lagrangian duality to obtain lower and upper bounds. We show that the dual program of a separable concave problem is a linear program. Moreover, we identify an excellent candidate to test on each region of the branch and we show an optimality sufficient condition for this candidate. Preliminary computational results are reported. 

J.C. Bermond,
J. Bond,
D. Peleg,
and S. Pérennes.
The power of small coalitions in graphs.
Discrete Applied Mathematics, Editor's Choice,
127(3):399414,
2003.
[PDF
]

J.C. Bermond and S. Ceroi.
Minimizing SONET ADMs in unidirectional WDM rings with grooming ratio 3.
Networks,
41(2):8386,
2003.
[PDF
]

J.C. Bermond,
S. Choplin,
and S. Pérennes.
Hierarchical ring networks design.
Theory of Computing Systems,
36(6):663682,
2003.
[PDF
]

JC. Bermond,
D. Coudert,
and ML. Yu.
On DRCCovering of $K_n$ by cycles.
Journal of Combinatorial Designs,
11(2):100112,
2003.
[WWW
] [PDF
] [POSTSCRIPT
]
Abstract: 
This paper considers the cycle covering of complete graphs motivated by the design of survivable WDM networks, where the requests are routed on subnetworks which are protected independently from each other. The problem can be stated as follows~: for a given graph $G$, find a cycle covering of the edge set of $K_n$, where $V(K_n) = V(G)$, such that each cycle in the covering satisfies the disjoint routing constraint (DRC), relatively to $G$, which can be stated as follows~: to each edge of $K_n$ we associate in G a path and all the paths associated to the edges of a cycle of the covering must be vertex disjoint. Here we consider the case where $G = C_n$, a ring of size $n$ and we want to minimize the number of cycles in the covering. We give optimal solutions for the problem as well as for variations of the problem, namely, its directed version and the case when the cycle length is fixed to 4. 

J.C. Bermond,
M. Di Ianni,
M. Flammini,
and S. Pérennes.
Acyclic orientations for deadlock prevention in usual networks.
Discrete Applied Mathematics,
129(1):3147,
2003.
[PDF
]

J.C. Bermond,
N. Marlin,
D. Peleg,
and S. Pérennes.
Directed Virtual Path Layout in ATM networks.
Theoretical Computer Science,
291(1):328,
2003.
[PDF
]

B. BuiXuan,
A. Ferreira,
and A. Jarry.
Computing shortest, fastest, and foremost journeys in dynamic networks.
International Journal of Foundations of Computer Science,
14(2):267285,
April 2003.

G. Calinescu,
C. G. Fernandes,
and B. Reed.
Multicuts in unweighted graphs and digraphs with bounded degree and bounded treewidth.
J. Algorithms,
48(2):333359,
2003.

H. Cirstea,
C. Kirchner,
L. Liquori,
and B. Wack.
Rewrite strategies in the Rewriting Calculus.
WRS, International Workshop on Reduction Strategies in Rewriting and Programming. Electr. Notes Theor. Comput. Sci.,
86(4),
2003.
[POSTSCRIPT
]

A. Clementi,
A. Ferreira,
P. Penna,
S. Pérennes,
and R. Silvestri.
The Minimum Range Assignment Problem on Linear Radio Networks.
Algorithmica,
35(2):95110,
2003.

A. Ferreira,
S. Pérennes,
A. W. Richa,
H. Rivano,
and N. Stier.
Models, Complexity and Algorithms for the Design of Multifiber WDM Networks.
Telecommunication Systems,
24(2):123138,
October 2003.
[WWW
] [PDF
]
Abstract: 
In this paper, we study multifiber optical networks with wavelength division multiplexing (WDM). We extend the definition of the wellknown Wavelength Assignment Problem (WAP) to the case of k fibers per link and w wavelengths per fiber, generalization that we will call (k,w)WAP. We develop a new model for the (k,w)WAP based on conflict hypergraphs. Furthermore, we consider two natural optimization problems that arise from the (k,w)WAP: minimizing the number of fibers k given a number of wavelengths w, on one hand, and minimizing w given k, on the other. We develop and analyze the practical performance of two methodologies based on hypergraph coloring. 

J. Galtier,
F. Hurtado,
M. Noy,
S. Pérennes,
and J. Hurrutia.
Simultaneous edge flipping in triangulations.
International Journal of Computational Geometry and Applications,
13(2):113133,
2003.

O. Goldschmidt,
A. Laugier,
and E. Olinick.
SONET/SDH ring assignment with capacity constraints.
Discrete Applied Math.,
129:99128,
June 2003.
[PDF
]

F. Havet.
On unavoidability of trees with $k$ leaves.
Graphs and Combinatorics,
19:101110,
2003.
[PDF
]

M. Loebl,
J. Nesetril,
and B. Reed.
A note on random homomorphism from arbitrary graphs to $\mathbb Z$.
Discrete Math.,
273(13):173181,
2003.
Note: EuroComb'01 (Barcelona).

C. McDiarmid and B. Reed.
Channel assignment on graphs of bounded treewidth.
Discrete Math.,
273(13):183192,
2003.
Note: EuroComb'01 (Barcelona).

B. Reed.
The height of a random binary search tree.
J. ACM,
50(3):306332 (electronic),
2003.

C. Touati,
E. Altman,
and J. Galtier.
Semidefinite programming approach for bandwidth allocation and routing in networks.
Game Theory and Applications,
9:169179,
2003.

M. Cosnard.
Introduction to the Complexity of Parallel Algorithms.
In R. Corrêa,
I. Dutra,
M. Fiallos,
and F. Gomes, editors,Parallel and Distributed Algorithms: Theory, Algorithmic Techniques and Applications,
Applied Optimization,
chapter 1, part I,
pages 325.
Kluwer Academic Publishers,
Boston (USA),
2002.

L. Devroye,
C. McDiarmid,
and B. Reed.
Giant components for two expanding graph processes.
In Mathematics and computer science, II (Versailles, 2002),
Trends Math.,
pages 161173.
Birkhäuser,
Basel,
2002.

A. Ferreira.
Parallel Computing: Models.
In C. Floudas and P. Pardalos, editors,Encyclopedia of Optimization.
Kluwer Academic Publisher, Boston (USA),
2002.

A. Ferreira,
J. Galtier,
and P. Penna.
Topological design, routing and handover in satellite networks.
In I. Stojmenovic, editor,Handbook of Wireless Networks and Mobile Computing,
pages 473507.
John Wiley and Sons,
2002.
[PDF
]

A. Ferreira and I. GuérinLassous.
Discrete Computing with Coarse Grained Systems.
In R. Corrêa,
I. Dutra,
M. Fiallos,
and F. Gomes, editors,Parallel and Distributed Algorithms: Theory, Algorithmic Techniques and Applications,
Applied Optimization,
chapter 5, part I,
pages 117143.
Kluwer Academic Publishers,
Boston (USA),
2002.

B. Beauquier and E. Darrot.
On Arbitrary Size Waksman Networks and their Vulnerability.
Parallel Processing Letters,
12(3),
2002.

J.C. Bermond,
E. Darrot,
and O. Delmas.
Design of fault tolerant onboard networks in satellites.
Networks,
40:202207,
2002.
[PDF
]

H.J. Böckenhauer,
J. Hromkovic,
R. Klasing,
S. Seibert,
and W. Unger.
Towards the Notion of Stability of Approximation for Hard Optimization Tasks and the Traveling Salesman Problem.
Theoretical Computer Science,
285(1):324,
2002.

E. Caceres,
F. Dehne,
A. Ferreira,
P. Flocchini,
I. Rieping,
A. Roncato,
N. Santoro,
and S. Song.
Efficient Parallel Graph Algorithms For Coarse Grained Multicomputers and BSP.
Algorithmica,
33:183200,
2002.

H. Cirstea,
C. Kirchner,
and L. Liquori.
Rewriting Calculus with(out) Types.
WRLA, International Workshop on Rewriting Logic and its Applications. Electr. Notes Theor. Comput. Sci.,
71,
2002.
[POSTSCRIPT
]

C. Cooper,
A. Frieze,
and B. Reed.
Random regular graphs of nonconstant degree: connectivity and Hamiltonicity.
Combin. Probab. Comput.,
11(3):249261,
2002.

C. Cooper,
A. Frieze,
B. Reed,
and O. Riordan.
Random regular graphs of nonconstant degree: independence and chromatic number.
Combin. Probab. Comput.,
11(4):323341,
2002.

D. Coudert,
A. Ferreira,
and S. Pérennes.
Isomorphisms of the De Bruijn Digraph and FreeSpace Optical Networks.
Networks (WileyInterscience),
40(3):155164,
October 2002.
[PDF
] [POSTSCRIPT
]
Abstract: 
The de Bruijn digraph $B(d,D)$ has degree $d$, diameter $D$, $d^D$ vertices and $d^{D+1}$ arcs. It is usually defined by words of size $D$ on an alphabet of cardinality $d$, through a cyclic left shift permutation on the words, after which the rightmost symbol is changed. In this paper, we show that any digraph defined on words of a given size, through an {\em arbitrary} permutation on the alphabet {\bf and} an {\em arbitrary} permutation on the word indices, is isomorphic to the de Bruijn digraph, provided that this latter permutation is {\em cyclic}. We use this result to improve from $O\left(d^{D+1}\right)$ to $\Theta\left(\sqrt{d^{D+1}}\right)$ the number of lenses required for the implementation of $B(d,D)$ by the Optical Transpose Interconnection System proposed by Marsden {\em et al.} (Optics Letters 18(13):10831085, July 1993). 

A. Ferreira,
I. GuérinLassous,
K. Marcus,
and A. RauChaplin.
Parallel Computation on Interval Graphs: Algorithms and Experiments.
Concurrency and Computation  Practice and Experience,
56(1):4770,
january 2002.

F. Havet.
Trees in Tournament.
Discrete Mathematics,
243(13):121134,
2002.
[PDF
]

F. Havet and J. Zerovnik.
Finding a Five Bicolouring of a TriangleFree Subgraph of the Triangular Lattice.
Discrete Mathematics,
244:103108,
2002.

B. Reed and B. Sudakov.
Asymptotically the list colouring constants are 1.
J. Combin. Theory Ser. B,
86(1):2737,
2002.

H. Everett,
C. M. H. de Figueiredo,
C. LinharesSales,
F. Maffray,
O. Porto,
and B. Reed.
Even pairs.
In Perfect graphs,
WileyIntersci. Ser. Discrete Math. Optim.,
pages 6792.
Wiley,
Chichester,
2001.

A. Ferreira.
Parallel Computing: Models.
In C. A. Floudas and P. Pardalos, editors,Encyclopedia of Optimization  Vol. IV,
pages 264269.
Kluwer Academic Publisher, Boston (USA),
2001.

R. Hayward and B. Reed.
Forbidding holes and antiholes.
In Perfect graphs,
WileyIntersci. Ser. Discrete Math. Optim.,
pages 113137.
Wiley,
Chichester,
2001.

B. Reed.
A gentle introduction to semidefinite programming.
In Perfect graphs,
WileyIntersci. Ser. Discrete Math. Optim.,
pages 233259.
Wiley,
Chichester,
2001.

B. Reed.
From conjecture to theorem.
In Perfect graphs,
WileyIntersci. Ser. Discrete Math. Optim.,
pages 1324.
Wiley,
Chichester,
2001.

J.P. Allouche and M. Cosnard.
Noninteger bases, iteration of continuous real maps, and an arithmetic selfsimilar set.
Acta Mathematica Hungarica,
91:325332,
2001.

E. Altman,
E. Baçsar,
T. Jiménez,
and N. Shimkin.
Competitive Routing in Networks with Polynomial Cost.
IEEE Trans. on Automatic Control,
2001.

E. Altman,
T. Jiménez,
and G. Koole.
Comparing tandem queueing systems and their fluid limits.
PEIS,
(2),
2001.

B. Beauquier,
O. Delmas,
and S. Pérennes.
Tight Bounds for Broadcasting in the Linear Cost Model.
Journal of Interconnection Network,
2(2):175188,
2001.

P. Bergé,
A. Ferreira,
J. Galtier,
and J.N. Petit.
A Probabilistic Study of InterSatellite Links Load in Polar Orbit Satellite Constellations.
International Journal on Telecommunication Systems,
18(13):123135,
2001.
[PDF
]

J.C. Bermond,
X. Muñoz,
and A. MarchettiSpaccamela.
A Broadcasting Protocol in Line Digraphs.
Journal of Parallel and Distributed Computing,
61(8):10131032,
August 2001.
[PDF
]

M. Cosnard and E. Jeannot.
Automatic Parallelization Techniques Based on Compact DAG Extraction and Symbolic Scheduling.
Parallel Processing Letters,
11(1):151168,
2001.

M. Diallo,
A. Ferreira,
and A. RauChaplin.
A note on communicationefficient deterministic p aralle algorithms for planar point location and 2D Voronoi diagram.
Parallel Processing Letters,
11(2/3):327340,
2001.

A. Ferreira,
J. Galtier,
J.N. Petit,
and H. Rivano.
Rerouting algorithms in a meshed satellite constellation.
Annals of Telecommunications,
56(3/4):169174,
march/april 2001.
[PDF
]
Abstract: 
In this paper we present a simple model for satellite constellations with polar orbits and intersatellite links. This model is used to propose and study two algorithms for routing and rerouting communications, which aim at improving the quality of service for long communications. In order to study these algorithms, we have developed a satellite constellation simulator. Some of its results are presented. 

M. Flammini and S. Pérennes.
On the optimality of general lower bounds for broadcasting and gossiping.
SIAM J. Discrete Math.,
14(2):267282,
2001.

P. Fraigniaud,
A. Pelc,
D. Peleg,
and S. Pérennes.
Assigning labels in unknown network with a leader.
Distributed Computing,
14(3):163183,
2001.

J. Galtier.
Geographical reservation for guaranteed handover and routing in low earth orbit constellations.
Telecommunication Systems,
18(1/3):101121,
2001.
[PDF
]

L. Gargano,
P. Hell,
and S. Pérennes.
Coloring all directed paths in a symmetric tree, with an application to optical networks.
Journal of Graph Theory,
38(4):183196,
2001.

L. Gargano,
A. Pelc,
S. Pérennes,
and U. Vaccaro.
Efficient communication in unknown networks.
Networks,
38(1):3949,
2001.

F. Havet.
Channel assignement and multicolouring of the induced subgraphs of the triangular lattice.
Discrete Mathematics,
233:219231,
2001.

M.C. Heydemann,
N. Marlin,
and S. Pérennes.
Complete Rotations in Cayley Graphs.
European Journal of Combinatorics,
22(2):179196,
2001.
[WWW
]

C. LinharesSales,
F. Maffray,
and B. Reed.
Recognizing planar strict quasiparity graphs.
Graphs Combin.,
17(4):745757,
2001.

D. Rautenbach and B. Reed.
The ErdosPósa property for odd cycles in highly connected graphs.
Combinatorica,
21(2):267278,
2001.
Note: Paul Erdos and his mathematics (Budapest, 1999).

E. Altman,
E. Baçsar,
T. Jiménez,
and N. Shimkin.
Routing into Two Parallel Links:GameTheoretic Distributed Algorithms.
Journal of Parallel and Distributed Computing,
(Special Issue on Routing in Computer and Communication Networks),
2000.

E. Altman,
T. Jiménez,
and G. Koole.
On optimal call admission control.
IEEE Trans. on Communications,
2000.

M. Becker,
A.L. Beylot,
O. Dalle,
R. Dhaou,
M. Marot,
P. Mussi,
C. Rigal,
and V. Sutter.
The ASIMUT Simulation Workshop.
Networking and Information Systems Journal,
3(2):335348,
2000.

C. Berge and B. Reed.
Optimal packings of edgedisjoint odd cycles.
Discrete Math.,
211(13):197202,
2000.

J.C. Bermond,
J. Bond,
C. Martin,
A. Pekec,
and F. S. Roberts.
Optimal orientation of annular networks.
JOIN,
1(1):2146,
2000.
[PDF
]

J.C. Bermond,
L. Gargano,
S. Pérennes,
A.A. Rescigno,
and U. Vaccaro.
Efficient Collective Communications in Optical Networks.
Theoretical Computer Science,
233(12):165189,
2000.
[PDF
]

J.C. Bermond,
S. Marshall,
and M.L. Yu.
Improved bounds for gossiping in meshbus networks.
JOIN,
1(1):119,
2000.
[PDF
]

P. Berthomé,
A. Ferreira,
S. Pérennes,
G. Plaxton,
and B. Maggs.
Sortingbased selection algorithms on hypercubic networks.
Algorithmica,
26(2):237254,
2000.

M. Bugliesi,
G. Delzanno,
L. Liquori,
and M. Martelli.
Object Calculi in Linear Logic.
Journal of Logic and Computation,
10(1):75104,
2000.
[POSTSCRIPT
]

D. Coudert,
A. Ferreira,
and X. Muñoz.
A MultihopMultiOPS Optical Interconnection Network.
IEEE/OSA Journal of Lightwave Technology,
18(12):20762085,
2000.
[POSTSCRIPT
]
Abstract: 
In this paper we study the design of regular multicast networks implemented with Optical Passive Star (OPS) couplers. We focus on an architecture based on both Kautz graphs and stackgraphs, and show that it is very costeffective with respect to its resources requirements, namely the number of OPS couplers, power budget, scalability and number of transceivers, and presents a large ratio numberofnodes/diameter. The important issue of medium access control is also addressed and control protocols for accessing the optical couplers are given and analyzed. Finally, we show through simulation that these control protocols efficiently implement shortest path routing on these networks. 

D. Coudert,
A. Ferreira,
and X. Muñoz.
Topologies for Optical Interconnection Networks Based on the Optical Transpose Interconnection System.
OSA Applied Optics  Information Processing,
39(17):29652974,
June 2000.
[POSTSCRIPT
]
Abstract: 
Many results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graphtheoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stackKautz networks as well as a generalization of the Kautz and de Bruijn digraphs. 

A. Ferreira,
A. Goldman,
and S. W. Song.
Broadcasting in bus interconnection networks.
Journal of Interconnection Networks  JOIN,
1(2):7394,
2000.

A. Ferreira and Nicolas Schabanel.
A randomized BSP/CGM algorithm for the maximal independent set.
Parallel Processing Letters,
9(3):411422,
2000.

J. Galtier.
Load Balancing Issues in the Prepartitioning Method.
Computers and Artificial Intelligence,
19(4),
2000.
[PDF
]

C. McDiarmid and B. Reed.
Channel assignment and weighted coloring.
Networks,
36(2):114117,
2000.

L. Perkovic and B. Reed.
An improved algorithm for finding tree decompositions of small width.
Internat. J. Found. Comput. Sci.,
11(3):365371,
2000.
Note: Selected papers from the Workshop on Theoretical Aspects of Computer Science (WG 99), Part 1 (Ascona).

B. Reed and R. Thomas.
Clique minors in graphs and their complements.
J. Combin. Theory Ser. B,
78(1):8185,
2000.

R. Balakhrishnan,
J.C. Bermond,
and P. Paulraja.
Combinatorics and Number Theory.
In Editors Special Issues of Discrete Mathematics,
volume 206,
pages 1220.
North Holland,
1999.

A. Ferreira.
On the design of parallel discrete algorithms for high performance computing systems.
In P. Pardalos, editor,Parallel Processing of Discrete Problems,
volume 106 of The IMA Volumes in Mathematics and its Aplications,
pages 7583.
Springer Verlag,
New York (USA),
1999.

A. Ferreira.
On the design of parallel discrete algorithms for high performance computing systems.
In P. Pardalos, editor,Parallel Processing of Discrete Problems,
volume 106 of The IMA Volumes in Mathematics and its Aplications,
pages 7583.
Springer Verlag,
New York (USA),
1999.

M. Molloy and B. Reed.
Graph colouring via the probabilistic method.
In Graph theory and combinatorial biology (Balatonlelle, 1996),
volume 7 of Bolyai Soc. Math. Stud.,
pages 125155.
János Bolyai Math. Soc.,
Budapest,
1999.

M. Molloy,
B. Reed,
and William Steiger.
On the mixing rate of the triangulation walk.
In Randomization methods in algorithm design (Princeton, NJ, 1997),
volume 43 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci.,
pages 179190.
Amer. Math. Soc.,
Providence, RI,
1999.

B. Beauquier.
AllToAll Communication in some WavelengthRouted AllOptical Networks.
Networks,
33(3):179187,
May 1999.

C. Berge and B. Reed.
Edgedisjoint odd cycles in graphs with small chromatic number.
Ann. Inst. Fourier (Grenoble),
49(3):783786,
1999.
Note: Symposium à la Mémoire de François Jaeger (Grenoble, 1998).

J.C. Bermond,
A. Bonnecaze,
T. Kodate,
S. Pérennes,
and P. Solé.
Symetric flows and broadcasting in hypercubes.
Annales de l'Institut Fourier,
49:787807,
1999.
[PDF
]

V. Bono,
M. Bugliesi,
M. DezaniCiancaglini,
and L. Liquori.
Subtyping for Extensible, Incomplete Objects.
Fundamenta Informaticae,
38(4):325364,
1999.
[POSTSCRIPT
]

R. Corrêa,
A. Ferreira,
and P. Rebreyend.
Integrating list heuristics in genetic algorithms for multiprocessor scheduling.
IEEE Transactions on Parallel and Distributed Systems,
10(8):825837,
August 1999.

R. Corrêa,
A. Ferreira,
and P. Rebreyend.
Scheduling multiprocessor tasks with genetic algorithms.
IEEE Transactions on Parallel and Distributed Systems,
10(8):825837,
August 1999.

M. Diallo,
A. Ferreira,
A. RauChaplin,
and S. Ubéda.
Scalable 2d convex hull and triangulation algorithms for coarsegrained multicomputers.
Journal of Parallel and Distributed Computing,
56(1):4770,
January 1999.

A. Ferreira,
C. Kenyon,
A. RauChaplin,
and S. Ubéda.
dDimensional Range Search on Multicomputers.
Algorithmica,
24(3/4):195208,
1999.
Note: Special Issue on Coarse Grained Parallel Algorithms.

A. Ferreira and S. Ubéda.
Computing the medial axis transform in parallel with 8 scan operations.
IEEE Transactions on Pattern Analysis & Machine Intelligence (PAMI),
21(3):277282,
March 1999.

Hugh Hind,
M. Molloy,
and B. Reed.
Total coloring with $\Delta+{\rm poly}(\log\Delta)$ colors.
SIAM J. Comput.,
28(3):816821 (electronic),
1999.

F. Maffray and B. Reed.
A description of clawfree perfect graphs.
J. Combin. Theory Ser. B,
75(1):134156,
1999.

N. V. R. Mahadev and B. A. Reed.
A note on vertex orders for stability number.
J. Graph Theory,
30(2):113120,
1999.

C. McDiarmid and B. Reed.
Colouring proximity graphs in the plane.
Discrete Math.,
199(13):123137,
1999.

M. Molloy and B. Reed.
Critical subgraphs of a random graph.
Electron. J. Combin.,
6:Research Paper 35, 13 pp. (electronic),
1999.

B. Reed.
A strengthening of Brooks' theorem.
J. Combin. Theory Ser. B,
76(2):136149,
1999.

B. Reed.
Edge coloring nearly bipartite graphs.
Oper. Res. Lett.,
24(12):1114,
1999.

B. Reed.
Mangoes and blueberries.
Combinatorica,
19(2):267296,
1999.

B. Reed.
The list colouring constants.
J. Graph Theory,
31(2):149153,
1999.

R. Corrêa,
A. Ferreira,
and S. Porto.
Selected Algorithmic Techniques for Parallel Optimization.
In D. Du and P. Pardalos, editors,Handbook of Combinatorial Optimization,
volume 3,
pages 407456.
Kluwer Academic Publisher, Boston (USA),
1998.

A. Ferreira.
Towards effective models for OPSbased lightwave networks.
In P. Berthomé and A. Ferreira, editors,Optical Interconnects and Parallel Processing: Trends at the Interface,
pages 209233.
Kluwer Academic Publisher,
Boston (USA),
1998.

A. Ferreira and I. GuérinLassous.
Algorithmique discrète parallèle : le chaînon manquant.
In J.F. Myoupo, editor,Parallélisme et Répartitions,
chapter II,
pages 2347.
Hermes,
Paris (F),
1998.

A. M. Frieze and B. Reed.
Probabilistic analysis of algorithms.
In Probabilistic methods for algorithmic discrete mathematics,
volume 16 of Algorithms Combin.,
pages 3692.
Springer,
Berlin,
1998.

B. Beauquier,
P. Hell,
and S. Pérennes.
Optimal Wavelengthrouted Multicasting.
DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science,
84(13),
May 1998.
[WWW
]

J.C. Bermond,
E. Darrot,
O. Delmas,
and S. Pérennes.
Hamilton circuits in the directed wrapped butterfly network.
Discrete Applied Mathematics,
84(13):2142,
1998.
[PDF
]

J.C. Bermond,
E. Darrot,
O. Delmas,
and S. Pérennes.
Hamilton cycle decomposition of the butterfly networks.
Parallel Processing Letters,
8(3):371385,
1998.
[PDF
]

J.C. Bermond,
L. Gargano,
and S. Pérennes.
Optimal sequential gossiping by short messages.
Discrete Applied Mathematics,
86(23):145155,
1998.
[PDF
]

J.C. Bermond,
L. Gargano,
A.A. Rescigno,
and U. Vaccaro.
Fast gossiping by short messages.
SIAM Journal on Computing,
27(4):917941,
1998.
[PDF
]

H. Bourdin,
A. Ferreira,
and K. Marcus.
A performance comparison between graph and hypergraph topologies for passive star WDM lightwave networks.
Computer Networks and ISDN Systems,
8(30):805819,
May 1998.

M. Molloy and B. Reed.
A bound on the total chromatic number.
Combinatorica,
18(2):241280,
1998.

M. Molloy and B. Reed.
The size of the giant component of a random graph with a given degree sequence.
Combin. Probab. Comput.,
7(3):295305,
1998.

S. Perennes.
Broadcasting and gossiping on de Bruijn, shuffle exchange and similar networks..
Discrete Applied Mathematics,
83:247262,
1998.

B. Reed.
$\omega,\ \Delta$, and $\chi$.
J. Graph Theory,
27(4):177212,
1998.

B. Reed and P. Seymour.
Fractional colouring and Hadwiger's conjecture.
J. Combin. Theory Ser. B,
74(2):147152,
1998.

A. Ferreira and M. Morvan.
Models for Parallel Algorithm Design: An Introduction.
In A. Migdalas,
P. Pardalos,
and S. Storoy, editors,Parallel Computing in Optimization,
pages 126.
Kluwer Academic Publisher, Boston (USA),
1997.

B. A. Reed.
Tree width and tangles: a new connectivity measure and some applications.
In Surveys in combinatorics, 1997 (London),
volume 241 of London Math. Soc. Lecture Note Ser.,
pages 87162.
Cambridge Univ. Press,
Cambridge,
1997.

J.C. Bermond,
R. Dawes,
and F.O. Ergincan.
De Bruijn and Kautz bus networks.
Networks,
30:205218,
1997.
[PDF
]

J.C. Bermond,
H.A. Harutyunyan,
A.L. Liestman,
and S. Pérennes.
A note on the dimensionalityof modified Knödel Graphs.
International Journal of Foundations of Computer Science,
8(2):109116,
1997.
[PDF
]

J.C. Bermond,
Z. Liu,
and M. Syska.
Mean eccentricities of de Bruijn networks.
Networks,
30:187203,
1997.
[PDF
]

P. Berthomé and A. Ferreira.
Communication Issues in Parallel Systems with Optical Interconnections.
International Journal of Foundations of Computer Science,
8(2):143162,
1997.
Note: Special Issue on Interconnection Networks.

M. Cosnard and E. Goles.
Discrete state neural networks and energies.
Neural Networks,
10(2):327334,
1997.

H. Everett,
S. Klein,
and B. Reed.
An algorithm for finding homogeneous pairs.
Discrete Appl. Math.,
72(3):209218,
1997.

B. Gaujal,
A. JeanMarie,
P. Mussi,
and G. Siegel.
High speed simulation of discrete event systems by mixing process oriented and equational approaches.
Parallel Computing,
23(12):219233,
April 1997.

H. Hind,
M. Molloy,
and B. Reed.
Colouring a graph frugally.
Combinatorica,
17(4):469482,
1997.

C. LinharesSales,
F. Maffray,
and B. Reed.
On planar perfectly contractile graphs.
Graphs Combin.,
13(2):167187,
1997.

M. Molloy and B. Reed.
A bound on the strong chromatic index of a graph.
J. Combin. Theory Ser. B,
69(2):103109,
1997.

S. Perennes.
A Proof of Jean de Rumeur's conjecture.
Discrete Applied Mathematics,
74:295299,
1997.

L. Perkovic and B. Reed.
Edge coloring regular graphs of high degree.
Discrete Math.,
165/166:567578,
1997.
Note: Graphs and combinatorics (Marseille, 1995).

S. van Bakel,
L. Liquori,
S. Ronchi della Rocca,
and P. Urzyczyn.
Comparing Cubes of Typed and Type Assignment System.
Annals of Pure and Applied Logics,
86(3):267303,
1997.
[POSTSCRIPT
]

R. Corrêa and A. Ferreira.
Parallel BestFirst BranchandBound in Discrete Optimization: A Framework.
In A. Ferreira and P. Pardalos, editors,Solving Combinatorial Optimization Problems in Parallel,
volume 1054 of LNCS StateoftheArt Surveys,
pages 171200.
SpringerVerlag,
1996.

A. Ferreira.
Parallel and Communication Algorithms for Hypercube Multiprocessors.
In A. Zomaya, editor,Handbook of Parallel and Distributed Computing,
chapter 19,
pages 568589.
McGrawHill,
New York (USA),
1996.

A. Ferreira and P. Pardalos.
SCOOP  Solving Combinatorial Optimization Problems in Parallel.
In A. Ferreira and P. Pardalos, editors,Solving Combinatorial Optimization Problems in Parallel,
volume 1054 of LNCS StateoftheArt Surveys,
pages 16.
SpringerVerlag,
1996.

F. Baude,
F. Belloncle,
D. Caromel,
N. Furmento,
P. Mussi,
Y. Roudier,
and G. Siegel.
Parallel ObjectOriented Programming for Parallel Simulations.
Information Sciences,
1996.

J.C. Bermond and F.O. Ergincan.
Bus Interconnection Networks.
Discrete Applied Mathematics,
68:115,
1996.
[PDF
]

J.C. Bermond,
C. Peyrat,
I. Sakho,
and M. Tchuente.
Parallelization of Gauss elimination algorithm on systolic arrays.
Journal of Parallel and Distributed Computing,
33:6975,
1996.

P. Berthomé,
A. Ferreira,
and S. Pérennes.
Decomposing hierarchical Cayley graphs, with applications to information dissemination and algorithm design.
IEEE Transactions on Parallel and Distributed Systems,
7(12):12921300,
December 1996.

O. Bournez and M. Cosnard.
On the computational power of dynamical systems and hybrid systems.
Theoretical Computer Science,
168(2):417459,
1996.

C. Cooper,
A. Frieze,
M. Molloy,
and B. Reed.
Perfect matchings in random $r$regular, $s$uniform hypergraphs.
Combin. Probab. Comput.,
5(1):114,
1996.

A. Ferreira,
A. Goldman,
and S. W. Song.
Gossiping in bus interconnection networks.
Parallel Algorithms and Applications,
8:309331,
1996.
Note: Special Issue on Algorithms for Enhanced Meshes.

A. Ferreira and M. Grammatikakis.
Randomized routing in generalized hypercubes.
Theoretical Computer Science,
158(12):5364,
1996.

A. Ferreira and J.M. Robson.
Fast and Scalable Parallel Algorithms for Knapsack and Similar Problems.
Journal of Parallel and Distributed Computing,
39(1):113,
November 1996.

S. E. Markossian,
G. S. Gasparian,
and B. A. Reed.
$\beta$perfect graphs.
J. Combin. Theory Ser. B,
67(1):111,
1996.

B. Reed.
Paths, stars and the number three.
Combin. Probab. Comput.,
5(3):277295,
1996.

B. Reed,
N. Robertson,
P. Seymour,
and R. Thomas.
Packing directed circuits.
Combinatorica,
16(4):535554,
1996.

B. A. Reed and F. B. Shepherd.
The GallaiYounger conjecture for planar graphs.
Combinatorica,
16(4):555566,
1996.

R. Corrêa and A. Ferreira.
A Distributed Implementation of Asynchronous Parallel Branch and Bound.
In A. Ferreira and J. Rolim, editors,Solving Irregular Problems in Parallel: State of the Art,
pages 157176.
Kluwer Academic Publisher, Boston (USA),
1995.

M. Albert,
A. Frieze,
and B. Reed.
Comments on: ``Multicoloured Hamilton cycles'' [Electron. J. Combin. 2 (1995), Research Paper 10, 13 pp. (electronic); MR1327570 (96b:05058)].
Electron. J. Combin.,
2:Research Paper 10, Comment 1, 1 HTML document (electronic),
1995.

M. Albert,
A. Frieze,
and B. Reed.
Multicoloured Hamilton cycles.
Electron. J. Combin.,
2:Research Paper 10, approx. 13 pp. (electronic),
1995.

J.C. Bermond,
F. Comellas,
and D.F. Hsu.
Distributed Loop Computer Networks: a survey.
Journal of Parallel and Distributed Computing,
24:210,
1995.

J.C. Bermond,
P. Fraigniaud,
and J.G. Peters.
Antepenultimate Broadcasting.
Networks,
26(3):125137,
1995.

P. Berthomé and A. Ferreira.
On Broadcasting Schemes in Restricted Optical Passive Star Systems.
DIMACS series in Discrete Mathematics and Theoretical Computer Science,
21:1929,
1995.

R. Corrêa and A. Ferreira.
Modeling Parallel BranchandBound for Asynchronous Implementations.
DIMACS series in Discrete Mathematics and Theoretical Computer Science,
22:4556,
1995.

R. Corrêa and A. Ferreira.
On the effectivenes of parallel branch and bound.
Parallel Processing Letters,
5(3):375386,
1995.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Parallel processing of pointer based quadtrees.
Computer Vision and Image Understanding,
62(1):110,
1995.

L. Devroye and B. Reed.
On the variance of the height of random binary search trees.
SIAM J. Comput.,
24(6):11571162,
1995.

T. Duboux,
A. Ferreira,
and M. Gastaldo.
A Scalable Design for VLSI Dictionary Machines.
Microprocessors & Microprogramming Journal,
41:359372,
1995.
Note: Special Issue on Parallel Programmable Architectures and Compilation for Multidimensional Processing.
Keywords:
parallelisme,
grain fin,
machine dico.

A. Ferreira.
Work and memory efficient parallel algorithms for the knapsack problem.
International Journal of High Speed Computing,
4:595606,
1995.

A. Frieze,
R. M. Karp,
and B. Reed.
When is the assignment bound tight for the asymmetric travelingsalesman problem?.
SIAM J. Comput.,
24(3):484493,
1995.

A. Frieze and B. Reed.
Covering the edges of a random graph by cliques.
Combinatorica,
15(4):489497,
1995.

B. Gamble,
W. Pulleyblank,
B. Reed,
and B. Shepherd.
Right angle free subsets in the plane.
Graphs Combin.,
11(2):121129,
1995.

C. McDiarmid and B. Reed.
Almost every graph can be covered by $\lceil{\Delta/2}\rceil$ linear forests.
Combin. Probab. Comput.,
4(3):257268,
1995.

M. Molloy and B. Reed.
The dominating number of a random cubic graph.
Random Structures Algorithms,
7(3):209221,
1995.

B. Reed.
Rooted routing in the plane.
Discrete Appl. Math.,
57(23):213227,
1995.
Note: Combinatorial optimization 1992 (CO92) (Oxford).

B. Reed and N. Sbihi.
Recognizing bullfree perfect graphs.
Graphs Combin.,
11(2):171178,
1995.

T. Duboux,
A. Ferreira,
and M. Gastaldo.
6: Algorithmique Parallèle  Structures de Données Arborescentes.
In G. Authié,
A. Ferreira,
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J. Roman,
C. Roucairol,
and B. Virot, editors,Algorithmes parallèles  analyse et conception,
pages 129171.
Hermes,
Paris (F),
1994.

J.C. Bermond and P. Fraigniaud.
Broadcasting and Gossiping in de Bruijn Networks.
SIAM Journal on Computing,
23(1):212225,
1994.

P. Berthomé and A. Ferreira.
Timeoptimal geometric algorithms in hypercubic networks.
Parallel Algorithms and Applications,
4:169181,
1994.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
A massively parallel knowledgebase server using a hypercube multiprocessor.
Parallel Computing,
20:13691382,
1994.

A. Ferreira and S. Ubéda.
Ultrafast parallel contour tracking, with applications to thinning.
Pattern Recognition,
27(7):867878,
1994.

C. McDiarmid,
B. Reed,
A. Schrijver,
and B. Shepherd.
Induced circuits in planar graphs.
J. Combin. Theory Ser. B,
60(2):169176,
1994.

B. Bollobás,
B. Reed,
and A. Thomason.
An extremal function for the achromatic number.
In Graph structure theory (Seattle, WA, 1991),
volume 147 of Contemp. Math.,
pages 161165.
Amer. Math. Soc.,
Providence, RI,
1993.

B. Reed.
Counterexamples to a conjecture of Las Vergnas and Meyniel.
In Graph structure theory (Seattle, WA, 1991),
volume 147 of Contemp. Math.,
pages 157159.
Amer. Math. Soc.,
Providence, RI,
1993.

B. A. Reed,
N. Robertson,
A. Schrijver,
and P. D. Seymour.
Finding disjoint trees in planar graphs in linear time.
In Graph structure theory (Seattle, WA, 1991),
volume 147 of Contemp. Math.,
pages 295301.
Amer. Math. Soc.,
Providence, RI,
1993.

J.C. Bermond and P. Hell.
On even factorizations and the chromatic index of the Kautz and de Bruijn digraphs.
Journal of Graph theory,
17(5):647655,
1993.
[PDF
]

J.C. Bermond,
E. Lazard,
D. Sotteau,
and M. Syska.
La Théorie des graphes.
Courrier du CNRS, la recherche en informatique,
80:5455,
1993.
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]

J.C. Bermond,
N. Homobono N.,
and C. Peyrat.
Connectivity of Kautz Networks.
Discrete Mathematics,
114:5162,
1993.

G. Cornuéjols and B. Reed.
Complete multipartite cutsets in minimal imperfect graphs.
J. Combin. Theory Ser. B,
59(2):191198,
1993.

A. Ferreira.
On spaceefficient algorithms for certain NPComplete problems.
Theoretical Computer Science,
120:311315,
1993.
Keywords:
parallelisme,
optimisation,
knapsack.

A. Ferreira and J. Zerovnik.
Bounding the probability of success of stochastic methods for global optimization.
International Journal on Computers & Mathematics with Applications,
25(10/11):18,
1993.
Note: 2nd Special Issue on Global Optimization, Control and Games.

A. Frieze and B. Reed.
Polychromatic Hamilton cycles.
Discrete Math.,
118(13):6974,
1993.

K. Kilakos and B. Reed.
Fractionally colouring total graphs.
Combinatorica,
13(4):435440,
1993.

C. McDiarmid and B. Reed.
On total colourings of graphs.
J. Combin. Theory Ser. B,
57(1):122130,
1993.

B. Reed.
Rooted routing in the plane.
CWI Quarterly,
6(3):241255,
1993.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Algorithmique SIMD.
In M.Cosnard,
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Masson,
1992.

K. Kilakos and B. Reed.
A semiintegral total colouring.
In Sets, graphs and numbers (Budapest, 1991),
volume 60 of Colloq. Math. Soc. János Bolyai,
pages 429438.
NorthHolland,
Amsterdam,
1992.

S. Akl,
M. Cosnard,
and A. Ferreira.
Datamovementintensive problems : two folk theorems in parallel computation revisited.
Theoretical Computer Science,
95:323337,
1992.

N. Alon,
C. McDiarmid,
and B. Reed.
Star arboricity.
Combinatorica,
12(4):375380,
1992.

J.C. Bermond,
C. Delorme,
and JJ. Quisquater.
Table of large $({\Delta},D)$graphs.
Discrete Applied Mathematics,
37/38:575577,
1992.

J.C. Bermond,
P. Hell,
A. L. Liestman,
and J. G. Peters.
Broadcasting in bounded degree graphs.
SIAM Journal on Discrete Mathematics,
5(1):1024,
1992.
[PDF
]

J.C. Bermond,
P. Hell,
A. L. Liestman,
and J. G. Peters.
Sparse broadcast graphs.
Discrete Applied Mathematics,
36:97130,
1992.

J.C. Bermond,
P. Hell,
and J.J. Quisquater.
Construction of large packet radio networks.
Parallel Processing Letters,
2(1):312,
1992.
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J.C. Bermond,
P. Michallon,
and D. Trystram.
Broadcasting in wraparound meshes with parallel monodirectional links.
Parallel Computing,
18:639648,
1992.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Parallel fractional cascading on hypercube multiprocessors.
Computational Geometry  Theory and Applications,
2:141167,
1992.

A. Ferreira and S.W. Song.
Achieving optimality for gate matrix layout and PLA folding : a graph theoretic approach.
Integration: the VLSI journal,
14:173195,
1992.

A. Frieze,
C. McDiarmid,
and B. Reed.
On a conjecture of Bondy and Fan.
Ars Combin.,
33:329336,
1992.

B. Reed and C. McDiarmid.
The strongly connected components of $1$in, $1$out.
Combin. Probab. Comput.,
1(3):265274,
1992.

N. Alon,
C. McDiarmid,
and B. Reed.
Acyclic coloring of graphs.
Random Structures Algorithms,
2(3):277288,
1991.

J.C. Bermond and J.C. Konig.
Un protocole distribué pour la 2connexité.
TSI,
10(4):269274,
1991.

J.C. Bermond and D. Tzvieli.
Minimal diameter double loop networks, part II: dense optimal families.
Networks,
21:19,
1991.

M. Cosnard and A. Ferreira.
On the real power of loosely coupled parallel architectures.
Parallel Processing Letters,
1(2):103111,
1991.

A. Ferreira.
A parallel time/hardware tradeoff $T.H = O(2^{n/2})$ for the knapsack problem.
IEEE Transactions on Computers,
40(2):221225,
1991.

J.C. Bermond,
K. Heinrich,
and M.L. Yu.
Existence of resolvable path designs.
Journal Europeen de Combinatoire,
11:205211,
1990.

J.C. Bermond,
K. Heinrich,
and M.L. Yu.
On resolvable mixed path designs.
Journal Europeen de Combinatoire,
11:313318,
1990.

M. Cosnard,
J. Duprat,
and A. Ferreira.
The complexity of searching in X+Y and other multisets.
Information Processing Letters,
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1990.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Parallel branch and bound on fine grained hypercube multiprocessors.
Parallel Computing,
15(13):201209,
1990.

A. Ferreira and M. Gastaldo.
Experimentations de deux algorithmes de tri sur un hypercube de transputers.
La Lettre du Transputer,
(5):31121,
1990.

A. Frieze,
C. McDiarmid,
and B. Reed.
Greedy matching on the line.
SIAM J. Comput.,
19(4):666672,
1990.

C. McDiarmid and B. Reed.
Linear arboricity of random regular graphs.
Random Structures Algorithms,
1(4):443445,
1990.

J.C. Bermond,
K. Berrada,
and J. Bond.
Extensions of networks with given diameter.
Discrete Math.,
75(13):3140,
1989.
Note: Graph theory and combinatorics (In honor of P. Erdös' 75, Cambridge, 1988).

J.C. Bermond,
O. Favaron,
and M. Mahéo.
Hamiltonian decomposition of Cayley graphs of degree $4$.
J. Combin. Theory Ser. B,
46(2):142153,
1989.

J.C. Bermond and J.M. Fourneau.
Independent connections: an easy characterization of baselineequivalent multistage interconnection networks.
Theoret. Comput. Sci.,
64(2):191201,
1989.

J.C. Bermond,
N. Homobono,
and C. Peyrat.
Large faulttolerant interconnection networks.
Graphs Combin.,
5(2):107123,
1989.

J.C. Bermond and C. Peyrat.
Induced subgraphs of the power of a cycle.
SIAM J. Discrete Math.,
2(4):452455,
1989.

M. Cosnard,
J. Duprat,
and A. Ferreira.
Complexity of selection in X+Y.
Theoretical Computer Science,
67:115120,
1989.

M. Cosnard and A. Ferreira.
Generating Permutations on a VLSI Suitable Linear Network.
The Computer Journal,
32(6):571573,
1989.

C. T. Hoàng and B. A. Reed.
$P\sb 4$comparability graphs.
Discrete Math.,
74(12):173200,
1989.
Note: Graph colouring and variations.

C. T. Hoàng and B. A. Reed.
Some classes of perfectly orderable graphs.
J. Graph Theory,
13(4):445463,
1989.

C. J. H. McDiarmid and B. A. Reed.
Building heaps fast.
J. Algorithms,
10(3):352365,
1989.

J.C. Bermond,
J.M. Fourneau,
and A. JeanMarie.
A graph theoretical approach to equivalence of multistage interconnection networks.
Discrete Appl. Math.,
22(3):201214,
1988/89.

J.C. Bermond and C. Peyrat.
Broadcasting in de Bruijn networks.
Congr. Numer.,
66:283292,
1988.
Note: Nineteenth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Baton Rouge, LA, 1988).

M. Bertschi and B. A. Reed.
Erratum: ``A note on even pairs'' [Discrete Math. 65 (1987), no. 3, 317318; MR0897656 (88f:05066)] by Reed.
Discrete Math.,
71(2):187,
1988.

M. Cosnard,
A. Ferreira,
and H. Herbelin.
The TwoList Algorithm for the Knapsack Problem on a FPS T20.
Parallel Computing,
(9):385388,
1988.

A. M. Frieze,
B. Jackson,
C. J. H. McDiarmid,
and B. Reed.
Edgecolouring random graphs.
J. Combin. Theory Ser. B,
45(2):135149,
1988.

C. L. Monma,
B. Reed,
and W. T. Trotter, Jr..
Threshold tolerance graphs.
J. Graph Theory,
12(3):343362,
1988.

J.C. Bermond,
J. Bond,
and D. Sotteau.
On regular packings and coverings.
Annals of Discrete mathematics,
34:81100,
1987.
[PDF
]

J.C. Bermond,
J.M. Fourneau,
and A. JeanMarie.
Equivalence of multistage interconnection networks.
Information Processing Letters,
26:4550,
1987.

C. T. Hoàng and B. Reed.
A note on short cycles in digraphs.
Discrete Math.,
66(12):103107,
1987.

B. A. Reed.
A note on even pairs.
Discrete Math.,
65(3):317318,
1987.

B. Reed.
A semistrong perfect graph theorem.
J. Combin. Theory Ser. B,
43(2):223240,
1987.

F. Baccelli and P. Mussi.
An asynchronous parallel interpreter for arithmetic expressions and its evaluation.
IEEE Transactions on Computers,
C353:245256,
March 1986.

J.C. Bermond,
C. Delorme,
and J.J. Quisquater.
Strategies for interconnection networks: some methods from graph theory.
J. Parallel Distributed Computing,
3(4):433449,
1986.
[WWW
]

J.C. Bermond and M. Paoli.
Research problem: Hamilton powers of graphs.
Discrete Mathematics,
62:329331,
1986.

B. Reed.
A note on the semistrong perfect graph conjecture.
Discrete Math.,
54(1):111112,
1985.

J.C. Bermond,
C. Delorme,
and G. Farhi.
Large graphs with given degree and diameter. II.
J. Combin. Theory Ser. B,
36(1):3248,
1984.

J.C. Bermond,
J.L. Fouquet,
M. Habib,
and B. Péroche.
On linear $k$arboricity.
Discrete Math.,
52(23):123132,
1984.

J.C. Bermond and M. Las Vergnas.
Regular factors in nearly regular graphs.
Discrete Math.,
50(1):913,
1984.

M. Hébert,
P. Mussi,
O. Faugeras,
and J.D. Boissonnat.
Polyhedral Approximation of 3D Objects without Holes.
Computer Vision, Graphics, and Image Processing,
25,
1984.

J.C. Bermond,
J. Bond,
M. Paoli,
and C. Peyrat.
Graphs and interconnection networks: diameter and vulnerability.
In Surveys in combinatorics (Southampton, 1983),
volume 82 of London Math. Soc. Lecture Note Ser.,
pages 130.
Cambridge Univ. Press,
Cambridge,
1983.

J.C. Bermond,
Bill Jackson,
and François Jaeger.
Shortest coverings of graphs with cycles.
J. Combin. Theory Ser. B,
35(3):297308,
1983.

J.C. Bermond,
C. Delorme,
and G. Farhi.
Large graphs with given degree and diameter. III.
In Graph theory,
volume 62 of NorthHolland Math. Stud.,
pages 2331.
NorthHolland,
Amsterdam,
1982.
Note: Présenté au Colloque Cambridge, England, 1981.

J.C. Bermond and G. Farhi.
Sur un problème combinatoire d'antennes en radioastronomie. II.
In Theory and practice of combinatorics,
volume 60 of NorthHolland Math. Stud.,
pages 4953.
NorthHolland,
Amsterdam,
1982.

J.C. Bermond,
C. Delorme,
and J.J. Quisquater.
Tables of large graphs with given degree and diameter.
Inform. Process. Lett.,
15(1):1013,
1982.

J.C. Bermond,
A. Germa,
M.C. Heydemann,
and D. Sotteau.
Longest paths in digraphs.
Combinatorica,
1(4):337341,
1981.
[PDF
]

J.C. Bermond and C. Thomassen.
Cycles in digraphsa survey.
J. Graph Theory,
5(1):143,
1981.

J.C. Bermond,
P. Frankl,
and F. Sterboul.
On the maximum number of edges in a hypergraph whose linegraph contains no cycle.
Discrete Math.,
30(3):295298,
1980.

J.C. Bermond,
A. Germa,
M.C. Heydemann,
and D. Sotteau.
Girth in digraphs.
J. Graph Theory,
4(3):337341,
1980.
[PDF
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J.C. Bermond,
C. Huang,
A. Rosa,
and D. Sotteau.
Decomposition of complete graphs into isomorphic subgraphs with five vertices.
Ars Combin.,
10:211254,
1980.
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]

J.C. Bermond,
D. Sotteau,
A. Germa,
and M.C. Heydemann.
Chemins et circuits dans les graphes orientés.
Ann. Discrete Math.,
8:293309,
1980.
Note: Présenté au Colloque Combinatorics 79, Univ. Montréal, Montreal, Canada, 1979.
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]

J.C. Bermond.
Hamiltonian Graphs,
chapter 6,
pages 127167.
Selected Topics in Graph Theory.
Academic Press,
1979.

J.C. Bermond,
A. Germa,
and M.C. Heydemann.
Hamiltonian cycles in strong products of graphs.
Canad. Math. Bull.,
22(3):305309,
1979.

J.C. Bermond,
A. Germa,
and D. Sotteau.
Resolvable decomposition of $K\sp{\ast} \sb{n}$.
J. Combin. Theory Ser. A,
26(2):179185,
1979.
[PDF
]

J.C. Bermond and Anton Marczyk.
Comparaison des puissances de graphes.
C. R. Acad. Sci. Paris Sér. AB,
288(1):A13A15,
1979.

J.C. Bermond,
J. M. S. Sim oesPereira,
and Christina M. Zamfirescu.
On nonHamiltonian homogeneously traceable digraphs.
Math. Japon.,
24(4):423426,
1979/80.

J.C. Bermond.
Hamiltonian decompositions of graphs, directed graphs and hypergraphs.
Ann. Discrete Math.,
3:2128,
1978.
Note: Présenté au Cambridge Combinatorial Conf., Advances in graph theory , Trinity College, Cambridge, England, 1977.

J.C. Bermond,
A. Germa,
and M.C. Heydemann.
Graphes représentatifs d'hypergraphes.
Cahiers Centre Études Rech. Opér.,
20(34):325329,
1978.
Note: Présenté au Colloque Mathématiques Discrètes: Codes et Hypergraphes, Brussels, 1978.

J.C. Bermond,
C. Huang,
and D. Sotteau.
Balanced cycle and circuit designs: even cases.
Ars Combin.,
5:293318,
1978.
[PDF
]

J.C. Bermond and P. Frankl.
On a conjecture of Chvátal on $m$intersecting hypergraphs.
Bull. London Math. Soc.,
9(3):310312,
1977.

J.C. Bermond,
A. Germa,
and D. Sotteau.
Hypergraphdesigns.
Ars Combinatoria,
3:4766,
1977.
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]

J. C. Bermond,
M. C. Heydemann,
and D. Sotteau.
Line graphs of hypergraphs. I.
Discrete Math.,
18(3):235241,
1977.
[PDF
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J.C. Bermond and J. Schönheim.
$G$decomposition of $K\sb{n}$, where $G$ has four vertices or less.
Discrete Math.,
19(2):113120,
1977.

Unsolved problems.
pp 678696. Congressus Numerantium, No. XV,
1976.
Note: Chairman: P. Erdos, With contributions by C. C. Chen, D. E. Daykin, B. Bollobás, P. Erdos, A. Frank, A. Gardiner, F. Jaeger, A. Bondy, L. Lovász, A. Recski, S. Maurer, A. Rényi, C. St. J. A. NashWilliams, B. Recamán, D. A. Waller, D. D. Grant, M. Las Vergnas, S. E. Eldridge, A. D. Keedwell, J. Sheehan, A. J. W. Hilton, J.C. Bermond, R. J. Wilson, J. A. Bondy, and R. L. Hemminger.

J.C. Bermond and V. Faber.
Decomposition of the complete directed graph into $k$circuits.
J. Combinatorial Theory Ser. B,
21(2):146155,
1976.

J.C. Bermond and Y. Kodratoff.
Une heuristique pour le calcul de l'indice de transitivité d'un tournoi.
Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge Informat. Théor.,
10(R1):8392,
1976.

Problems.
In Recent advances in graph theory (Proc. Second Czechoslovak Sympos., Prague, 1974),
pages 541544.
Academia,
Prague,
1975.
Note: Contributed by P. Erdos, M. Simonovits, V. T. Sós, L. Lovász, J.C. Bermond, G. O. H. Katona, T. Tarján, R. A. Brualdi, L. S. Mel' nikov and B. Toft.

J.C. Bermond.
$1$graphes réguliers minimaux de girth donné.
Cahiers Centre Études Recherche Opér.,
17(24):125135,
1975.
Note: Présenté au Colloque sur la Théorie des Graphes, Paris, 1974.

J.C. Bermond and J. C. Meyer.
Hypergraphes et configurations.
Cahiers Centre Études Recherche Opér.,
17(24):137154,
1975.
Note: Présenté au Colloque sur la Théorie des Graphes, Paris, 1974.

J.C. Bermond.
An application of the solution of Kirkman's schoolgirl problem: the decomposition of the symmetric oriented complete graph into $3$circuits.
Discrete Math.,
8:301304,
1974.

J.C. Bermond.
Nombre chromatique total du graphe $r$parti complet.
J. London Math. Soc. (2),
9:279285,
1974/75.

J.C. Bermond.
Some Ramsey numbers for directed graphs.
Discrete Math.,
9:313321,
1974.

J.C. Bermond and J. C. Meyer.
Graphe représentatif des arêtes d'un multigraphe.
J. Math. Pures Appl. (9),
52:299308,
1973.
[PDF
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J.C. Bermond and P. Rosenstiehl.
Pancyclisme du carré du graphe aux arêtes d'un graphe.
Cahiers Centre Études Recherche Opér.,
15:285286,
1973.
Note: Présenté au Colloque sur la Théorie des Graphes,Brussels, 1973.

J.C. Bermond.
Arbres maximaux ayant au plus $n$ sommets pendants.
C. R. Acad. Sci. Paris Sér. AB,
274:A1878A1881,
1972.

J.C. Bermond.
Ordres à distance minimum d'un tournoi et graphes partiels sans circuits maximaux.
Math. Sci Humaines,
(37):525,
1972.

J.C. Bermond.
Graphes orientés fortement $k$connexes et graphes ``$k$ arc hamiltoniens''.
C. R. Acad. Sci. Paris Sér. AB,
271:A141A144,
1970.

G. D'Angelo,
G. Di Stefano,
and A. Navarra.
Gathering asynchronous and oblivious robots on basic graph topologies under the Look ComputeMove model.
In Steve Alpern,
Robbert Fokkink,
Leszek Gasieniec,
Roy Lindelauf,
and VS Subrahmanian, editors,Search Games and Rendezvous.
Springer,
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Note: Volume dedicated to the Workshop on Search and Rendezvous that took place in May 2012 in Lorentz Centre. To appear. [WWW
] [PDF
]
Abstract: 
Recent and challenging models of robotbased computing systems consider identical, oblivious and mobile robots placed on the nodes of anonymous graphs. Robots operate asynchronously in order to reach a common node and remain with it. This task is known in the literature as the athering or rendezvous problem. The target node is neither chosen in advance nor marked differently compared to the other nodes. In fact, the graph is anonymous and robots have minimal capabilities. In the context of robotbased computing systems, resources are always limited and precious. Then, the research of the minimal set of assumptions and capabilities required to accomplish the gathering task as well as for other achievements is of main interest. Moreover, the minimality of the assumptions stimulates the investigation of new and challenging techniques that might reveal crucial peculiarities even for other tasks. The model considered in this chapter is known in the literature as the LookComputeMove model. Identical robots initially placed at different nodes of an anonymous input graph operate in asynchronous LookComputeMove 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 makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot. This means that the time between Look, Compute, and Move operations is finite but unbounded, and it is decided by the adversary for each robot. Hence, robots may move based on significantly outdated perceptions. The only constraint is that moves are instantaneous, and hence any robot performing a Look operation perceives all other robots at nodes of the ring and not on edges. Robots are all identical, anonymous, and execute the same deterministic algorithm. They cannot leave any marks at visited nodes, nor can they send messages to other robots. In this chapter, we aim to survey on recent results obtained for the gathering task over basic graph topologies, that are rings, grids, and trees. Recent achievements to this matter have attracted many researchers, and have provided interesting approaches that might be of main interest to the community that studies robotbased computing systems. 

S. Bessy and F. Havet.
Enumerating the edgecolourings and total colourings of a regular graph.
Journal of Combinatorial Optimization,
.
Note: To appear.
[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 $k$edgecolourings of a $k$regular graph on $n$ vertices is $k\cdot(k1!)^{n/2}$. Our proof is constructible and leads to a branching algorithm enumerating all the $k$edgecolourings of a $k$regular graph using a time $O^*((k1!)^{n/2})$ 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 $4$totalcolourings of a connected cubic graph is at most $3.2^{3n/2}$. Again, our proof yields a branching algorithm to enumerate all the $4$totalcolourings of a connected cubic graph. 

S. Caron,
F. Giroire,
D. Mazauric,
J. Monteiro,
and S. Pérennes.
P2P Storage Systems: Study of Different Placement Policies.
ELSEVIER Journal of PeertoPeer Networking and Applications, Springer,
.
Note: To appear.
[PDF
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Abstract: 
In a P2P storage system using erasure codes, a data block is encoded in many redundancy fragments. These fragments are then sent to distinct peers of the network. In this work, we study the impact of different placement policies of these fragments on the performance of storage systems. Several practical factors (easier control, software reuse, latency) tend to favor data placement strategies that preserve some degree of locality. We compare three policies: two of them are {\em local}, in which the data are stored in logical neighbors, and the other one, {\em 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 such 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 {\em local} policies. When the bandwidth is limited, these bursty variations induce longer maintenance time and henceforth a higher risk of data loss. We 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. Additionally, we propose a new {\em external reconstruction} strategy that greatly improves the performance of local placement strategies. Finally, we give analytical methods to estimate the mean time to the occurrence of data loss for the three policies. 

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,
.
Note: To appear.
[WWW
] [PDF
]
Abstract: 
We study the problem of dynamically updatingallpairs 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 BellmanFord 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 realworld 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 BellmanFord and DUAL. In terms of messages, the new algorithm outperforms both BellmanFord and DUAL on the realworld 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 BellmanFord. 

G. D'Angelo,
G. Di Stefano,
and A. Navarra.
Flow problems in multiinterface networks.
IEEE Transactions on Computers,
.
Note: To appear.
[WWW
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Abstract: 
In heterogeneous networks, devices communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available ones, each device might establish several connections. A connection may be established when the devices at its endpoints share at least one active interface. In this paper, we consider two fundamental optimization problems. In the first one (Maximum Flow in MultiInterface Networks MFMI), we aim to establish the maximal bandwidth that can be guaranteed between two given nodes of the input network. In the second problem (MinimumCost Flow in MultiInterface Networks MCFMI), 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 MFMI is polynomially solvable while MCFMI is NPhard even for a bounded number of different interfaces and bounded degree networks. Moreover, we provide polynomial approximation algorithms for MCFMI and exact algorithms for relevant subproblems. Finally, we experimentally analyze the proposed approximation algorithm, showing that in practical cases it guarantees a low approximation ratio. 

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,
September.
Note: To appear.
[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 1020\27775643210f 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 virtualizationbased 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 testbed, and the experiment results illustrate the efficacy and efficiency of this approach. 

F. Havet and L. Sampaio.
On the Grundy and $b$chromatic Numbers of a Graph.
Algorithmica,
pp 115,
.
Note: To appear.

F. Havet and X. Zhu.
The game Grundy number of graphs.
Journal of Combinatorial Optimization,
.
Note: To appear.
[WWW
] [PDF
]
Keywords:
colouring game,
game Grundy number,
trees,
partial 2trees.
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 2tree is at most 7. 

M. AjmoneMarsan,
S. Buzzi,
L. Chiaraviglio,
M. Meo,
C. Guerrero,
F. Idzikowski,
Y. Ye,
and J. Lopez Vizcaino.
TREND: Toward Real Energyefficient Network Design.
In SustainIT 2012  The Second IFIP Conference on Sustainable Internet and ICT for Sustainability,
Pisa, Italy,
pages 16,
October 2012.
[PDF
]
Abstract: 
This paper briefly describes the objectives of the TREND (Toward Real Energyefficient 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. 

S. Baruah,
V. Bonifaci,
G. D'Angelo,
H. Li,
A. MarchettiSpaccamela,
S. Van Der Ster,
and L. Stougie.
The preemptive uniprocessor scheduling of mixedcriticality implicitdeadline sporadic task systems.
In 24th Euromicro Conference on RealTime Systems (ECRTS12),
Pisa, Italy,
pages 145154,
July 2012.
IEEE.
[WWW
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]
Abstract: 
Systems in many safetycritical 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 safetycritical 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 EDFVD (for Earliest Deadline First with Virtual Deadlines) is described for the scheduling of such mixedcriticality task systems.
Analyses of EDFVD significantly superior to previouslyknown ones are presented, based on metrics such as processor speedup factor (EDFVD is proved to be optimal with respect to this metric) and utilization bounds. 

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 1117,
2012.
ACM.
[WWW
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]
Abstract: 
In this work we study the computational power of graphbased 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 BFStree in our different models. 

S. Belhareth,
D. Coudert,
D. Mazauric,
N. Nisse,
and I. Tahiri.
Reconfiguration with physical constraints in WDM networks.
In IEEE ICC Workshop on New Trends in Optical Networks Survivability,
Ottawa, Canada,
pages 63466350,
June 2012.
IEEE.
[WWW
] [PDF
]
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 nonlinear function depending on the load of the links used by the new lightpath. We prove that determining the optimal rerouting order is NPcomplete 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. 

JC. 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 12,
December 2012.
[WWW
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]
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 SRLGdisjoint 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 NPcomplete and determine some polynomial cases. 

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 403404,
2012.
Springer, LNCS.
[WWW
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]
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 LookComputeMove} 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 nontrivial 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. 

L. Blin,
J. Burman,
and N. Nisse.
Nettoyage perpétuel de réseaux.
In 14es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 3134,
2012.
[WWW
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Abstract: 
Dans le cadre du {\it nettoyage de graphes contaminÃs} ({\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 plaÃons notre Ãtude 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 VoirCalculerAgir} 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.
Existetil 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. 

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 16,
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. 

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
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Abstract: 
The Autonomous System (AS) topology of the Internet (up to 61k ASs) is growing at a rate of about 10\ 0xbff74688er 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 largescale 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. 

G. D'Angelo,
M. D'Emidio,
D. Frigioni,
and V. Maurizio.
Engineering a new loopfree shortest paths routing algorithm.
In 11th International Symposium on Experimental Algorithms (SEA2012),
volume 7276 of Lecture Notes in Computer Science,
Bordeaux, France,
pages 123134,
June 2012.
Springer.
[WWW
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]
Abstract: 
We present LFR (Loop Free Routing), a new loopfree 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 loopfree 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 realworld 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 realworld instances, whereas DUAL is the best choice on artificial instances. 

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,
EinGedi, Israel,
pages 148158,
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 distancevector algorithms as an attractive alternative to linkstate solutions for largescale 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 distancevector 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 distancevector 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. 

G. D'Angelo,
M. D'Emidio,
D. Frigioni,
and C. Vitale.
Fully Dynamic Maintenance of ArcFlags in Road Networks.
In 11th International Symposium on Experimental Algorithms (SEA2012),
volume 7276 of Lecture Notes in Computer Science,
Bordeaux, France,
pages 135147,
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 realworld 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 speedup techniques, as for example ArcFlags, whose aim is to compute additional data in a preprocessing phase in order to accelerate the shortest paths queries in an online 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 ArcFlags 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 realworld road networks subject to fully dynamic sequences of operations.
Our experiments show a significant speedup in the updating phase of the ArcFlags, at the cost of a small space and time overhead in the preprocessing phase. 

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 327338,
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 LookComputeMove 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 socalled 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 wellstudied 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. 

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 330344,
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 LookComputeMove 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. 

O. Dalle and E. Mancini.
Integrated tools for the simulation analysis of peertopeer backup systems.
In Proceedings of the 5th International ICST Conference on Simulation Tools and Techniques,
SIMUTOOLS '12,
pages 178183,
March 2012.
ICST (Institute for Computer Sciences, SocialInformatics and Telecommunications Engineering).
[WWW
] [PDF
]
Abstract: 
In order to evaluate the performance and estimate the resource usage of peertopeer 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 metamodel for peertopeer backup systems and a toolchain, based on SimGrid, to help in their analysis.
We validated the metamodel and toolchain 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. 

F. V. Fomin,
F. Giroire,
A. JeanMarie,
D. Mazauric,
and N. Nisse.
Satisfaire un internaute impatient est difficile.
In 14es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 7982,
2012.
Note: Best paper.
[WWW
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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\'et\'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\'et\'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 NPdifficile si $G$ est cordal, et d\'ecider si $ic(G,v_0) \leq 4$ est PSPACEcomplet 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 sousgraphe 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. 

F. V. Fomin,
F. Giroire,
A. JeanMarie,
D. Mazauric,
and N. Nisse.
To Satisfy Impatient Web surfers is Hard.
In 6th International Conference on FUN with Algorithms (FUN),
volume 7288,
pages 166176,
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 NPhard.
Deciding if the surveillance number of a DAG equals 4 is PSPACEcomplete.
Moreover, computing the surveillance number is NPhard 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. 

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 247258,
May 2012.
Springer.
[WWW
] [PDF
]
Abstract: 
Recently, energyaware 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 energyaware 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 3027775643210f energy savings in comparison with the traditional energyaware routing model. 

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. 

F. Idzikowski,
R. Duque,
F. Jimenez,
E. Le Rouzic,
L. Chiaraviglio,
and M. AjmoneMarsan.
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 13,
September 2012.
[PDF
]
Abstract: 
We discuss how to save energy in IPoverWDM 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. 

A. Kosowski,
B. Li,
N. Nisse,
and K. Suchan.
kChordal Graphs: from Cops and Robber to Compact Routing via Treewidth.
In 14es Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 8386,
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 $k1$ 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 treedecomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k1$ vertices.
This allows us to prove that any $k$chordal graph with maximum degree $\Delta$ has treewidth at most $(k1)(\Delta1)+2$, improving the $O(\Delta (\Delta1)^{k3})$ bound of Bodlaender and Thilikos (1997).
Moreover, any graph admitting such a treedecomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$.
As an application, for any $n$node graph admitting such a treedecomposition, 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. 

A. Kosowski,
B. Li,
N. Nisse,
and K. Suchan.
kChordal 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 610622,
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 $k1$ 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 treedecomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k1$ vertices.
This allows us to prove that any $k$chordal graph with maximum degree $\Delta$ has treewidth at most $(k1)(\Delta1)+2$, improving the $O(\Delta (\Delta1)^{k3})$ bound of Bodlaender and Thilikos (1997).
Moreover, any graph admitting such a treedecomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$.
As an application, for any $n$node graph admitting such a treedecomposition, 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. 

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. 

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 247255,
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 lossbased 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. 

J. Araujo,
JC. 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 118,
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 endnodes. 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 NPhard 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 BranchandBound algorithms on
random celllike graphs, namely the PoissonVoronoi tessellations. 

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 4955,
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 NPcomplete problem, even if G is
bipartite. We also prove that hn(G) can be computed in polynomial time for cactus
and P4 sparse graphs.


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 peertopeer storage solutions rely on the in
troduction of redundant data to be faulttolerant 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 ReedSolomon, 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 ReedSolomon 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.


J. BangJensen,
F. Havet,
and N. Trotignon.
Finding an induced subdivision of a digraph.
In VI LatinAmerican Algorithms, Graphs and Optimization Symposium (LAGOS 2011),
volume 37,
Bariloche, Argentina,
pages 0914,
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 2cycles. We give a number of examples of polynomial instances as well as several NPcompleteness proofs.


Sanjoy Baruah, K.,
Vincenzo Bonifaci,
G. D'Angelo,
Alberto MarchettiSpaccamela,
Suzanne Ster, Van Der,
and Leen Stougie.
MixedCriticality 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 555566,
August 2011.
Springer.
[WWW
] [PDF
]
Abstract: 
We consider the scheduling of mixedcriticality task systems, that is, systems where each task to be scheduled has multiple levels of worstcase execution time estimates. We design a scheduling algorithm, EDFVD, whose effectiveness we analyze using the processor speedup metric: we show that any 2level task system that is schedulable on a unitspeed processor is correctly scheduled by EDFVD using speed $\phi$; here $\phi$ 2 criticality levels.We finally consider 2level instances on m identical machines. We prove speedup bounds for scheduling an independent collection of jobs and for the partitioned scheduling of a 2level task system. 

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 4761,
2011.
Springer.
[WWW
]
Abstract: 
Population protocols are a communication model for large
sensor networks with resourcelimited mobile agents. The agents move
asynchronously and communicate via pairwise 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 wildlife 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. 

J. Beauquier and J. Burman.
Selfstabilizing 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 selfstabilizing 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. 

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 modÄle 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. 

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 508514,
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. },
xeditorialboard={yes},
xproceedings={yes},
xinternationalaudience={yes},
xpays = {CL},
sorte = "confint",


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 Ã©tudions quelles propriÃ©tÃ©s d'un rÃ©seau peuvent Ãªtre calculÃ©es Ã partir d'une petite quantitÃ© d'informations locales fournie par ses noeuds. Notre modÃ¨le est une restriction de CONGEST, un modÃ¨le distribuÃ© classique. Il est proche du modÃ¨le de complexitÃ© de communication avec messages simultanÃ©s 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 Ã une entitÃ© centrale, le superviseur. Celuici doit alors dÃ©terminer une certaine propriÃ©tÃ© du rÃ©seau. Nous montrons que des questions telles que: ''Estce que le graphe contient un triangle? un carrÃ© ? Quel est son diamÃ¨tre?" ne peuvent pas Ãªtre rÃ©solues dans ce modÃ¨le. En revanche, pour de nombreuses classes de graphes : celles de dÃ©gÃ©nÃ©rescence bornÃ©e (incluant les graphes planaires, ceux de largeur arborescente bornÃ©e... ), les sommets peuvent succinctement donner une description complÃ¨te du graphe au superviseur. Nous laissons
ouverte la question de dÃ©cider la connexitÃ©.},
xeditorialboard={yes},
xproceedings={yes},
xinternationalaudience={no},
xpays= {CL},
sorte = "confnat",


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 rÃ©seau WDM, utiliser une nouvelle longueur d'onde dans une ï¬bre demande Ã recalibrer les autres longueurs d'ondes. Cela gÃ©nÃ¨re un coÃ»t (e.g., Ã©nergÃ©tique) qui dÃ©pend non linÃ©airement du nombre de longueurs d'ondes utilisant la ï¬bre. Lorsqu'un ensemble de requÃªtes doivent changer de chemins optiques dans le rÃ©seau (lors d'une opÃ©ration de maintenance sur un lien du rÃ©seau), l'ordre dans lequel les requÃªtes sont dÃ©placÃ©es inï¬ue sur le coÃ»t total de l'opÃ©ration. Nous initions l'Ã©tude du problÃ¨me d'optimisation correspondant. Nous prouvons que dÃ©terminer l'ordre de dÃ©placements optimal est NPcomplet pour un rÃ©seau de 2 nÅuds. Nous donnons des bornes gÃ©nÃ©rales et identiï¬ons des classes d'instances faciles. Enï¬n, nous proposons et Ã©valuons par simulations des heuristiques pour ce problÃ¨me. 

JC. Bermond,
L. Gargano,
S. Pérennes and
A.A. Rescigno,
and U. Vaccaro.
Optimal Time Data Gathering in Wireless Networks
with OmniDirectional Antennas.
In SIROCCO 2011,
volume 6796 of Lecture Notes in Computer Science,
Gdansk, Poland,
pages 306317,
June 2011.
SpringerVerlag.
[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 nonzero 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 NPcomplete. On the positive side,
we design
a simple $(1+2/m)$ factor approximation algorithm for general networks. 

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
]

C. Caillouet,
X. Li,
and T. Razafindralambo.
A Multiobjective Approach for Data Collection in Wireless Sensor Networks.
In 10th International Conference on Ad Hoc Networks and Wireless (AdHocNow),
Padderborn, Germany,
July 2011.
[WWW
]

C. Caillouet and T. Razafindralambo.
Compromis énergiedélai 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
]

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 LatinAmerican Algorithms, Graphs and Optimization Symposium (LAGOS'11),
volume 37 of Electronic Notes in Discrete Mathematics,
pages 5762,
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 $(q , q â 4)$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 $(q , q â 4)$graphs. All these coloring problems are known to be NPhard for general
graphs. 

G. Classen,
D. Coudert,
A. Koster,
and N. Nepomuceno.
A ChanceConstrained 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 3742,
June 2011.
[PDF
]
Abstract: 
In this paper, we propose a chanceconstrained 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~$42$\,\27775643210n average. 

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 16,
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) chanceconstrained 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 chanceconstrained programs and propose
cutsetbased 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. 

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 484489,
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 lowdemand scenarios. This problem relies on a fixedcharge capacitated network design (FCCND), which is very hard to optimize. We then propose heuristic algorithms to produce feasible solutions in a short time. 

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. 

G. D'Angelo,
Mattia D'Emidio,
Daniele Frigioni,
and Vinicio Maurizio.
A SpeedUp 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 578593,
June 2011.
Springer.
[WWW
] [PDF
]
Abstract: 
We propose a simple and practical speedup 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. 

G. D'Angelo,
Gabriele Di Stefano,
and Alfredo Navarra.
Bandwidth Constrained Multiinterface 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 202213,
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 Gâ=â(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 NPhard even for small values of k and $\Delta$, where $\Delta$ is the maximum degree of the network. In particular, the problem is NPhard for
any fixed kâ$\ge$â2 and $\Delta$â$\ge$â3, while it is polynomially solvable when kâ=â1, or $\Delta$â$\le$â2 and kâ=âO(1). Moreover, we show that the problem is not approximable within $\eta$logB or $\Omega$(loglogV) for any fixed kâ$\ge$â3, $\Delta$â$\ge$â3, 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 $\Delta$â$\le$â2. 

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 174185,
July 2011.
Springer.
[WWW
] [PDF
]
Abstract: 
The paper deals with a recent model of robotbased computing which makes use of identical, memoryless mobile robots placed on nodes of anonymous graphs. The robots operate in LookComputeMove 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 symmetrybreaking nor into symmetrypreserving techniques. 

G. D'Angelo,
Gabriele Di Stefano,
and Alfredo Navarra.
Maximum Flow and MinimumCost Flow in MultiInterface 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 NPHard. 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 realworld networks. 

G. D'Angelo,
Gabriele Di Stefano,
and Alfredo Navarra.
MinMax Coverage in Multiinterface 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 190201,
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 Gâ=â(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 NPhard for any fixed $\Delta$â$\ge$â5 and kâ$\ge$â16, 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((1â+âb)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. 

G. D'Angelo,
Daniele Frigioni,
and Camillo Vitale.
Dynamic ArcFlags 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 8899,
April 2011.
Springer.
[WWW
] [PDF
]
Abstract: 
In this work we introduce a new data structure, named RoadSigns, which allows us to efficiently update the ArcFlags of a graph in a dynamic scenario. RoadSigns can be used to compute ArcFlags, can be efficiently updated and do not require large space consumption for many realworld graphs like, e.g., graphs arising from road networks. In detail, we define an algorithm to preprocess RoadSigns 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 realworld road networks showing that they yields a significant speedup in the updating phase of ArcFlags, at the cost of a very small space and time overhead in the preprocessing phase. 

O. Dalle and E. Mancini.
Traces Generation To Simulate LargeScale Distributed Applications.
In S. Jain,
R. R. Creasey,
J. Himmelspach,
K. P. White,
and M. Fu, editors,
Winter Simulation Conference,
Phoenix, AZ, ÉtatsUnis,
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 lowlevel 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 postprocess them in order to feed simulation models.
We designed it to be scalable, modular and extensible. 

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, ÉtatsUnis,
pages 258263,
04 2011.
[WWW
] [PDF
]
Abstract: 
ADL are particularly well suited for componentbased 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. 

S. Felix and J. Galtier.
Shortest Paths and Probabilities on TimeDependent Graphs  Applications to Transport Networks.
In Proceedings of the 11th International Conference on ITS Telecommunications,
Saint Petersburg, Russia,
pages 5662,
August 2011.
[WWW
]
Abstract: 
In this paper, we focus on timedependent graphs
which seem to be a good way to model transport networks. In
the first part, we remind some notations and techniques related
to timedependent 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. 

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 rÃ©centes Ã©tudes montrent que la charge de trafic des
routeurs n'a qu'une faible influence sur leur consommation
Ã©nergÃ©tique. Par consÃ©quent, la consommation dans les rÃ©seaux est
fortement liÃ©e au nombre d'Ã©quipements du rÃ©seau activÃ©s (interfaces,
chassis, etc). Dans un objectif de minimisation de l'Ã©nergie dans les
rÃ©seaux, il est intÃ©ressant de minimiser le nombre (pondÃ©rÃ©)
d'Ã©quipements utilisÃ©s lors du routage. Dans cet article, nous
considÃ©rons une architecture simplifiÃ©e oÃ¹ un lien entre deux routeurs
relie deux interfaces. Quand un lien n'est pas activÃ©, les deux
interfaces correspondantes peuvent Ãªtre Ã©teintes. Par consÃ©quent, afin
de rÃ©duire la consommation d'Ã©nergie, l'objectif est de trouver un
routage qui minimise le nombre de liens utilisÃ©s et satisfait toutes
les demandes. Nous montrons des rÃ©sultats d'inapproximabilitÃ© de ce
problÃ¨me, mÃªme si l'on considÃ¨re des instances particuliÃ¨res. Nous
prouvons des bornes en gÃ©nÃ©ral et pour des topologies particuliÃ¨res
telles que la grille, l'arbre ou le graphe complet. Nous proposons
ensuite une heuristique dont nous Ã©valuons les performances Ã l'aide
de simulations sur des topologies rÃ©elles. Nous Ã©tudions ensuite
l'impact de ces solutions efficaces en Ã©nergie sur la tolÃ©rance aux
pannes et sur la longueur moyenne des routes. 

Y. Liu and G. Simon.
PeerAssisted Timeshifted Streaming Systems: Design and Promises.
In IEEE International Conference on Communications (ICC'2011),
Kyoto, Japan,
06 2011.
IEEE.
[PDF
]
Abstract: 
Timeshifted streaming (or catchup TV) allows viewers to watch their TV programs within an expanded time window. In this paper, we emphasize the challenging characteristics of timeshifted TV systems that prevent known delivery systems to be used. We model timeshifted TV as multipleinterval graph, then we present a PeerAssisted CatchUp 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 catchup 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 selfadaptive unstructured peertopeer systems. 

F. Maffray and G. Morel.
Algorithmes linÃ©aires pour les graphes sans $P_5$ 3colorables.
In 12e congrès annuel de la ROADEF,
2011.

E. AlvarezMiranda,
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 1324,
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 NPhard in general, and it is polynomialtime solvable when graphs $G$ are restricted to 2trees. 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 $\frac{ y_vp_v^}{p_v^+p_v^}$ 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 polynomialtime algorithms for these problems on 2trees, respectively. Our study shows that the risk models have advantages over the tradional robust optimization model, which yields NPhard problems even if the original optimization problems are polynomialtime solvable. 

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 3338,
March 2010.
[PDF
]
Abstract: 
Given an undirected graph G = (V, E) and a weight function w : V â 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 NPhard 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 P4sparse 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, P4free graphs) are P4sparse, and that P4sparse graphs are P5free. The WEIGHTED COLORING problem is in P on cographs [3] and NPhard on P5free graphs [4]. We show that WEIGHTED COLORING can be solved in polynomial time on a subclass of P4sparse graphs that strictly contains cographs, and we present a 2approximation algorithm on general P4sparse graphs. The complexity of WEIGHTED COLORING on P4 sparse graphs remains open. 

J. Beauquier and J. Burman.
Selfstabilizing 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 362378,
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{selfstabilizing} (a tolerating statecorrupting 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 constantstate agents. Hence, we assume an existence of resourceunlimited 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. 

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 305314,
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 semilinear 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. 

JC. 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 minislots (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. 

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). 

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 noninterfering 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. 

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 7588,
September 2010.
[PDF
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Keywords:
P2P storage system,
data placement,
performance,
data durability,
Markov chain model.
Abstract: 
Peertopeer 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. 

S. Caron,
F. Giroire,
D. Mazauric,
J. Monteiro,
and S. Pérennes.
P2P Storage Systems: Data Life Time for Different Placement Policies.
In Maria Gradinariu PotopButucaru et Hervé Rivano, editor,
12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
Belle Dune France,
pages 4p,
2010.
[WWW
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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. 

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 copwin graphs as dismantlable graphs. In this talk, we will characterize in a similar way the class CWFR(s, s') of copwin 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 copwin graphs for this game with s'< s and Gromovâs hyperbolicity. In the particular case s' = 1 and s = 2, we prove that the class of copwin graphs is exactly the wellknown 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 copwin graphs (which we call kwinnable 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 kwinnable for any value of k. 

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 121132,
June 2010.
Springer.
Note: Http://hal.inria.fr/inria00495443.
[WWW
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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. 

N. Cohen,
D. Coudert,
D. Mazauric,
N. Nepomuceno,
and N. Nisse.
Tradeoffs in routing reconfiguration problems.
In Maria Gradinariu PotopButucaru et Hervé Rivano, editor,
12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
Belle Dune France,
pages 4p,
2010.
[WWW
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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. 

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
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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 

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
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Abstract: 
The properties found in complex networks (e.g., smallworld, scalefree) 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 networkâs 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. 

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%.

P. Giabbanelli,
D. Mazauric,
and JC. 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 112,
2010.
SpringerVerlag.
[PDF
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Abstract: 
The average shortest path distance between all pairs of nodes in realworld networks tends to be small compared to the number of nodes. Providing a closedform 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 graphtheoretic techniques to establish a closedform 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 firstorder 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 firstorder 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 graphtheoretic and probabilistic techniques. 

P. Giabbanelli,
D. Mazauric,
and S. Pérennes.
Computing the average path length and a labelbased routing in a smallworld graph.
In 12èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel'10),
Belle Dune France,
pages 4p,
2010.
[WWW
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Keywords:
Recursive graph,
Labeling scheme,
Decentralized routing.
Abstract: 
{W}e study two characteristics of a smallworld 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 closedform formula of the average distance, proved using the recursive structure. {T}hus, we characterize that the graph is smallworld and not ultra smallworld as was still possible. {O}ur proof is of particular interest for other graphs based on similar recursive structures. 

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
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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 polynomialtime constantfactor 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 mediumsized 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. 

F. Giroire,
J. Monteiro,
and S. Pérennes.
PeertoPeer Storage Systems: a Practical Guideline to be Lazy.
In Proceedings of the IEEE Global Communications Conference (GLOBECOM),
Miami, EUA,
pages 16,
12 2010.
[WWW
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Abstract: 
Distributed and peertopeer storage systems are foreseen as an alternative to the traditional data centers and inhouse backup solutions. In the past few years many peerto 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 closedform 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 closeform formulas to estimate the bandwidth consumption for a lazy repair, and the loss rate taking into account the repair time. 

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
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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), mÃÂªme 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) oÃÂ¹ l'agent choisit al\'eatoirement une arÃÂªte incidente, et celles (A) oÃÂ¹ 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, extrÃÂªmes 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 ÃÂªtre 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 mÃÂªme lorsque l'agent a le sens de l'orientation. 

N. Hanusse,
D. Ilcinkas,
A. Kosowski,
and N. Nisse.
Locating a target with an agent guided by unreliable local advice.
In 29th ACM SIGACTSIGOPS Symposium on Principles of Distributed Computing (PODC'10),
volume XXXX,
pages 10p,
2010.
ACM.
Note: To appear.
[PDF
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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 worstcase 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 $k$ 

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 170179,
December 2010.
[PDF
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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 NPcomplete. We then show that deciding if $\Gamma(G)\geq V(G)k$ is fixed parameter tractable with respect to the parameter $k$. 

L. Hogie,
D. Papadimitriou,
I. Tahiri,
and F. Majorczyk.
Simulating routing schemes on largescale topologies.
In 24th ACM/IEEE/SCS Workshop on Principles of Advanced and Distributed Simulation (PADS),
Atlanta,
pages 8p,
May 2010.
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 underdevelopment routing protocols on the Internet is not practicable at a largescale (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 interdomain 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 largescale simulations of (interdomain) 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. 

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
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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\¨F÷¿Põ (!
ingle segment protections. In SSPO, we study the extra protection capabilities, node failure and dual link failure survivability, offered by the single 100\é2ingle 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. 

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\¨F÷¿Põ È!
ingle segment protections. In SSPO, we study the extra protection capabilities, node failure and dual link failure survivability, offered by the single 100\é2ingle 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. 

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 585596,
2010.
Schloss Dagstuhl  LeibnizZentrum fuer Informatik.
[WWW
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]
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 NPhard 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 NPcomplete, 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{MCTrapezoid}. 

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 1520,
2010.
[WWW
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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 rÃ©partis entre les pairs. {N}ous Ã©tudions dans ce rapport l'impact des diffÃ©rents 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 particuliÃ¨rement, 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. 

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 

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,
1519 March 2010.
[WWW
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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 postprocessing. {I}n this paper, we address issues related to the management of these data and their online 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 adhoc instrumentation and data processing. {I}n this paper, we propose {OSIF}, a new componentbased 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}. 

P. Uribe,
JC. 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 18,
1519 March 2010.

E. Altman,
P. Nain,
and JC. 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
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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 statedependent ({\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. 

J. Araujo,
N. Cohen,
F. Giroire,
and F. Havet.
Good edgelabelling of graphs.
In proceedings of the LatinAmerican Algorithms, Graphs and Optimization Symposium (LAGOS'09),
volume 35 of Electronic Notes in Discrete Mathematics,
Gramado, Brazil,
pages 275280,
December 2009.
Springer.
[PDF
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Abstract: 
A good edgelabelling 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 nondecreasing labels. This notion was introduced in [JC. Bermond, M. Cosnard, and S. PÃ©rennes. Directed acyclic graphs with unique path property. Technical Report RR6932, 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 edgelabelling. First, we exhibit infinite families of graphs for which no such edgelabelling can be found. We then show that deciding if a graph admits a good edgelabelling is NPcomplete. Finally, we give large classes of graphs admitting a good edgelabelling: C3free outerplanar graphs, planar graphs of girth at least 6, subcubic {C3,K2,3}free graphs. 

J. Araujo and C. Linhares Sales.
Grundy number on $P_4$classes.
In proceedings of the LatinAmerican Algorithms, Graphs and Optimization Symposium (LAGOS'09),
volume 35 of Electronic Notes in Discrete Mathematics,
Gramado, Brazil,
pages 2127,
December 2009.
Springer.
[PDF
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Abstract: 
In this article, we define a new class of graphs, the fatextended P4laden 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: P4reducible, extended P4reducible, P4sparse, extended P4sparse, P4extendible, P4lite, P4tidy, P4laden and extended P4laden, which are all strictly contained in the fatextended P4laden class. 

J. Araujo,
P. Moura,
and M. Campêlo.
Sobre a complexidade de Coloração Mista.
In Encontro Regional de Pesquisa Operacional do Nordeste,
Fortaleza, Brazil,
pages 110,
December 2009.
[PDF
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Abstract: 
Grafos mistos sËao estruturas matemÂ´aticas que mesclam caracterÂ´Ä±sticas de grafos direcionados e nËaodirecionados. Formalmente, um grafo misto pode ser definido por uma tripla GM = (V; A;E), onde V , A e E representam, respectivamente, um conjunto de vÂ´ertices, de arcos e de arestas. Uma kcoloracÂ¸ Ëao mista de GM = (V; A;E) Â´e funcÂ¸ Ëao c : V ! f0; : : : ; k Â¡ 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 ColoracÂ¸ Ëao Mista consiste em determinar o nÂ´umero cromÂ´atico misto de GM, denotado por ÃM(GM), que Â´e menor inteiro k tal que GM admite uma kcoloracÂ¸ Ëao mista. Esse problema modela variacÂ¸ Ëoes de problemas de escalonamento que consideram simultaneamente restricÂ¸ Ëoes de precedËencia e de compartilhamento de recursos. Neste trabalho, mostramos que ColoracÂ¸ Ëao Mista Â´e NPdifÂ´Ä±cil para as classes dos grafos cordais, dos grafos linha de grafos bipartidos e dos grafos linha de grafos periplanares. 

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 2736,
August 2009.
ACM.
[PDF
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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 Ã¢â¬ÅtailÃ¢â¬ 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. 

JC. 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 809820,
May 2009.
Springer.
[WWW
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]
Abstract: 
AllOptical Label Switching (AOLS) is a new technology that performs forwarding without any OpticalElectricalOptical (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. 

JC. 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 5771,
May 2009.
Springer.
[WWW
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Abstract: 
AllOptical Label Switching (AOLS) is a new technology that performs packet forwarding without any OpticalElectricalOptical (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 nonexistence 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 polynomialtime dynamic programming algorithm for a bounded number of sources, thus extending the algorithm of~\cite{BCM+09b} for a single source. 

JC. Bermond,
D. Mazauric,
and P. Nain.
Algorithmes distribués d'ordonnancement dans les réseaux sansfil.
In 10èmes Journées Doctorales en Informatique et Réseaux (JDIR),
Belfort, France,
February 2009.
[PDF
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Abstract: 
Nous consid\'erons dans cet article le probl\`eme d'ordonnancement distribu\'e dans les r\'eseaux sansfil. 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. 

JC. 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
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Abstract: 
Nous prÃ©sentons des algorithmes efficaces pour la collecte d'informations par une station de base au sein d'un rÃ©seau sansfil multi sauts en prÃ©sence d'interfÃ©rences. Nous nous focalisons sur les rÃ©seaux en grille car ils sont un bon modÃ¨le des rÃ©seaux d'accÃ¨s comme des rÃ©seaux alÃ©atoires de capteurs. Le temps est divisÃ© en Ã©tapes Ã©lÃ©mentaires. Au cours d'une Ã©tape, un nÅud peut transmettre au plus un message Ã l'un de ces voisins. Chaque appareil est Ã©quipÃ© d'un interface half duplex et ne peut donc Ã©mettre et recevoir Ã la mÃªme Ã©tape. Ainsi, au cours d'une Ã©tape, l'ensemble des transmissions valides induit un couplage de la grille. Le problÃ¨me consiste Ã minimiser le nombre d'Ã©tapes nÃ©cessaires Ã la collecte de tous les messages par la station de base. Le meilleur algorithme connu Ã©tait une 3/2 approximation. Nous donnons un algorithme trÃ¨s simple qui approche l'optimum Ã 2 prÃ¨s, puis nous prÃ©sentons un algorithme plus Ã©voluÃ© qui est une +1 approximation. Nos rÃ©sultats sont valides lorsque les appareils ne disposent d'aucune mÃ©moire tampon et doivent retransmettre un message Ã l'Ã©tape suivant sa rÃ©ception. 

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 (AdHocNow),
volume 5793 of Lecture Notes in Computer Science,
pages 6982,
2009.
Springer.
[WWW
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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 opengrids was a multiplicative 1.5approximation 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. 

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 1726,
July 2009.
Springer.
[WWW
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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 scientiÂ¯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. 

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 126140,
May 2009.
SpringerVerlag.
[PDF
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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. 

N. Cohen,
F. V. Fomin,
G. Gutin,
E. J. Kim,
S. Saurabh,
and A. Yeo.
Algorithm for Finding Vertex Outtrees and Its Application to Internal Outbranching Problem.
In 15th Annual International Conference on Computing and Combinatorics (COCOON),
volume 5609 of Lecture Notes in Computer Science,
pages 3746,
2009.
[WWW
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Abstract: 
An outtree T is an oriented tree with exactly one vertex of indegree zero and a vertex x of T is called internal if its outdegree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a subgraph isomorphic to a given outtree with k vertices. Both algorithms run in Oâ(5.704^k) time. We apply the deterministic algorithm to obtain an algorithm of runtime Oâ(c^k), where c is a constant, for deciding whether an input digraph contains a spanning outtree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM'08). 

N. Cohen,
F. Havet,
and T. Müller.
Acyclic edgecolouring 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 417421,
September 2009.
[PDF
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Abstract: 
A proper edgecolouring with the property that every cycle contains edges of at least three distinct colours is called an {\it acyclic edgecolouring}. The {\it acyclic chromatic index} of a graph $G$, denoted $\chi'_a(G)$ is the minimum $k$ such that $G$ admits an {\it acyclic edgecolouring} 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 $\chi'_a(G)\leq \Delta(G) + 25$. 

D. Coudert,
F. Giroire,
and I. Sau.
EdgeSimple 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 134145,
June 2009.
Springer.
[WWW
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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{edgesimple} 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 edgesimple 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. 

D. Coudert,
F. Huc,
D. Mazauric,
N. Nisse,
and JS. 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
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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. 

D. Coudert,
F. Huc,
D. Mazauric,
N. Nisse,
and JS. 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
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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 preestablished 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 precomputed 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 copsandrobber 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. 

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 109116,
March 2009.
Elsevier.
[WWW
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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 predetermined 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 NPcomplete 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]. 

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 Ã©tudions la minimisation de la consommation d'Ã©nergie des rÃ©seaux sansfil fixes Ã transmission par liens microondes, par l'optimisation jointe du routage des flux de donnÃ©es et la sÃ©lection de la configuration des liens. Nous prÃ©sentons une formulation mathÃ©matique exacte basÃ©e sur un multiflot entier de coÃ»t minimum avec des fonctions de coÃ»t en escalier, rendant le problÃ¨me trÃ¨s difficile Ã rÃ©soudre. Nous proposons ensuite une fonction linÃ©aire par morceaux convexe, obtenue par interpolation linÃ©aire des points de configuration efficaces en Ã©nergie, qui fournit une bonne approximation de la consommation d'Ã©nergie sur les liens, et prÃ©sentons une relaxation qui exploite la convexitÃ© des fonctions de coÃ»t. Ceci rapporte des limites infÃ©rieures sur la consommation d'Ã©nergie, et finalement un algorithme heuristique basÃ© sur l'optimum fractionnaire est utilisÃ© pour produire des solutions rÃ©alisables. Les rÃ©sultats attestent du potentiel de notre nouvelle approche. 

D. Coudert,
N. Nepomuceno,
and H. Rivano.
Minimizing Energy Consumption by PowerEfficient 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 powerefficient configuration can be characterized by a modulation constellation size and a transmission power level. Every link holds a set of powerefficient 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." 

O. Dalle,
F. Giroire,
J. Monteiro,
and S. Pérennes.
Analyse des Corrélations entre Pannes dans les Systèmes de Stockage PairàPair.
In Augustin Chaintreau and Clemence Magnien, editors,
11ème rencontres francophones sur les Aspects Algorithmiques des Télécommunications (Algotel'2009),
CarryLeRouet France,
pages 4p,
2009.
Note: Best Student Paper Award.
[WWW
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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 celleci 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 celleci 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. 

O. Dalle,
F. Giroire,
J. Monteiro,
and S. Pérennes.
Analysis of Failure Correlation Impact on PeertoPeer Storage Systems.
In Proceedings of the 9th IEEE International Conference on PeertoPeer Computing (P2P),
pages 184193,
September 2009.
[WWW
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Abstract: 
Peertopeer storage systems aim to provide a reliable longterm storage at low cost. In such systems, peers fail continuously, hence, the necessity of selfrepairing 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. 

A. Ferreira.
Roadmapping the Digital Revolution: Visions from COST Foresight 2030 (An exercise in multidisciplinarity).
In Proceedings of IEEE Wireless VITAE'09,
Aalborg, Denmark,
pages 5p,
May 2009.
IEEE Press.
[PDF
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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 multidisciplinary 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. 

M. Flammini,
A. MarchettiSpaccamela,
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 154162,
August 2009.
ACM.
[WWW
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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, NPcomplete results, approximation algorithms, and inapproximability results. 

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 112,
May 2009.
IEEE.
[WWW
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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 NPhard already for g = 2. We present a 4approximation 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. 

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 639645,
September 2009.

P. Giabbanelli.
Why having inperson lectures when elearning and podcasts are available?.
In Proceedings of the 14th Western Canadian Conference on Computing Education (ACM SIGCSE),
pages 4244,
2009.

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 326345,
September 2009.
[PDF
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Abstract: 
We describe a method to detect botnet command and control traffic and individual endhosts. We introduce the notion of Ã¢â¬ destination traffic atomsÃ¢â¬ which aggregate the destinations and services that are communicated with. We then compute the Ã¢â¬ persistenceÃ¢â¬ , 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 apriori 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. 

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 320323,
October 2009.
[PDF
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Keywords:
P2P storage system,
data placement,
performance evaluation,
data durability.
Abstract: 
Large scale peertopeer 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. 

C. Gomes and J. Galtier.
Optimal and Fair Transmission Rate Allocation Problem in Multihop Cellular Networks.
In 8th International Conference on ADHOC Networks & Wireless (ADHOC NOW),
volume 5793 of Lecture Notes in Computer Science,
Murcia, Spain,
pages 327340,
September 2009.
Springer.
[PDF
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Abstract: 
We deal with the rate allocation problem for downlink in a Multihop 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 singlehop cellular network problem. The validity of our proof is confirmed experimentally. 

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 139143,
September 2009.
[PDF
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Abstract: 
A \emph{star} is an arborescence in which the root dominates all the other vertices. A \emph{galaxy} is a vertexdisjoint 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 NPcomplete (even when restricted to acyclic digraphs) but that it becomes polynomialtime solvable when restricted to strongly connected digraphs. 

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
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Keywords:
réseau mobile adhoc,
graphe dynamique,
MANET,
connexité,
algorithme.
Abstract: 
Avec la multiplication des terminaux communiquant, les r\'eseaux adhoc 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. 

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
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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. 

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
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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. 

K. Kawarabayashi and B. Reed.
A nearly linear time algorithm for the half integral parity disjoint paths packing problem.
In Proceedings of the ACMSIAM Symposium on Discrete Algorithm (SODA 2009),
pages 11831192,
January 2009.
[WWW
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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 RobertsonSeymour 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. 

K. Kawarabayashi and B. Reed.
Hadwiger's Conjecture is decidable.
In 41th ACM Symposium on Theory of Computing (STOC 2009),
pages 445454,
2009.
[WWW
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Abstract: 
The famous Hadwiger's conjecture asserts that every graph with no Ktminor is (t1)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 wellknown result by Thomassen [46] for 5listcoloring 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 (t1)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 Ktminor nor is (t1)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 4coloring 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 t5 such that GZ 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. 

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 4751,
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. 

Z. Li and I. Sau.
Graph Partitioning and Traffic Grooming with Bounded Degree Request Graph.
In 35th International Workshop on GraphTheoretic Concepts in Computer Science (WG 2009),
volume 5911 of Lecture Notes in Computer Science,
pages 250261,,
June 2009.
Note: Best student paper award.
[PDF
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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 AddDrop 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 $C1$, $C\geq 4$, and the request graph does not contain a perfect matching. In particular, we answer a conjecture of~[Mu{\~n}oz and Sau, WG 08] . 

C. Linhares Sales and L. Sampaio.
bcoloring of mtight graphs.
In T. Liebling and J. Szwarcfiter, editors,
LAGOS'09  V LatinAmerican Algorithms, Graphs and Optimization Symposium,
volume 35 of Electronic Notes in Discrete Mathematics,
Gramado, Brazil,
pages 209  214,
March 2009.
Elsevier.
[WWW
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JC. 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
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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++ INETFramework 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. 

JC. 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
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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 componentbased design must be adopted in order to build a tool for generating valuable performance results. 

G. Mertzios,
I. Sau,
and S. Zaks.
A New Intersection Model and Improved Algorithms for Tolerance Graphs.
In 35th International Workshop on GraphTheoretic Concepts in Computer Science (WG 2009),
volume 5911 of Lecture Notes in Computer Science,
pages 285295,
06 2009.
[PDF
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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 constraintbased temporal reasoning, resource allocation and scheduling problems, among others. In this article we propose the first nontrivial intersection model for general tolerance graphs, given by threedimensional 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. 

C. Molle and ME. Voge.
Effects of the Acknowledgment Traffic on the Capacity of Wireless Mesh Networks.
In 69th IEEE Vehicular Technology Conference (VTC2009Spring),
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 crosslayer 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. Crosslayer 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. 

M. Molloy and B. A. Reed.
Asymptotically optimal frugal colouring.
In Proceedings of Twentieth Annual ACMSIAM Symposium on Discrete Algorithms (SODA),
pages 106114,
2009.
[WWW
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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(â) term. We also provide an efficient algorithm to produce such a colouring. 

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 252265,
2009.
SpringerVerlag.
[PDF
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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 kchordal 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 kchordal graphs, our routing scheme achieves an additive stretch of at most k Ã¢ÂÂ 1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k Ã¢ÂÂ 1.
In order to compute the routing tables of any nnode 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{Ã¢ÂÂD, n}), where Ã¢ÂÂ 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 3chordal graphs). The routing scheme uses addresses of size log n bits and local memory of size 2(d Ã¢ÂÂ 1) log n bits in a node of degree d. 

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
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Abstract: 
{OSA} ({O}pen {S}imulation {A}rchitecture) is a collaborative platform for componentbased discreteevent 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 componentbased framework, layered patterns and aspectoriented programming. {I}n cases studies, the {OSA} project is among others involved in a largescale simulation, and
a distributed simulation over the {REST}ful protocol. 

I. Sau and D. M. Thilikos.
On SelfDuality of Branchwidth in Graphs of Bounded Genus.
In 8th Cologne Twente Workshop on Graphs and Combinatorial Optimization (CTW),
Paris, France,
pages 1922,
June 2009.
[PDF
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Abstract: 
A graph parameter is selfdual in some class of graphs embeddable in some surface if its value does not change in the dual graph more than a constant factor. Selfduality has been examined for several widthparameters, such as branchwidth in graphs in some surface. In this direction, we prove that ${\mathbf bw}(G^*) \leq 6\times {\mathbf bw}(G) +2g4$ for any graph $G$ embedded in a surface of Euler genus $g$. 

I. Sau and D. M. Thilikos.
Subexponential Parameterized Algorithms for BoundedDegree 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 5966,
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. 

A. Silva,
P. Reyes,
and M. Debbah.
Congestion in Randomly Deployed Wireless AdHoc 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 AdHoc Networks,
Wireless Sensor Networks.
Abstract: 
Congestion in wireless adhoc 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: nodelevel congestion, which is caused by buffer overflow in the node, or linklevel congestion, when wireless channels are shared by several nodes arising in collisions. We study a measure of linklevel congestion in static wireless adhoc 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. 

F. Solano Donado and J. Moulierac.
Routing in AllOptical Label Switchedbased Networks with Small Label Spaces.
In 13th Conference on Optical Network Design and Modeling (ONDM),
Braunschweig, Germany,
pages 6p,
February 2009.
IFIP/IEEE.
[WWW
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Abstract: 
With the development of AllOptical Label Switching (AOLS) network, nodes are capable of forwarding labeled packets without performing OpticalElectricalOptical (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. 

L. AddarioBerry,
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 4152,
July 2008.
Springer.

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 1120,
2008.
Springer.
[WWW
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]
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. 

O. Amini,
S. Griffiths,
and F. Huc.
4cycles in mixing digraphs.
In Electronic Notes in Discrete MathematicsVolume 30, The IV LatinAmerican Algorithms, Graphs, and Optimization Symposium (LAGOS 07),
volume 30,
Puerto Varas, Chile,
pages 6368,
February 2008.
[PDF
]
Abstract: 
It is known that every simple graph with $n^{3/2}$ edges contains a 4cycle. A similar statement for digraphs is not possible since no condition on the number of edges can guarantee an (oriented) 4cycle. We find a condition which does guarantee the presence of a 4cycle 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. 

O. Amini,
D. Peleg,
S. Pérennes,
I. Sau,
and S. Saurabh.
DegreeConstrained Subgraph Problems : Hardness and Approximation Results.
In 6th International Workshop on Approximation and Online Algorithms (ALGOWAOA 2008),
volume 5426 of Lecture Notes in Computer Science,
Karlsruhe, Germany,
pages 2942,
September 2008.
[PDF
]
Abstract: 
A general instance of a \sc DegreeConstrained Subgraph problem consists of an edgeweighted or vertexweighted 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 DegreeConstrained 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 DegreeBounded 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 NPhard 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 lowdegree 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 DegreeDense $k$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 $\delta < 1/3$. 

O. Amini,
I. Sau,
and S. Saurabh.
Parameterized Complexity of the Smallest DegreeConstrained Subgraph Problem.
In The International Workshop on Parameterized and Exact Computation (IWPEC 2008),
volume 5008 of Lecture Notes in Computer Science,
Victoria, Canada,
pages 1329,
May 2008.
[PDF
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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 fixedparameter 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 MultiColor Clique}. In the second part of the paper we provide {\em explicit} fixedparameter tractable (FPT) algorithms for the problem in graphs with bounded local treewidth and graphs with excluded minors, {\em faster} than those coming from the metatheorem of Frick and Grohe [FrickG01] about problems definable in first order logic over ``locally treedecomposable structures". In particular, this implies faster fixedparameter tractable algorithms in planar graphs, graphs of bounded genus, and graphs with bounded maximum degree.}, OPTxeditorialboard={yes}, OPTxproceedings={yes}, OPTxinternationalaudience={yes}, sorte = "confint", 

M. Asté,
F. Havet,
and C. LinharesSales.
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
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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 CoNPComplete to decide if $\Gamma(G)\leq c\times \chi(G)$ and it is CoNPComplete to decide if $\Gamma(G)\leq c\times \omega(G)$. 

JC. 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,
VillarssurOllon, Switzerland,
pages 262276,
June 2008.
SpringerVerlag.
[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 halfduplex 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 multihop wireless network and the time is slotted so that onehop 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. 

JC. Bermond and ML. Yu.
Optimal gathering algorithms in multihop radio tree networks with interferences.
In Proceedings of the 7th international conference on Ad Hoc Networks and Wireless (AdHocNow),
volume 5198 of Lecture Notes in Computer Science,
pages 204217,
September 2008.
Springer.
[PDF
]
Abstract: 
We study the problem of gathering information from the nodes of a multihop radio network into a predefined 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 unitlength 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. 

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 500501,
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. 

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),
SaintMalo,
pages 3740,
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. 

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 546550,
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 NPcomplete. 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. 

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 ON016,
Beijing, China,
pages 5170  5174,
May 2008.
[WWW
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]
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 NPcomplete 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. 

O. Dalle,
B.P. Zeigler,
and G.A. Wainer.
Extending DEVS to support multiple occurrence in componentbased 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 followup 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 multioccurrence 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. 

F. Giroire,
J. Chandrashekar,
G. Iannaccone,
D. Papagiannaki,
E. Schooler,
and N. Taft.
The Cubicle vs. The Coffee Shop: Behavioral Modes in Enterprise EndUsers.
In Proceeding of the Passive and Active Monitoring conference (PAM08),
volume 4979 of Lecture Notes in Computer Science,
pages 202211,
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 inthenetwork 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 endhosts for approximately 5 weeks, we study how endhost 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 endhost 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. 

C. Gomes,
G. Huiban,
and H. Rivano.
A BranchandPrice Approach to the Bandwidth Allocation Problem in Wireless Networks.
In International Symposium on Combinatorial Optimization (CO),
pages 1p,
March 2008.
Note: Abstract.
[PDF
]

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
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Abstract: 
Wireless Mesh Networks (WMNs) are costeffective 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 maxmin bandwidth guarantee. 

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
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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. 

C. Gomes,
S. Pérennes,
and H. Rivano.
Bottleneck Analysis for Routing and Call Scheduling in Multihop Wireless Networks.
In 4th IEEE Workshop on Broadband Wireless Access (BWA),
NewOrleans, 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 minimumlength schedule of selected links in a TDMA (Time Division Multiple Access) based wireless network. As we deal with multihop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. We present a crosslayer formulation of the problem that computes joint routing and scheduling. We use a branchandprice algorithm to solve optimally the problem. A column generation algorithm is used to cope with the exponential set of rounds. The branchandbound algorithm provides monorouting. 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 RoundUp Property (IRUP) seems to hold for our problem. 

F. Havet,
B. Reed,
and J.S. Sereni.
L(2,1)labelling of graphs.
In Proceedings of the ACMSIAM Symposium on Discrete Algorithm (SODA 2008),
pages 621630,
January 2008.
[WWW
] [PDF
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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. 

L. Hogie,
G. Danoy,
P. Bouvry,
and F. Guinand.
A ContextAware 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 507519,
September 2008.
Springer.
[PDF
]
Abstract: 
Delay Tolerant Networks (DTNs) are a subclass of mobile ad hoc networks (MANETs). They are mobile wireless networks that feature inherent connection disruption. In particular such net works are generally nonconnected. 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 ContextAware 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 costeffectiveness of CABP is enlightened. 

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 127137,
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 NPhard, 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. 

F. Huc,
C. LinharesSales,
and H. Rivano.
The Proportional Colouring Problem: Optimizing Buffers in Radio Mesh Networks.
In IV LatinAmerican Algorithms, Graphs, and Optimization Symposium (LAGOS 07),
volume 30 of Electronic Notes in Discrete Mathematics,
Puerto Varas, Chile,
pages 141146,
February 2008.
Elsevier.
[PDF
]
Abstract: 
In this paper, we consider a new edge colouring problem: the proportional edgecolouring. 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 NPhard. 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. 

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
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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 mÃªmes, et doit v\'erifier les trois propri\'et\'es suivantes: (1)~{\it connexit\'e} : la zone nettoy\'ee doit toujours Ãªtre 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 Ãªtre 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 Ãªtre 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 faÃ§on 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 faÃ§on 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 faÃ§on 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 faÃ§on monotone connexe r\'eparti. 

K. Kawarabayashi and B. Reed.
A nearly linear time algorithm for the half integral disjoint paths packing.
In Proceedings of the ACMSIAM Symposium on Discrete Algorithm (SODA 2008),
pages 446454,
2008.
[PDF
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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. 

Z. Li and B. Reed.
Optimization and Recognition for ${K}_5$minor Free Graphs in Linear Time.
In Proceedings of LATIN,
pages 206215,
2008.

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
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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. 

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 171185,
November 2008.
[WWW
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Abstract: 
Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum perflow 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 primaldual 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. 

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
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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. 

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
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Abstract: 
Dans cet article, nous \'etudions la capacit\'e des r\'eseaux radio maill\'es d\'edi\'es Ã l'acc\`es Ã 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. 

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
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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. 

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 4157,
September 2008.
Note: Third prize in the CLEI'08 Master's Thesis Contests.
[PDF
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Abstract: 
The assessment of routing protocols for ad hoc networks is a difficult task, due to the networksâ highly dynamic behavior and the absence of benchmarks. Recently, a graph theoretic model â the evolving graphs â 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 adhoc 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. 

X. Muñoz and I. Sau.
Traffic Grooming in Unidirectional WDM Rings with BoundedDegree Request Graph.
In 34th International Workshop on GraphTheoretic Concepts in Computer Science (WG 2008),
volume 5344 of Lecture Notes in Computer Science,
pages 300311,
June 2008.
[PDF
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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 graphtheoretical 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. 

N. Nisse and K. Suchan.
Fast Robber in Planar Graphs.
In Proceedings of the 34th International Workshop on GraphTheoretic Concepts in Computer Science (WG),
volume 5344 of Lecture Notes in Computer Science,
pages 3344,
2008.
[WWW
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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 copnumber} 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 copnumber of planar graphs becomes unbounded. More precisely, we prove that $\Omega(\sqrt{\log n})$ cops are necessary to capture a fast robber in the $n \times n$ squaregrid. This proof consists in designing an elegant evasionstrategy for the robber. Then, it is interesting to ask whether a high value of the copnumber 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 copnumber 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 copnumber. Note that, generally, the copnumber of a graph $H$ is not closed by taking induced subgraphs $G$, even if $H$ is planar and $G$ is an distancehereditary inducedsubgraph. 

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
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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 copnumber} 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 sousgraphe 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. 

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
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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. 

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 561573,
December 2007.
SpringerVerlag.
[WWW
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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 AddDrop 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, 44:194202, 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 edgedisjoint 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 polynomialtime 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. 

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 4548,
May 2007.
[WWW
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Abstract: 
Le groupage est un problÃ¨me central dans l'Ã©tude des rÃ©seaux optiques. Dans cet article, on propose le premier rÃ©sultat d'inapproximabilitÃ© pour le problÃ¨me du groupage, en affirmant la conjecture de Chow et Lin (2004, Networks, 44, 194202), selon laquelle le groupage est APXcomplet. On Ã©tudie aussi une version amortie du problÃ¨me de sousgraphe le plus dense dans un graphe donnÃ©: trouver le sousgraphe de taille minimum ayant le degrÃ© minimum au moins d, d>=3. On dÃ©montre que ce dernier n'a pas d'approximation Ã un facteur constant. 

O. Amini and B. Reed.
List Colouring Constants of Triangle Free Graphs.
In IV LatinAmerican Algorithms, Graphs and Optimization Symposium (LAGOS 07),
Puerto Varas, Chile,
pages 6p,
November 2007.
[WWW
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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, 149153) 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 â L(v) is triangle free and has maximum degree at most \Delta. 

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
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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 NPhard to determine the chromatic number of a graph. The Theorem of HajÂ´os [HajÂ´os, 1961] shows a necessary and sufficient condition to a graph have chromatic number at least k: the graph must contain a kconstructible subgraph. A graph is kconstructible if it can be obtained from a complete graph by successively applying a set of welldefined operations. In this article, we prove that the weighted coloring problem [Guan and Zhu, 1997] admits a version of the HajÂ´osâ 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. 

N. Ben Ali,
J. Moulierac,
B. Belghith,
and M. Molnár.
mQMA: multiconstrained QoS Multicast Aggregation.
In IEEE Global Telecommunications Conference (IEEE GLOBECOM 2007),
Washington DC, USA,
pages 5p,
November 2007.
[PDF
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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 multiconstrained 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 multiconstrained multicast routing algorithm. Moreover, mQMA reduces dramatically the number of trees to be maintained. 

JC. 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 110,
March 2007.
[PDF
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JC. Bermond,
F. Giroire,
and S. Pérennes.
Design of Minimal Fault Tolerant OnBoard 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 261273,
June 2007.
[PDF
]

JC. Bermond,
F. Havet,
F. Huc,
and C. LinharesSales.
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 5356,
May 2007.
[WWW
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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. 

S. Bessy,
N. Lichiardopol,
and J.S. Sereni.
Two proofs of BermondThomassen conjecture for regular tournaments.
In Proceedings of the sixth CzechSlovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications,
volume 28 of Electronic Notes in Discrete Mathematics,
pages 4753,
2007.
Elsevier.
[WWW
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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 3744,
2007.
Birkhauser.

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 98111,
2007.
Springer.
[PDF
]

A. Chattopadhyay and B. Reed.
Properly 2Colouring 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 395408,
2007.
Springer.
[PDF
]

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 5575,
2007.
[WWW
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O. Dalle.
Componentbased 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 213218,
February 2007.
[PDF
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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 11551162,
July 2007.
Note: Invited paper.
[PDF
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O. Dalle and C. Mrabet.
An Instrumentation Framework for componentbased simulations based on the Separation of Concerns paradigm.
In Proc. of 6th EUROSIM Congress (EUROSIM'2007),
Ljubljana, Slovenia,
pages 10p,
September 2007.
[PDF
]

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
]

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
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]
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 (WiFi), 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 "smallworld" 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. 

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 310,
July 2007.
Note: Invited Paper.
[PDF
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Abstract: 
The assessment of routing protocols for wireless networks is a difficult task, because of the networksâ 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 â the evolving graphs â 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. 

A. Ferreira,
A. Goldman,
and J. Monteiro.
Using Evolving Graphs Foremost Journey to Evaluate AdHoc Routing Protocols.
In Proceedings of 25th Brazilian Symposium on Computer Networks (SBRC'07),
Belem, Brazil,
pages 1730,
June 2007.
[PDF
]
Abstract: 
The performance evaluation of routing protocols for ad hoc networks is a difficult task. However, a graph theoretic model â the evolving graphs â was recently proposed to help capture the behavior of dynamic networks with fixedschedule 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 endtoend 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. 

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 223231,
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 tradeoff 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. 

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
]

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 103108,
October 2007.
Bogazici University, Istanbul, Turkey,
IEEE.
[WWW
] [PDF
]
Abstract: 
Wireless Mesh Networks is a scalable and costeffective solution for nextgeneration 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 tradeoff generated by using these two conflicting objective functions. This relationship corresponds to a convex piecewise linear function. 

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 costeffective 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 maxmin bandwidth guaranty. 

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 117120,
May 2007.
[WWW
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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. 

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 515519,
September 2007.
[PDF
]

G. Huiban and P. Datta.
MultiMetrics 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 tradeoff between network performance and number of reconfigurations applied to the virtual topology. This tradeoff is considered via a multimetrics approach.
The above problem is solved through a Mixed Integer Linear Programming (MILP) formulation with a multivariate objective function. However the problem is NPhard 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 runtime of the MILP becomes practically infeasible. It also appears that the tradeoff'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. 

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 415428,
December 2007.
Springer.
[WWW
] [PDF
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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. 

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 382390,
June 2007.

A. King and B. Reed.
Asymptotics of the chromatic number for quasiline graphs.
In European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2007),
volume 29 of Electronic Notes in Discrete Mathematics,
Sevilla, Spain,
pages 327331,
September 2007.

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 90107,
November 2007.
Springer.
[PDF
]

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
]

F. Mazoit and N. Nisse.
Monotonicity of Nondeterministic Graph Searching.
In Proceedings of the 33rd International Workshop on GraphTheoretic Concepts in Computer Science (WG),
volume 4769 of Lecture Notes in Computer Science,
Dornburg, Germany,
pages 3344,
June 2007.
Springer.
[WWW
] [PDF
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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{nondetermi\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 nondeterministic graph searching is however left open.
In this paper, we prove that nondeterministic 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 nondeterminisitic graph searching belongs to NP. Moreover, the exact algorithms designed by Fomin \emph{et al.} do compute optimal nondeterministic search strategies. 

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 20282032,
2007.
[PDF
]

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 154165,
2007.
[WWW
] [PDF
]

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 5165,
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. 

N. Nisse and D. Soguet.
Stratégies d'encerclement avec information.
In 9èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 4952,
2007.
[WWW
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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. 

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 storeandforward $\Delta$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. 

A. da Silva,
A. da Silva,
and C. LinharesSales.
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
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E. Altman,
J. Galtier,
and C. Touati.
Fair power and transmission rate control in wireless networks.
In The Third Annual Conference on Wireless On demand Network Systems and Services,
pages 134143,
2006.
[PDF
]

O. Amini,
JC. Bermond,
F. Giroire,
F. Huc,
and S. Pérennes.
Design of Minimal Fault Tolerant Networks: Asymptotic Bounds.
In Huitièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'06),
Trégastel, France,
pages 3740,
May 2006.
[WWW
] [PDF
]
Abstract: 
This paper deals with the design of on board networks in satellites (also called Traveling wave tube Amplifiers (TWTA)). These networks should connect signals arriving on some ports of the satellite to amplifiers, even in case of failures of some amplifiers. They are made of links and expensive switches each with 4 links. So, the aim is to design networks having as few switches as possible and satisfying the following property: \emph{there exist $p$ edgedisjoint paths from the $p$ signals arriving on $p + \lambda$ ports (inputs) to any set of $p$ amplifiers (outputs) chosen from the $p+k$ total number of outputs}. We call such networks \emph{valid $(p,\lambda,k)$networks} and want to determine the minimum number of switches $\mathcal{N}(p, \lambda,k)$ of such networks. By symmetry we suppose $\lambda \leq k$. We give tight results for small values of $k$ and asymptotic results when $k = O(\log p)$ which are tight when $k=\Theta(\lambda)$ and when $\lambda=0$. 

M. Ancona,
W. Cazzola,
S. Drago,
and G. Quercini.
Visualizing and Managing Network Topologies via Rectangular Dualization.
In ISCC '06: Proceedings of the 11th IEEE Symposium on Computers and Communications,
Washington, DC, USA,
pages 10001005,
2006.
IEEE Computer Society.
[PDF
]
Abstract: 
Rectangular dualization is an effective, hierarchically oriented visualization method for network topologies and can be used in many other problems having in common with networks the condition that objects and their interoccurring relations are represented by means of a planar graph. However, only 4connected triangulated planar graphs admit a rectangular dual. In this paper we present a linear time algorithm to optimally construct a rectangular layout for a general class of graphs and we discuss a variety of application fields where this approach represents an helpful support for visualization tools. 

R. Bayon,
N. Lygeros,
and J.S. Sereni.
Orders with ten elements are circle orders.
In Book of abstracts of the nineteenth Panhellenic Conference/Summer School on nonlinear science and complexity,
Thessaloniki,
pages 1p,
July 2006.
[WWW
] [PDF
]

D. Benza,
M. Cosnard,
L. Liquori,
and M. Vesin.
Arigatoni: Overlaying Internet via Low Level Network Protocols.
In JVA: John Vincent Atanasoff International Symposium on Modern Computing,
pages 8291,
2006.
IEEE.
[PDF
]

JC. Bermond,
R. Corrêa,
and J. Yu.
Gathering algorithms on paths under interference constraints.
In 6th Conference on Algorithms and Complexity,
volume 3998 of Lecture Notes in Computer Science,
Roma, Italy,
pages 115126,
May 2006.
[WWW
] [PDF
]

JC. Bermond,
M. Cosnard,
D. Coudert,
and S. Pérennes.
Optimal Solution of the Maximum All Request Path Grooming Problem.
In Advanced International Conference on Telecommunications (AICT),
pages 6p,
2006.
IEEE.
[PDF
]
Abstract: 
We give an optimal solution to the Maximum All Request Path Grooming (MARPG) problem motivated by a traffic grooming application. The MARPG problem consists in finding the maximum number of connections which can be established in a path of size $N$, where each arc has a capacity or bandwidth $C$ (grooming factor). We present a greedy algorithm to solve the problem and an explicit formula for the maximum number of requests that can be groomed. In particular, if $C = s(s 1)/2$ and $N > s(s1)$, an optimal solution is obtained by taking all the requests of smallest length, that is of length 1 to $s$. However this is not true in general since anomalies can exist. We give a complete analysis and the exact number of such anomalies. 

JC. Bermond,
D. Coudert,
X. Muñoz,
and I. Sau.
Traffic Grooming in Bidirectional WDM ring networks.
In IEEELEOS ICTON / COST 293 GRAAL,
volume 3,
pages 1922,
June 2006.
[PDF
]
Abstract: 
We study the minimization of ADMs (AddDrop Multiplexers) in Optical WDM Networks with Bidirectional Ring topology considering symmetric shortest path routing and alltoall unitary requests. We insist on the statement of the problem, which had not been clearly stated before in the bidirectional case. Optimal solutions had not been found up to date. In particular, we study the case $C = 2$ and $C = 3$ (giving either optimal constructions or nearoptimal solutions) and the case $C = k(k 1)/2$ (giving optimal decompositions for specific congruence classes of $N$). We state a general Lower Bound for all the values of $C$ and $N$, and we improve this Lower Bound for $C=2$ and $C=3$ (when $N=4t 3)$. We also include some comments about the simulation of the problem using Linear Programming. 

JC. Bermond,
J. Galtier,
R. Klasing,
N. Morales,
and S. Pérennes.
Gathering in specific radio networks.
In Huitièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'06),
Trégastel, France,
pages 8588,
May 2006.
[WWW
] [PDF
]

JC. Bermond,
J. Galtier,
R. Klasing,
N. Morales,
and S. Pérennes.
Hardness and approximation of Gathering in static radio networks.
In FAWN06,
Pisa, Italy,
pages 7579,
March 2006.
[WWW
] [PDF
]

L. Blin,
P. Fraigniaud,
N. Nisse,
and S. Vial.
Distributed Chasing of Network Intruders.
In Proceeding of the 13th International Colloquium on Structural Information and Communication Complexity (SIROCCO),
volume 4056 of Lecture Notes in Computer Science,
Chester, UK,
pages 7084,
July 2006.
Springer.
[WWW
] [PDF
]
Abstract: 
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 \emph{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, computed in the centralized and synchronous setting. 

L. Blin,
P. Fraigniaud,
N. Nisse,
and S. Vial.
Encerclement réparti d'un fugitif dans un réseau par des agents mobiles..
In 8èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 8992,
2006.
[WWW
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Abstract: 
\emph{L'encerclement} dans les graphes est l'un des outils les plus populaires pour analyser la recherche, par une \'equipe d'agents, d'un fugitif omniscient, arbitrairement rapide et invisible dans un r\'eseau. Les solutions existantes au probl\`eme de l'encerclement dans les graphes souffrent cependant d'un s\'erieux inconv\'enient : elles sont toutes centralis\'ees et supposent que les agents \'evoluent dans un environnement synchrone. En particulier : (1) la strat\'egie d'encerclement dans un r\'eseau est calcul\'ee partant d'une connaissance compl\`ete du r\'eseau, et (2) les mouvements des agents sont control\'es par un m\'ecanisme centralis\'e qui d\'ecide \`a chaque \'etape quel agent doit se d\'eplacer et quel mouvement il doit r\'ealiser.
Cet article traite de l'encerclement dans les graphes r\'ealis\'e de mani\`ere r\'epartie. Nous pr\'esentons un protocole r\'eparti qui permet \`a des agents, dont la m\'emoire est de taille logarithmique en la taille du r\'eseau, de nettoyer le r\'eseau de facon d\'ecentralis\'ee. La mani\`ere dont les agents se d\'eplacent pour r\'ealiser la strat\'egie d'encerclement est calcul\'ee en temps r\'eel par les agents euxm\^eme, {\emph sans qu'ils ne connaissent la topologie du r\'eseau \`a l'avance}. Tout cela est r\'ealis\'e dans un environnement asynchrone, c'est\`adire que notre protocole impl\'emente le m\'ecanisme de synchronisation n\'ecessaire de mani\`ere d\'ecentralis\'ee. La performance de la strat\'egie d'encerclement est mesur\'ee par le nombre d'agents utilis\'es pour capturer l'intrus. Selon cette mesure, nous prouvons que notre protocole a un rapport de comp\'etitivit\'e de $3/2$ et que c'est le meilleur ratio atteignable par n'importe quel protocole r\'eparti. En fait, pour tout r\'eseau, notre protocole calcule une strat\'egie dont nous prouvons qu'elle utilise au plus $OPT+1$ agents, o\`u $OPT$ est le nombre minimum d'agents n\'ecessaire pour nettoyer un r\'eseau de facon centralis\'ee et synchrone. 

R. Chand,
M. Cosnard,
and L. Liquori.
Resource Discovery in the Arigatoni Overlay Network.
In Proceedings of the International Workshop on Innovative Internet Community Systems (I2CS),
pages 13p,
2006.
[PDF
]

R. Cilibrasi,
Z. Lotker,
A. Navarra,
S. Pérennes,
and P. Vitanyi.
About the Lifespan of Peer to Peer Networks.
In Proceedings of the 10th International Conference On Principles Of Distributed Systems (OPODIS),
volume 4305 of Lecture Notes in Computer Science,
Bordeaux,
pages 290304,
December 2006.
SpringerVerlag.
[WWW
] [PDF
]

H. Cirstea,
K. Claude,
L. Liquori,
and B. Wack.
Polymorphic Type Inference for the Rewriting Calculus.
In JFLA: Journées Francophones des Langages Applicatifs,
pages 5769,
2006.
INRIA.

D. Coudert,
S. Pérennes,
H. Rivano,
and ME. Voge.
Shared Risk Resource Groups and Survivability in Multilayer Networks.
In IEEELEOS ICTON / COST 293 GRAAL,
volume 3,
pages 235238,
June 2006.
Note: Invited Paper.
[PDF
]
Abstract: 
We study the minimization of ADMs (AddDrop Multiplexers) in Optical WDM Networks with Bidirectional Ring topology considering symmetric shortest path routing and alltoall unitary requests. We insist on the statement of the problem, which had not been clearly stated before in the bidirectional case. Optimal solutions had not been found up to date. In particular, we study the case C = 2 and C = 3 (giving either optimal constructions or nearoptimal solutions) and the case C = k(k 1)/2 (giving optimal decompositions for specific congruence classes of N). We state a general Lower Bound for all the values of C and N, and we improve this Lower Bound for C=2 and C=3 (when N=4t 3). We also include some comments about the simulation of the problem using Linear Programming. 

O. Dalle.
OSA: an Open Componentbased Architecture for DiscreteEvent Simulation.
In 20th European Conference on Modeling and Simulation (ECMS),
Bonn, Germany,
pages 253259,
May 2006.
[PDF
]

A. Ferreira,
A. Goldman,
and J. Monteiro.
Performance Evaluation of Dynamic Networks using an Evolving Graph Combinatorial Model.
In Proceedings of the 2nd IEEE International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob 2006),
Montreal, CA,
pages 173180,
June 2006.
Note: Best Student Paper Award.
[WWW
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F. V. Fomin,
P. Fraigniaud,
and N. Nisse.
Strategies d'encerclement non deterministes.
In 8èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 8184,
2006.
[WWW
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Abstract: 
Nous d\'efinissons l'encerclement nond\'eterministe dans les graphes. Nous montrons comment ce nouvel outil peut \^etre utilis\'e pour la conception d'algorithmes et pour l'analyse combinatoire de la largeur lin\'eaire (pathwidth) comme de la largeur arborescente (treewidth) des graphes. Nous prouvons l'\'equivalence entre cette approche sous forme de ``jeu'' (graph searching) et la d\'ecomposition arborescente $q$branch\'ee d'un graphe. Cette d\'ecomposition peut \^etre interpr\'et\'ee comme une version param\'etr\'ee des d\'ecompositions arborescente et lin\'eaire qui sont deux cas extr\^emes de la d\'ecomposition arborescente $q$branch\'ee. L'\'equivalence entre l'encerclement nond\'eterministe et la d\'ecomposition arborescente $q$branch\'ee nous permet de proposer un algorithme exact (en temps exponentiel) pour calculer la largeur arborescente $q$branch\'ee pour tout $q \geq 0$. Cet algorithme est donc valide \`a la fois pour la largeur lin\'eaire et po ur la largeur arborescente. Notre algorithme est aussi rapide que le meilleur algorithme connu pour la largeur lin\'eaire. 

P. Fraigniaud and N. Nisse.
Connected Treewidth and Connected Graph Searching.
In Proceeding of the 7th Latin American Symposium on Theoretical Informatics (LATIN),
pages 479490,
2006.
[WWW
] [PDF
]
Abstract: 
We give a constructive proof of the equality between \emph{treewidth} and \emph{connected treewidth}. More precisely, we describe an $O(nk^3)$time algorithm that, given any $n$node width$k$ treedecomposition of a connected graph $G$, returns a connected treedecomposition of $G$ of width $\leq k$. The equality between treewidth and connected treewidth finds applications in \emph{graph searching} problems. First, using equality between treewidth and connected treewidth, we prove that the \emph{connected} search number $\cs(G)$ of a connected graph $G$ is at most $\log{n}+1$ times larger than its search number. Second, using our constructive proof of equality between treewidth and connected treewidth, we design an \\$O(\log n\sqrt{\log OPT})$approximation algorithm for connected search, running in time $O(t(n)+nk^3\log^{3/2}k+m\log n)$ for $n$node $m$edge connected graphs of treewidth at most $k$, where $t(n)$ is the timecomplexity of the fastest algorith m for approximating the treewidth, up to a factor $O(\sqrt{\log OPT})$. 

P. Fraigniaud and N. Nisse.
Monotony Properties of Connected Visible Graph Searching.
In Proceedings of 32nd International Workshop on GraphTheoretic Concepts in Computer Science (WG),
volume 5911 of Lecture Notes in Computer Science,
Montpellier, France,
pages 229240,
June 2006.
Springer.
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 nonconnected 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.unitrier.de/~ley/db/conf/wg/wg2006.php}, pdf = {http://wwwsop.inria.fr/members/Nicolas.Nisse/publications/WG06_nisse.ps} 

J. Galtier.
Adaptive power and transmission rate control in cellular CDMA networks.
In IEEE GLOBECOM,
pages 6p,
2006.
[PDF
]

J. Galtier.
Analysis of the slotted nonpersistent CSMA protocol with poissonian packet size using a semiMarkov graph representation.
In 8th International Conference on Transparent Optical Networks,
volume 3,
pages 258262,
June 2006.
IEEE.
[PDF
]

F. Giroire.
Directions to use Probabilistic Algorithms for Cardinality for DNA Analysis.
In Journées Ouvertes Biologie Informatique Mathématiques (JOBIM 2006),
pages 35,
July 2006.
[PDF
]
Abstract: 
Probabilistic algorithms for cardinality allow to estimate the number of distinct words of very large multisets. Best of them are very fast (only few tens of CPU operations per element) and use constant memory (standard error of $c \sqrt M$ attained using $M$ units of memory) to be compared with the linear memory used by exact algorithms. Hence they allow to do multiple experiments in few minutes with few KiloBytes on files of several GigaBytes that would be unfeasible with exact counting algorithms. Such algorithms are used here to analyze base correlation in human genome. 

L. Hogie,
Pascal Bouvry,
and Frédéric Guinand.
An Overview of MANETs Simulation.
In L. Brim and I. Linden, editors,
Electronic Notes in Theoretical Computer Science, in the proceedings of MTCoord'05,
volume 150 of LNCS,
Namur, Belgium,
pages 81101,
March 2006.
Elsevier.
[WWW
]
Abstract: 
Mobile Ad hoc NETworks (MANETs) are dynamic networks populated by mobile stations. Stations in MANETs are usually laptops, PDAs or mobile phones. These devices feature Bluetooth and/or IEEE 802.11 (WiFi) network interfaces and communicate in a decentralized manner. Mobility is a key feature of MANETs. Because of their high cost and their lack of flexibility of such networks, experimentation is mostly achievable through simulation. Numerous tools exist for MANETs simulation, including ns2 and GloMoSim which are the two most popular ones. This paper provides a State of the Art of MANETs simulators and associated simulation techniques. First it gives an overview of the domain. Then it provides a map of the main characteristics that MANETs simulation tools should feature and the current support of these. Finally, a description for each simulator is provided, including an explanation of what make them appealing solutions. 

L. Hogie,
P. Bouvry,
F. Guinand,
G. Danoy,
and E. Alba.
A BandwidthEfficient Broadcasting Protocol for Mobile Multihop Ad hoc Networks.
In ICN/ICONS/MCL '06: Proceedings of the International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies,
pages 7171,
October 2006.
IEEE Computer Society.
[WWW
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Abstract: 
This paper presents a new broadcasting protocol called Delayed Flooding with Cumulative Neighborhood (DFCN) designed for wireless ad hoc networks. DFCN enables bandwidthefficient broadcasting in wide area network composed of large number of mobile devices. The protocol was validated trough simulation which proved its efficiency and costeffectiveness. Comparison with other well known protocols has shown that the proposed protocol outperforms them in such terms as a number of emissions and redundant receptions. 

L. Hogie,
P. Bouvry,
F. Guinand,
G. Danoy,
and E. Alba.
Simulating Realistic Mobility Models for Large Heterogeneous MANETs.
In Demo proceeding of the 9th ACM/IEEE International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWIM'06),
pages 1p,
October 2006.
IEEE.
[WWW
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Abstract: 
Mobile ad hoc networks (MANETs) are composed of communicat ing mobile devices capable of spontaneously interconnecting without any preexisting infrastructure. The wide spread of mobile devices(i.e.
phones, PDAs, laptops) enables the deployment of metropolitan ad hoc networks, referred to as MobileMANs. Until recently, MobileMAN simu lation suffered from a lack of appropriate tools. Therefore a new class of simulators dedicated to MobileMANs is appearing. This paper presents Mad hoc, a MANETs simulator which belongs to this class. In addi tion to providing particular models for the simulation of numerous nodes evolving in a metropolitan environment, Mad hoc comes with appropri ate tools for the development and the monitoring of ad hoc applications. Mad hocÃs applications are presented. 

L. Liquori.
iRho: the Software: [System Description].
In Proceedings of the First International Workshop on Developments in Computational Models (DCM 2005),
volume 135 of Electronic Notes in Theoretical Computer Science,
pages 8594,
2006.
Elsevier.
[PDF
]

L. Liquori,
F. Honsell,
and R. Redamalla.
A Language for Verification and Manipulation of Web Documents.
In Proceedings of the International Workshop on Automated Specification and Verification of Web Sites (WWV 2005),
volume 157 of Electronic Notes in Theoretical Computer Science,
pages 6778,
2006.
Elsevier.

F. Luna,
A. J. Nebro,
B. Dorronsoro,
E. Alba,
P. Bouvry,
and L. Hogie.
Optimal Broadcasting in Metropolitan MANETs Using Multiobjective Scatter Search.
In Applications of Evolutionary Computing,
volume 3907 of Lecture Notes in Computer Science,
pages 255266,
March 2006.
Springer.
[WWW
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Abstract: 
Mobile Adhoc Networks (MANETs) are composed of a set of communicating devices which are able to spontaneously interconnect without any preexisting infrastructure. In such scenario, broadcasting becomes an operation of capital importance for the own existence and operation of the network. Optimizing a broadcasting strategy in MANETs is a multiobjective problem accounting for three goals: reaching as many stations as possible, minimizing the network utilization, and reducing the makespan. In this paper, we face this multiobjective problem with a stateoftheart multiobjective scatter search algorithm called AbSS (Archivebased Scatter Search) that computes a Pareto front of solutions to empower a human designer with the ability of choosing the preferred configuration for the network. Results are compared against those obtained with the previous proposal used for solving the problem, a cellular multiobjective genetic algorithm (cMOGA). We conclude that AbSS outperforms cMOGA with respect to three different metrics. 

J. Moulierac.
On the number of multicast aggregated trees in a domain.
In 2nd Student Workshop of IEEE Infocom,
pages 2p,
April 2006.
[PDF
]
Abstract: 
Multicast tree aggregation is an efficient proposition that can solve the multicast forwarding state scalability problem. Existing works on tree aggregation have focused on developing and simulating protocols that build trees dynamically. However, the underlying problem of the impact of the tree construction algorithm on the performance of the protocols remains untouched. In this paper, we propose a study on the number of trees that need to be configured in a domain depending on the tree construction algorithm. We ran extensive simulations on several real domains and with different tree construction algorithms. Our results show that for a given set of multicast groups, even when this set includes all the possible groups, the number of trees that need to be configured is small. This allows a network administrator to configure offline all these trees in order to maintain a stable set of trees and to have knowledge of the routes used by the multicast packets. Knowing the set of all the possible trees is also useful to determine the best subset to configure and to give an upper bound of the number of different trees. 

J. Moulierac,
A. Guitton,
and M. Molnár.
Multicast Tree Aggregation in Large Domains.
In IFIP Networking,
number 3976,
pages 691702,
2006.
[PDF
]
Abstract: 
Tree aggregation is an ecient proposition that can solve the problem of multicast forwarding state scalability. The main idea of tree aggregation is to force several groups to share the same delivery tree: in this way, the number of multicast forwarding states per router is reduced. Unfortunately, when achieving tree aggregation in large do mains, few groups share the same tree and the aggregation ratio is small. In this paper, we propose a new algorithm called TALD (Tree Aggrega tion in Large Domains) that achieves tree aggregation in domains with a large number of nodes. The principle of TALD is to divide the domain into several subdomains and to achieve the aggregation in each of the subdomain separately. In this way, there is possible aggregation in each of the subdomain and the number of forwarding states is signicantly reduced. We show the performance of our algorithm by simulations on a Rocketfuel network of 200 routers. 

J. Moulierac,
A. Guitton,
and M. Molnár.
On the number of MPLS LSP using Multicast Tree Aggregation.
In IEEE Globecom,
pages 5p,
November 2006.
[PDF
]
Abstract: 
Multicast tree aggregation is an efficient proposition that can solve the multicast forwarding state scalability problem. Existing works on tree aggregation have focused on developing and simulating protocols that build trees dynamically. However, the underlying problem of the impact of the tree construction algorithm on the performance of the protocols remains untouched. In this paper, we propose a study on the number of trees that need to be configured in a domain depending on the tree construction algorithm. We ran extensive simulations on several real domains and with different tree construction algorithms. Our results show that for a given set of multicast groups, even when this set includes all the possible groups, the number of trees that need to be configured is small. This allows a network administrator to configure offline all these trees in order to maintain a stable set of trees and to have knowledge of the routes used by the multicast packets. Knowing the set of all the possible trees is also useful to determine the best subset to configure and to give an upper bound of the number of different trees. 

J. Moulierac and M. Molnàr.
Active Monitoring of Link Delays in Case of Asymmetric Routes.
In IEEE International Conference on Networking (ICN),
pages 6p,
April 2006.
[PDF
]
Abstract: 
Network monitoring receives signicant interest recently. Indeed, knowledge of link availability and link characteristics is of signicant importance in order to provide efcient routing. In this paper, we consider active network monitoring of link delays in a Service Provider or Enterprise IP network using round trip delays. Our proposition guarantees that all links are monitored contrary to previous propositions. Indeed, previous propositions assume symmetric routing in networks when placing the monitoring stations. With this assumption, round trips may be different when routes are asymmetric and link delays are not signi cant. We say that links are not monitored in this case. Previous propositions do not monitor 5.76\27775643210f links in average and 10\ 134577319n worst cases during our simulations while we monitor always 100\1175304120f links. Moreover, in our proposition, the amount of trafc is reduced and the measures are more precise since the distance from a monitoring station (beacon) to the edges is limited by a given bound. Finally, we show during the simulations that the set of beacons is rather stable in case of link failures. 

N. Nepomuceno,
P. Rogério Pinheiro,
and A. L. V. Coelho.
Aplicação de uma Metodologia Hìbrida ao Problema de Carregamento de Contêineres.
In XXXVIII Simpósio Brasileiro de Pesquisa Operacional (SBPO),
Goiania, Brazil,
pages 15961603,
2006.
[PDF
]

N. Nepomuceno,
P. Rogério Pinheiro,
and A. L. V. Coelho.
Metaheurìstica e Programação Linear Inteira: Um Algoritmo Hìbrido para o Problema de Carregamento de Contêineres.
In XIII Congreso LatinoIberoamericano de Investigación Operativa (CLAIO),
Montevideo, Uruguay,
pages 6p,
2006.
[PDF
]

H. Rivano,
F. Theoleyre,
and F. Valois.
Capacity Evaluation Framework and Validation of SelfOrganized Routing Schemes.
In Workshop on Wireless Adhoc and Sensor Networks (IWWAN 2006),
volume 3,
pages 779785,
2828 Sept. 2006.
IEEE.
[WWW
] [PDF
]
Abstract: 
Assuming a given network topology and a routing protocol, this work is focused on the capacity evaluation of routing protocols based on either a selforganization scheme or a flat approach. To reach this goal, we propose to use linearprogramming formulation to model radio resource sharing as linear constraints. Four models are detailed to evaluate the capacity of any routing scheme in wireless multihops networks. First, two models of fairness are proposed: either each node has a fair access to the channel, or the fairness is among the radio links. Besides, a pessimistic and an optimistic scenarios of spatial reutilization of the medium are proposed, yielding a lower bound and an upper bound on the network capacity for each fairness case. Finally, using this model, we provide a comparative analysis of some flat and selforganized routing protocols 

M.E. Voge.
Graphes Colorés  Arbre Couvrant Coloré.
In Huitièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'06),
Trégastel,
pages 4144,
May 2006.
[WWW
]

M.E. Voge.
How to transform a multilayer network into a colored graph.
In IEEELEOS ICTON/COST 293 GRAAL,
volume 3,
pages 116119,
June 2006.

L. AddarioBerry,
K. Dalal,
and B. Reed.
Degree constrained subgraphs.
In Proceedings of GRACO2005,
volume 19 of Electron. Notes Discrete Math.,
Amsterdam,
pages 257263 (electronic),
2005.
Elsevier.

S. Alouf,
E. Altman,
J. Galtier,
J.F. Lalande,
and C. Touati.
Quasioptimal bandwidth allocation for multispot MFTDMA satellites.
In IEEE INFOCOM 2005,
Miami, FL,
pages 7194,
March 2005.
[WWW
] [PDF
] [POSTSCRIPT
]

JC. Bermond,
L. Braud,
and D. Coudert.
Traffic Grooming on the Path.
In 12th International Colloquium on Structural Information and Communication Complexity  SIROCCO,
Le Mont SaintMichel, France,
pages 3448,
May 2426 2005.
LNCS 3499.
[PDF
] [POSTSCRIPT
]
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 Multiplexer (shortly ADM) used in the network (related to the cost of the nodes).Here we consider 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 NPcomplete 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 alltoall traffic (requests being all pairs of vertices). 

J.C. Bermond and J. Peters.
Efficient Gathering in Radio Grids with Interference.
In Septièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'05),
Presqu'île de Giens,
pages 103106,
May 2005.
[PDF
]

C. Chaudet,
E. Fleury,
I. GuérinLassous,
H. Rivano,
and M.E. Voge.
Optimal positioning of active and passive monitoring devices.
In CoNEXT 2005,
Toulouse, France,
October 2005.
[WWW
] [PDF
]
Abstract: 
Network measurement is essential for assessing performance issues, identifying and locating problems. Two common strategies are the passive approach that attaches specific devices to links in order to monitor the traffic that passes through the network and the active approach that generates explicit control packets in the network for measurements. One of the key issues in this domain is to minimize the overhead in terms of hardware, software, maintenance cost and additional traffic.
In this paper, we study the problem of assigning tap devices for passive monitoring and beacons for active monitoring. Minimizing the number of devices and finding optimal strategic locations is a key issue, mandatory for deploying scalable monitoring platforms. In this article, we present a combinatorial view of the problem from which we derive complexity and approximability results, as well as efficient and versatile Mixed Integer Programming (MIP) formulations. 

C. Chaudet,
E. Fleury,
I. GuérinLassous,
H. Rivano,
and M.E. Voge.
Surveillance passive dans l'Internet.
In Septièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'05),
Presqu'île de Giens,
pages 121124,
May 2005.
[WWW
] [PDF
]
Abstract: 
Afin d'obtenir les informations nécessaires à une bonne gestion des ressources de leur réseau, les opérateurs placent des sondes passives sur les liens de leurs points de présence. Dans cet article, nous donnons des écritures en programmes linéaires mixtes des problèmes de placement de sondes simples ou avec échantillonnage, et donnons une stratégie pour la maintenance de la surveillance partielle de trafics dynamiques dans un point de présence. Ces formulations améliorent les résultats de deux articles récents de la littérature. 

D. Coudert,
S. Perennes,
QC. Pham,
and JS. Sereni.
Rerouting requests in WDM networks.
In AlgoTel'05,
Presqu'île de Giens, France,
pages 1720,
mai 2005.
[PDF
]
Abstract: 
We model a problem related to routing reconfiguration in WDM networks. We establish some similarities and differences with two other known problems: the pathwidth and the pursuit problem. We then present a distributed lineartime algorithm to solve the problem on trees. Last we give the solutions for some classes of graphs, in particular complete $d$ary trees and grids. 

S. Fiorini,
N. Hardy,
B. Reed,
and A. Vetta.
Approximate minmax relations for odd cycles in planar graphs.
In Integer programming and combinatorial optimization,
volume 3509 of Lecture Notes in Comput. Sci.,
Berlin,
pages 3550,
2005.
Springer.

S. Fiorini,
N. Hardy,
B. Reed,
and A. Vetta.
Planar graph bipartization in linear time.
In Proceedings of GRACO2005,
volume 19 of Electron. Notes Discrete Math.,
Amsterdam,
pages 265271 (electronic),
2005.
Elsevier.

M. Flammini,
L. Moscardelli,
A. Navarra,
and S. Pérennes.
Asymptotically Optimal Solutions for Small World Graphs.
In Proceedings of the 19th International Symposium on Distributed Computing, (DISC 2005),
volume 3724 of Lecture Notes in Computer Science,
pages 414428,
September 2005.
Springer Verlag.
[WWW
]

M. Flammini,
A. Navarra,
and S. Pérennes.
The Real approximation factor of the MST heuristic for the Minimum Energy Broadcasting.
In Proceedings of the 4th International Workshop on Experimental and Efficient Algorithms, (WEA 2005),
volume 3503 of Lecture Notes in Computer Science,
pages 2231,
May 2005.
Springer Verlag.
[WWW
]

F. V. Fomin,
P. Fraigniaud,
and N. Nisse.
Nondeterministic Graph Searching: From Pathwidth to Treewidth.
In Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science (MFCS),
pages 364375,
2005.
[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 gametheoretic 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 qbranched tree decompositions. The equivalence between nondeterministic graph searching and qbranched tree decomposition enables us to design an exact (exponential time) algorithm computing qbranched 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. 

P. Fraigniaud and N. Nisse.
Stratégies d'encerclement connexes dans un réseau.
In 7èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel),
pages 1316,
2005.
[WWW
] [PDF
]
Abstract: 
Le probl\`eme de l'encerclement dans les r\'eseaux a \'et\'e introduit par Parson (1976)~: \'etant donn\'e un r\'eseau "contamin\'e" (par exemple dans lequel un intrus s'est introduit), l'\emph{encerclement} du r\'eseau est le nombre minimum d'agents n\'ecessaires pour "nettoyer" le r\'eseau (c'est\`adire capturer l'intrus). Une strat\'egie d'encerclement est dite connexe si \`a chaque \'etape de la strat\'egie, l'ensemble des liens nettoy\'es induit un sousr\'eseau connexe. Les strat\'egies d'encerclement connexes sont essentielles si l'on souhaite assurer des communications s\^ures entre les agents. Dans le cas des r\'eseaux en arbres, Barri\`ere {\sl et al.} (2002, 2003) ont prouv\'e que le rapport entre l'encerclement connexe et l'encerclement est major\'e par 2, et que cette borne est optimale. Dans cet article, nous donnons une borne pour ce rapport dans le cas des r\'eseaux arbitraires. Pour cela nous utilisons une notion cruciale de th\'eorie des graphes~: la largeur arborescente. L'\'egalit\'e entre la largeur arborescente connexe d'un graphe et sa largeur arborescente d\'ecoule du th\'eor\`eme de Parra et Scheffler (1995). Nous donnons ici une preuve constructive de cette \'egalit\'e. Plus pr\'ecisemment, nous proposons un algorithme qui \'etant donn\'es un graphe $G$ de $n$ sommets et une d\'ecomposition arborescente de largeur $k$ de $G$, calcule en temps $O(n~k^3)$ une d\'ecomposition arborescente connexe de largeur $\leq k$ de $G$. Une cons\'equence importante de notre r\'esultat est qu'il permet de borner par $\lceil\log{n}\rceil+1$ le rapport entre encerclement connexe et encerclement d'un r\'eseau de $n$ n{\oe}uds. 

J. Galtier,
A. Laugier,
and P. Pons.
Algorithms to evaluate the reliability of a network.
In The 5th International Workshop on Design of Reliable Communication Networks,
pages 93100,
2005.
[WWW
] [PDF
]

F. Giroire.
Order statistics and estimating cardinalities of massive data sets.
In Conrado MartÃnez, editor,
2005 International Conference on Analysis of Algorithms,
volume AD of DMTCS Proceedings,
pages 157166,
2005.
Discrete Mathematics and Theoretical Computer Science.
[WWW
] [PDF
]
Abstract: 
We introduce a new class of algorithms to estimate the cardinality of very large multisets using constant memory and doi ng only one pass on the data. It is based on order statistics rather that on bit patterns in binary representations of numbers. We analyse three families of estimators. They attain a standard error of $\frac 1{\sqrt M}$ using $M$ unit s of storage, which places them in the same class as the best known algorithms so far. They have a very simple internal loop, which g ives them an advantage in term of processing speed. The algorithms are validated on internet traffic traces. 

C. Gomes and G. Robson Mateus.
LowCost Design Approach to WDM Mesh Networks.
In 4th International Conference on Networking (ICN),
pages 6067,
2005.

A. Guitton and J. Moulierac.
Scalable Tree Aggregation for Multicast.
In 8th International Conference on Telecommunications (ConTEL),
pages 129134,
June 2005.
Note: Best Student Paper Award.
[PDF
]
Abstract: 
IP multicast is not widely deployed yet over Internet. This is mainly due to the forwarding entries scalability and control explosion problems. In this paper, we propose an algorithm called STA (Scalable Tree Aggregation) which reduces the number of trees by allowing several groups to be aggregated to the same tree: the less trees, the less forwarding entries and the less control messages to maintain trees. STA performs faster aggregations than previous aggregation algorithms by evaluating fewer trees for each group, while keeping the same performance. We show the scalability and the fastness of STA by extensive simulations and we compare its performance to the previous algorithm. 

F. Havet,
R. J. Kang,
and J.S. Sereni.
Improper colouring of unit disk graphs.
In Proceedings of the 7th International Conference on Graph Theory (ICGT'05),
volume 22 of Electronic Notes in Discrete Mathematics,
pages 123128,
September 2005.
Elsevier.
[WWW
] [PDF
]

F. Havet and J.S. Sereni.
Channel assignment and improper choosability of graphs.
In Proceedings of the 31st Workshop on GraphTheoretic Concepts in Computer Science (WG'05),
volume 3787 of Lecture Notes in Computer Science,
pages 8190,
June 2005.
Springer Verlag.
[WWW
] [PDF
]

G. Huiban and G. Robson Mateus.
A MILP model for the reconfiguration problem in multifiber WDM networks.
In SBRC Simpósio Brasileiro de Redes de Computadores,
May 2005.
[WWW
] [PDF
]
Abstract: 
We address the reconfiguration problem in multifiber WDM networks. It consists of finding out which adaptations should be made to the virtual topology and the routing when the traffic evolves. We propose a Mixed Integer Linear Programming (MILP) model solving the problem for different objective functions. We tried to make a concise model in relations with the number of variables and restrictions, to reduce the memory occupation during the optimization process. We also add some cuts to the model.
We make some experiments with this model and compare the results obtained with a simple greedy algorithm and with an algorithm from the literature 

G. Huiban and G. Robson Mateus.
A multiobjective approach of the virtual topology design and routing problem in WDM networks.
In ICT International Conference on Telecommunications,
May 2005.
IEEE Computer Society Press.
[WWW
] [PDF
]
Abstract: 
We deal with the classical virtual topology design and routing problems in optical WDM (Wavelength Division Multiplexing) networks. We propose a multiobjective based algorithm to compute the Pareto set of solutions of the problem. Although the computational cost may be high, such approach permits the decision maker to have a better perception of the gain and the loss of choosing any given solution.
We describe briefly the treated problem, and the MILP (Mixed Integer Linear Programing) model used. We present the method applied to obtain the Pareto set. We report some computational results and they fully justify the interest of carrying out a multiobjective study. 

R. J. Kang,
T. Müller,
and J.S. Sereni.
Improper colouring of (random) unit disk graphs.
In Proceedings of European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2005),
Discrete Mathematics and Theoretical Computer Science,
pages 193198,
September 2005.
[WWW
] [PDF
]

R. Klasing,
Z. Lotker,
A. Navarra,
and S. Pérennes.
From Balls and Bins to Points and Vertices.
In Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005),
volume 3827 of Lecture Notes in Computer Science,
pages 757766,
December 2005.
Springer Verlag.
[WWW
] [PDF
]

R. Klasing,
E. Markou,
T. Radzik,
and F. Sarracco.
Approximation bounds for Black Hole Search problems.
In Proceedings of the 9th International Conference on Principles of Distributed Systems (OPODIS 2005),
volume 3974 of Lecture Notes in Computer Science,
December 2005.
Springer Verlag.
[WWW
]

R. Klasing,
E. Markou,
T. Radzik,
and F. Sarracco.
Hardness and approximation results for black hole search in arbitrary graphs.
In Proceedings of the 12th Colloquium on Structural Information and Communication Complexity (SIROCCO 2005),
volume 3499 of Lecture Notes in Computer Science,
pages 200215,
May 2005.
Springer Verlag.
[WWW
]

J.F. Lalande,
M. Syska,
and Y. Verhoeven.
Arrondi aléatoire et protection des réseaux WDM.
In Ecole Polytechnique de l'Université de Tours, editor,
ROADEF,
number 6,
Tours, France,
pages 241242,
2005.
[WWW
] [PDF
] [POSTSCRIPT
]

A. Laugier and S. Raymond.
Recherche de graphes expansifs dans le graphe du Web.
In Roadef,
2005.
[WWW
]

Z. Li and B. Reed.
Heap building bounds.
In Algorithms and data structures,
volume 3608 of Lecture Notes in Comput. Sci.,
Berlin,
pages 1423,
2005.
Springer.

C. Meagher and B. Reed.
Fractionally total colouring $G\sb {n,p}$.
In Proceedings of GRACO2005,
volume 19 of Electron. Notes Discrete Math.,
Amsterdam,
pages 297303 (electronic),
2005.
Elsevier.

J. Moulierac and A. Guitton.
QoS Scalable Tree Aggregation.
In IFIP Networking,
number 3462 of LNCS,
pages 14051408,
May 2005.
[PDF
]
Abstract: 
{Some of the main reasons which prevents the deployment of IP multicast are forwarding state scalability and control explosion prob lems. In this paper, we propose an algorithm called QSTA (QoS Scalable Tree Aggregation) which reduces the number of forwarding states by al lowing several groups to share the same tree. QSTA accepts groups only if there is enough available bandwidth. QSTA accepts much more groups and performs faster aggregations than previous algorithms.}


S. Petat and M.E. Voge.
Groupage sur un chemin orienté.
In Septièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'05),
Presqu'île de Giens,
pages 2124,
May 2005.
[PDF
]

H. Rivano,
F. Théoleyre,
and F. Valois.
Influence de l'autoorganisation sur la capacité des réseaux ad hoc.
In Septièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'05),
Presqu'île de Giens,
pages 5356,
May 2005.
[WWW
] [PDF
]
Abstract: 
Les réseaux ad hoc tirent parti de la collaboration des noeuds pour acheminer des informations. Si de nombreuses approches ont vu le jour, la problématique du routage demeure un point crucial. Deux approches se détachent : une première résidant dans une vision à plat du réseau et une seconde, plus récente, où le routage repose sur une autoorganisation du réseau. Il s'agit de fournir une solution d'organisation afin de tirer parti des propriétés structurelles et d'améliorer des services tels que le routage. Les performances obtenues sont intéressantes bien que les autoorganisations réduisent le nombre de liens radio effectivement utilisés. Nous proposons donc ici de quantifier les changements, en terme de bande passante disponible, entre un réseau à plat et un réseau structuré. 

S. Bessy.
Un algorithme d'approximation pour le sousdigraphe fortement connexe minimal.
In Sixièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'04),
pages 5761,
2004.
INRIA.
[WWW
]

S. Bessy and S. Thomassé.
Three minmax theorems concerning cyclic orders of strong digraphs.
In Acts of IPCO X 2004,
volume 3064 of Lecture Notes in Computer Sciences,
pages 132138,
2004.
SpringerVerlag.
[WWW
]

C. Cooper,
R. Klasing,
and M. Zito.
Dominating Sets in Web Graphs.
In Proceedings of the Third Workshop on Algorithms and Models for the WebGraph (WAW 2004),
volume 3243 of Lecture Notes in Computer Science,
pages 3143,
October 2004.
SpringerVerlag.

A. Ferreira and A. Jarry.
Complexity of Minimum Spanning Tree in Evolving Graphs and the MinimumEnergy Broadcast Routing Problem.
In Proceedings of WiOpt'04  Modeling and Optimization in Mobile, AdHoc and Wireless Networks,
Cambridge, United Kingdom,
March 2004.

M. Flammini,
R. Klasing,
A. Navarra,
and S. Pérennes.
Improved approximation results for the Minimum Energy Broadcasting Problem.
In 2nd ACM/SIGMOBILE Annual International Joint Workshop on Foundation of Mobile Computing (DIALMPOMC 2004),
pages 8591,
2004.
ACM Press.
[WWW
] [POSTSCRIPT
]

S. Funke,
A. Kesselman,
Z. Lotker,
and M. Segal.
Improved Algorithms for the Connected Sensor Cover Problem.
In ADHOCNOW 04,
pages 5659,
2004.

J. Galtier.
Optimizing the IEEE 802.11b Performance using Slow Congestion Window Decrease.
In Proccedings of the 16th ITC Specialist Seminar on performance evaluation of wireless and mobile systems,
Antwerpen, Belgium,
pages 165176,
August/September 2004.
[PDF
]

C. Gomes and G. Robson Mateus.
Routing and Wavelength Assignment in a Mesh Network.
In 3rd International Information and Telecommunication Technologies Symposium (I2TS),
2004.

A. Jarry.
Integral Symmetric 2Commodity Flows.
In Proceedings of STACS'04,
Montpellier,
March 2004.

A. Jarry and A. Laugier.
On the minimum number edges of twoconnected graphs with given diameter.
In GT04,
Paris, France,
July 2004.

A. Jarry and Z. Lotker.
Connectivity in Evolving Graph with Geometric Properties.
In Dial MPOMC 2004 The Second ACM/SIGMOBILE Annual International Joint Workshop on Foundations of Mobile Computing,
2004.

R. Klasing,
A. Navarra,
A. Papadopoulos,
and S. Pérennes.
Adaptive Broadcast Consumption (ABC), a new heuristic and new bounds for the Minimum Energy Broadcast Routing Problem.
In Proc. 3rd FIPTC6 Networking Conference ( Networking 2004),
volume 3042 of Lecture Notes in Computer Science,
pages 866877,
2004.
SpringerVerlag.
[POSTSCRIPT
]

G. Kozma,
Z. Lotker,
M. Sharir,
and G. Stupp.
Geometrically Aware Communication in Random Wireless Networks.
In 24th ACM Symp. on Principles of Distributed Computing,
pages 310319,
2004.

L. Liquori and B. P. Serpette.
iRho: an imperative rewriting calculus.
In Proc. of ACMPPDP: International Conference on Principles and Practice of Declarative Programming,
pages 167178,
2004.
[POSTSCRIPT
]

Z. Lotker,
M. Martinez de Albeniz,
and S. Pérennes.
RangeFree Ranking in Sensors Networks and Its Applications to Localization.
In ADHOCNOW 2004,
pages 158171,
2004.
[POSTSCRIPT
]

J. Moulierac,
J.C. König,
and M. Molnár.
Diffusion contrainte dans un groupe.
In ALGOTEL  Rencontre francophone sur les aspects Algorithmiques des Télécommunications,
2004.
[PDF
]
Abstract: 
{Dans ce papier nous traitons de problemes particuliers de communications de groupe dans les reseaux. Le probleme de diffusion contrainte dans un groupe consiste \`a envoyer un message d'un \'emetteur \`a un ensemble de destinataires en imposant son passage par des noeuds sp\'ecifiques appel\'es les traducteurs. Dans un premier temps, nous prouvons que ce probleme est NPdifficile et nous proposons une heuristique rapprochee pour le resoudre, ou r est le facteur d'approximation de l'heuristique pour le probleme de Steiner. Dans un deuxieme temps, nous presentons une heuristique permettant de resoudre le probeme de diffusion contrainte dans un groupe auquel on a rajoute une contrainte d'equilibrage.}


E. Altman,
I. Buret,
B. Fabre,
J. Galtier,
C. Guiraud,
T. Tocker,
and C. Touati.
Slot allocation in a TDMA satellite system: simulated annealing approach.
In Proceedings of AIAA International Communication Satellite Systems Conference and Exhibit,
Yokohama, Japan,
April 2003.
[PDF
]

E. Altman,
J. Galtier,
and C. Touati.
Radio Planning in Multibeam Geostationary Satellite Networks.
In Proceedings of AIAA International Communication Satellite Systems Conference and Exhibit,
Yokohama, Japan,
April 2003.
[PDF
]

E. Altman,
J. Galtier,
and C. Touati.
Semidefinite programming approach for bandwidth allocation and routing in networks.
In Proceedings of ITC 18,
Berlin, Germany,
pages 10911100,
August/September 2003.
[PDF
]

G. Barthe,
H. Cirstea,
C. Kirchner,
and L. Liquori.
Pure Patterns Type Systems.
In POPL, Symposium on Principles of Programming Languages,
pages 250261,
2003.
ACM.
[POSTSCRIPT
]

R. Bayon,
N. Lygeros,
and J.S. Sereni.
Nouveaux progrès dans l'énumération des modèles mixtes.
In Knowledge discovery and discrete mathematics : JIM'2003,
Université de Metz, France,
pages 243246,
2003.
INRIA.
[WWW
] [PDF
]

J.C. Bermond and D. Coudert.
Traffic Grooming in Unidirectional WDM Ring Networks using Design Theory.
In IEEE ICC,
volume 2,
Anchorage, Alaska,
pages 14021406,
May 2003.
Note: ON073.
[PDF
] [POSTSCRIPT
]
Abstract: 
We address the problem of traffic grooming in WDM rings with alltoall uniform unitary traffic. We want to minimize the total number of SONET adddrop multiplexers (ADMs) required. We show that this problem corresponds to a partition of the edges of the complete graph into subgraphs, where each subgraph has at most $C$ edges (where $C$ is the grooming ratio) and where the total number of vertices has to be minimized. Using tools of graph and design theory, we optimally solve the problem for practical values and infinite congruence classes of values for a given $C$, and thus improve and unify all the preceding results. We disprove a conjecture of Chiu and Modiano (IEEE/OSA JLT 2000) saying that the minimum number of ADMs cannot be achieved with the minimum number of wavelengths, and also another conjecture of Hu (OSA JON 2002). 

J.C. Bermond,
D. Coudert,
and X. Muñoz.
Traffic Grooming in Unidirectional WDM Ring Networks: The Alltoall Unitary Case.
In The 7th IFIP Working Conference on Optical Network Design & Modelling  ONDM,
Budapest, Hongrie,
pages 11351153,
2003.
[PDF
] [POSTSCRIPT
]
Abstract: 
We address the problem of traffic grooming in WDM rings with alltoall uniform unitary traffic. We want to minimize the total number of SONET adddrop multiplexers (ADMs) required. This problem corresponds to a partition of the edges of the complete graph into subgraphs, where each subgraph has at most $C$ edges (where $C$ is the grooming ratio) and where the total number of vertices has to be minimized. Using tools of graph and design theory, we optimally solve the problem for practical values and infinite congruence classes of values for a given $C$. Among others, we give optimal constructions when $C\geq N(N1)/6$ and results when $C=12$. We also show how to improve lower bounds by using refined counting techniques, and how to use efficiently an ILP program by restricting the search space. 

J.C. Bermond,
O. DeRivoyre,
S. Pérennes,
and M. Syska.
Groupage par tubes.
In Conference ALGOTEL2003, Banyuls, May 2003,
pages 169174,
2003.
[PDF
]

J.C. Bermond,
O. Delmas,
F. Havet,
M. Montassier,
and S. Pérennes.
Réseaux de télécommunications minimaux embarqués tolérants.
In Conference ALGOTEL2003, Banyuls, May 2003,
pages 2732,
2003.
[PDF
]

P. Berthomé,
M. Diallo,
and A. Ferreira.
Generalized Parametric MultiTerminal Flows Problem.
In Proceedings of WG'03,
volume 2880 of Lecture Notes in Computer Science,
pages 7180,
June 2003.
SpringerVerlag.

S. Bhadra and A. Ferreira.
Complexity of Connected Components in Evolving Graphs and the Computation of Multicast Trees in Dynamic Networks.
In S. Pierre,
M. Barbeau,
and E. Kranakis, editors,
Proceedings of AdhocNow'03,
volume 2865 of Lecture Notes in Computer Science,
Montreal,
pages 259270,
October 2003.
Springer Verlag.

M. Bouklit,
D. Coudert,
JF. Lalande,
C. Paul,
and H. Rivano.
Approximate multicommodity flow for WDM networks design.
In J. Sibeyn, editor,
SIROCCO 10,
number 17 of Proceedings in Informatics,
Umea, Sweden,
pages 4356,
2003.
Carleton Scientific.
[PDF
] [POSTSCRIPT
]
Abstract: 
The design of WDM optical networks is an issue for telecom operators since the spreading of this technology will not occur unless enough performance guarantees are provided. Motivated by the quest for efficient algorithms for the Routing and Wavelength Assignment problem (RWA), we address approximations of the fractional multicommodity flow problem which is the central part of a complex randomized rounding algorithm for the integral problem. Through the use of dynamic shortest path computations and other combinatorial approaches, we improve on the best known algorithm. We also provide directions for further improvements. 

M. Bouklit,
D. Coudert,
JF. Lalande,
and H. Rivano.
Approximation combinatoire de multiflot fractionnaire : améliorations.
In AlgoTel'03,
Banyulssurmer, France,
mai 2003.
[PDF
] [POSTSCRIPT
]
Abstract: 
Motiv\'e par la recherche d'algorithmes performants de dimensionnement de r\'eseaux optiques WDM, nous consid\'erons les $(1+\epsilon)$approximations du calcul de multiflot fractionnaire. Nous proposons des am\'eliorations d'un algorithme de la litt\'erature en utilisant des calculs de plus courts chemins dynamiques, \'eventuellement sp\'ecialis\'e au cas du routage optique dans les r\'eseaux WDM multifibres sans conversion. 

B. BuiXuan,
A. Ferreira,
and A. Jarry.
Evolving graphs and least cost journeys in dynamic networks.
In Proceedings of WiOpt'03  Modeling and Optimization in Mobile, AdHoc and Wireless Networks,
Sophia Antipolis,
pages 141150,
March 2003.
INRIA Press.

H.J. Böckenhauer,
D. Bongartz,
J. Hromkovic,
R. Klasing,
G. Proietti,
S. Seibert,
and W. Unger.
On $k$EdgeConnectivity Problems with Sharpened Triangle Inequality (Extended Abstract).
In Proc. 5th Italian Conference on Algorithms and Complexity ( CIAC 2003),
volume 2653 of Lecture Notes in Computer Science,
pages 189200,
2003.
SpringerVerlag.

A. Ciaffaglione,
L. Liquori,
and M. Miculan.
Imperative ObjectBased Calculi in Coinductive Type Theories.
In LPAR, International Conference on Logic for Programming Artificial Intelligence and Reasoning,
volume 2850 of Lecture Notes in Computer Science,
pages 5977,
2003.
[PDF
]

A. Ciaffaglione,
L. Liquori,
and M. Miculan.
Reasoning on an imperative objectbased calculus in Higher Order Abstract Syntax.
In MERLIN, International Workshop on Mechanized Reasoning about Languages with Variable Binding,
2003.
ACM.
[PDF
]

H. Cirstea,
L. Liquori,
and B. Wack.
Rewriting Calculus with Fixpoints: Untyped and Firstorder Systems.
In TYPES, International Workshop on Types for Proof and Programs,
volume 3085 of Lecture Notes in Computer Science,
pages 147161,
2003.
Springer Verlag.
[POSTSCRIPT
]

A. Clementi,
G. Huiban,
G. Rossi,
and Y. Verhoeven.
On the approximation ratio of the MST based heuristic for the energyefficient broadcast problem in static adhoc radio networks.
In Parallel and Distributed Processing Symposium (IPDPS),
pages 8,
April 2003.
IEEE Computer Society Press.
[WWW
] [PDF
]
Abstract: 
We present a technique to evaluate the approximation ratio on random instances of the Minimum Energy Broadcast Problem in AdHoc Radio Networks which is known to be NPhard and approximable within 12. Our technique relies on polynomialtime computable lower bound on the optimal cost of any instance.
The main result of this paper is that the approximation ratio has never achieved a value greater than 6.4. Furthermore, the worst values of this ratio are achieved for small network sizes. We also provide a clear geometrical motivation of such good approximation results. 

D. Coudert,
H. Rivano,
and X. Roche.
A combinatorial approximation algorithm for the multicommodity flow problem.
In K. Jansen and R. SolisOba, editors,
WAOA 03,
number 2909 of Lecture Notes in Computer Science,
Budapest, Hungary,
pages 256259,
September 2003.
SpringerVerlag.
[PDF
] [POSTSCRIPT
]
Abstract: 
This work is motivated by the need for approximation algorithms for the integral multicommodity flow problem which arise in numerous optimization scenarios, including the design of telecommunication networks. We improve on one of the most efficient known combinatorial approximation algorithm for fractional multicommodity flow by using an incremental approach. This approach is validated by experimental results, which show a significant speedup. 

O. Dalle and P. Mussi.
Cooperative Software Development and Computational Resource Sharing.
In NMSC System Simulation Workshop,
ESTEC, Noordwijk, The Netherlands,
March 2003.
European Space Agency.

A. Ferreira,
S. Perennes,
A.W. Richa,
H. Rivano,
and N. Stier Moses.
Models, complexity and algorithms for the design of multifiber WDM networks.
In Telecommunications, 2003. ICT 2003. 10th International Conference on,
volume 1,
pages 1218,
23 Feb.1 March 2003.
[PDF
]
Abstract: 
We study multifiber optical networks with wavelength division multiplexing (WDM). Assuming that the lightpaths use the same wavelength from source to destination, we extend the definition of the wellknown wavelength assignment problem (WAP), to the case where there are k fibers per link, and w wavelengths per fiber are available: This generalization is called the (k,w)WAP. We develop a new model for the (k,w)WAP, based on conflict hypergraphs: conflict hypergraphs more accurately capture the lightpath interdependencies, generalizing the conflict graphs used for singlefiber networks. By relating the (k,w)WAP with the hypergraph coloring problem, we prove that the former is NPcomplete, and present further results with respect to the complexity of that problem. We consider the two natural optimization problems that arise from the (k,w)WAP: the problem of minimizing k given w, and that of minimizing w given k. We develop and analyze the practical performances of two methodologies based on hypergraph coloring, one for each of the two optimization problems, on existing backbone networks in Europe and in the USA. The first methodology relies on two heuristics based on a randomized approximation algorithm and the second consists on an integer programming formulation. 

F. Giroire,
A. Nucci,
N. Taft,
and C. Diot.
Increasing the Robustness of IP Backbones in the Absence of Optical Level Protection.
In Proceedings of the TwentySecond Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM),
2003.
[WWW
] [PDF
]
Abstract: 
There are two fundamental technology issues that challenge the robustness of IP backbones. First, SONET protection is gradually being removed because of its high cost (while SONET framing is kept for failure detection purposes). Protection and restoration are provided by the IP layer that operates directly over a DWDM infrastructure. Second, ISPs are systematically forced to use the shortest distance path between two Points of Presence in order to meet their promised SLAs. In this context, IP backbones are extremely vulnerable to fiber cuts that can bring down a significant fraction of the IP routes. We propose two solutions (an ILP model and a heuristic algorithm) to optimally map a given IP topology onto a fiber infrastructure. The version of the mapping problem that we address incorporates a number of real constraints and requirements faced by carriers today. The optimal mapping maximizes the robustness of the network while maintaining the ISP's SLA delay requirements. In addition, our heuristic takes into consideration constraints such as a shortage of wavelengths and priorities among POPs and routes. The heuristic is evaluated on the Sprint backbone network. We illustrate the tradeoffs between the many requirements. 

C. Gomes and G. Robson Mateus.
Alocação de Caminhos Comutatos por Rótulo em Redes Multiplexadas por Comprimento de Onda.
In SPG,
2003.

A. Jarry and A. Laugier.
Graphes 2connexes à diamètre donné.
In ROADEF 2003,
number 5 of Proceedings in Informatics,
Avignon, France,
pages 102104,
June 2003.
Université d'Avignon et des Pays de Vaucluse.

J.F. Lalande,
S. Pérennes,
and M. Syska.
Groupage dans les réseaux dorsaux WDM.
In ROADEF 2003,
number 5 of Proceedings in Informatics,
Avignon, France,
pages 254255,
June 2003.
Université d'Avignon et des Pays de Vaucluse.

A. Laugier and S. Petat.
Network Design and bmatching.
In Proc. of International Network Optimization Conference,
pages 374379,
2003.
[POSTSCRIPT
]

E. Trajano,
D. Guigue,
E. Costa,
C. Gomes,
H. Almeida,
K. Silva,
and N. Cavalcanti.
SOS  A Tool for the Automatic Segmentation of Musical Flows.
In IX SBCM,
2003.

E. Altman,
J. Galtier,
and C. Touati.
Fair power and transmission rate control in wireless networks.
In Proc. of IEEE GlobeCom'02,
Taipei, Taiwan,
November 2002.

E. Altman,
J. Galtier,
and C. Touati.
SemiDefinite Programming Approach for Bandwidth Allocation and Routing in Networks.
In Proc. of 10th Int. Symp. on Dynamic Games and Application  Networking Games & Resource Allocation Workshop (NGRA2002),
Petrozavodsk, Russia,
July 2002.
Altman and Mazaloz.

E. Altman,
J. Galtier,
and C. Touati.
Utility Based Fair Bandwidth Allocation.
In IASTED International Conference on Networks, Parallel and Distributed Processing, and Applications (NPDPA 2002),
2002.

J.C. Bermond,
S. Choplin,
and S. Pérennes.
Hierarchical Ring Network Design.
In 9th International Colloquium on Structural Information and Communication Complexity (SIROCCO'02),
pages 116,
2002.
Carleton Scientific.

H.J. Böckenhauer,
D. Bongartz,
J. Hromkovic,
R. Klasing,
G. Proietti,
S. Seibert,
and W. Unger.
On the hardness of constructing minimal 2connected spanning subgraphs in complete graphs with sharpened triangle inequality.
In Proc. of the 22nd Conference on Foundations of Software Technology and Theoretial Computer Science (FSTTCS 2002),
volume 2556 of Lecture Notes in Computer Science,
pages 5970,
2002.
SpringerVerlag.

D. Coudert and H. Rivano.
Lightpath assignment for multifibers WDM networks with wavelength translators.
In Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE,
volume 3,
pages 26862690vol.3,
1721 Nov. 2002.
Note: OPNT015.
[PDF
]
Abstract: 
We consider the problem of finding a lightpath assignment for a given set of communication requests on a multifiber WDM optical network with wavelength translators. Given such a network and w, the number of wavelengths available on each fiber, k, the number of fibers per link, and c, the number of partial wavelength translations available on each node, our problem stands for deciding whether it is possible to find a wlightpath for each request in the set such that there is no link carrying more that k lightpaths using the same wavelength nor node where more than c wavelength translations take place. Our main theoretical result is the writing of this problem as a particular instance of integral multicommodity flow, hence integrating routing and wavelength assignment in the same model. We then provide three heuristics mainly based upon randomized rounding of fractional multicommodity flow and enhancements that are three different answers to the tradeoff between efficiency and tightness of approximation, and discuss their practical performances on both theoretical and realworld instances. 

D. Coudert and H. Rivano.
Routage optique dans les réseaux WDM multifibres avec conversion partielle..
In AlgoTel'02,
Mèze, France,
pages 1724,
May 2002.
[WWW
] [PDF
] [POSTSCRIPT
]
Abstract: 
Nous consid\'erons le probl\`eme du routage optique d'un ensemble donn\'e de requ\^etes de communications dans un r\'eseau \wdm multifibres avec conversion partielle. \'Etant donn\'e un tel r\'eseau disposant de $w$ longueurs d'onde par fibre, $k$ fibres par lien et $c$ conversions possibles par \noeud du r\'eseau, le probl\`eme revient \`a d\'ecider s'il est possible de trouver un chemin $w$color\'e pour chaque requ\^ete, de sorte qu'au plus $k$ chemins utilisent une m\^eme longueur d'onde sur un m\^eme lien du r\'eseau et qu'aucun \noeud n'op\`ere plus de $c$ conversions. Notre r\'esultat principal r\'eside dans l'\'ecriture de ce probl\`eme sous la forme d'une instance particuli\`ere de multiflot entier, int\'egrant dans un m\^eme mod\`ele le routage et l'affectation de longueurs d'onde. Nous fournissons ensuite trois heuristiques bas\'ees sur l'arrondi al\'eatoire de multiflots fractionnaires, qui sont trois r\'eponses diff\'erentes au compromis efficacit\'e/pr\'ecision des approximations. Nous les validons en comparant leur performances sur des instances th\'eoriques ou issue du monde r\'eel. 

A. Ferreira.
On models and algorithms for dynamic communication networks: The case for evolving graphs.
In 4$^{\rm e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2002),
Mèze, France,
May 2002.

A. Ferreira,
S. Pérennes,
A. Richa,
H. Rivano,
and N. Stier.
On the design of multifiber WDM networks.
In AlgoTel'02,
Mèze, France,
pages 2532,
May 2002.
[WWW
] [PDF
] [POSTSCRIPT
]
Abstract: 
In this paper, we address multifiber optical networks with Wavelength Division Multiplexing (\wdm). Assuming that the lightpaths use the same wavelength from source to destination, we extend the definition of the wellknown Wavelength Assignment Problem (\wap) to the case where there are $k$ fibers per link, and $w$ wavelengths per fiber are available. This generalization is called the $(k,w)$\wap. We develop a new model for the $(k,w)$\wap based on \emph{ conflict hypergraphs}. Conflict hypergraphs accurately capture the lightpath interdependencies, generalizing the conflict graphs used for singlefiber networks. By relating the $(k,w)$\wap with the hypergraph coloring problem, we prove that the former is \npc, and present further results with respect to the complexity of that problem. We consider the two natural optimization problems that arise from the $(k,w)$\wap : the problem of minimizing $k$ given $w$, and that of minimizing $w$ given $k$. We develop and analyze the practical performances of two methodologies based on hypergraph coloring, one for each of the two optimization problems, on existing backbone networks in Europe and in the USA. The first methodology relies on an integer programming formulation, and the second consists of a heuristic based on a randomized algorithm. 

F. Havet.
Design of Fault Tolerant Satellite Networks with Priorities via Selectors.
In Proc. of SIROCCO'02,
Andros, Greece,
pages 165180,
June 2002.

F. Havet.
Robustness of a Routing Tree for the Push Tree Problem.
In $4^{e}$ rencontres francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'02),
Mèze, France,
pages 8186,
May 2002.

G. Huiban,
S. Pérennes,
and M. Syska.
Traffic Grooming in WDM Networks with MultiLayer Switches.
In IEEE ICC,
NewYork,
April 2002.
Note: CDRom.

A. Jarry.
Disjoint Paths in Symmetric Digraphs.
In International Colloquium on Structural Information and Communi cation Complexity  SIROCCO,
Andros, Greece,
pages 211222,
June 2002.
Carleton.

P. Mussi.
Tuning Car Following Algorithms for Realistic Behaviour.
In AI, Simulation & Planning in High Autonomy Systems,
Lisbon, Portugal,
pages 281284,
April 2002.

B. Reed and B. Sudakov.
List colouring of graphs with at most $(2o(1))\chi$ vertices.
In Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002),
Beijing,
pages 587603,
2002.
Higher Ed. Press.

J.C. Bermond,
L. Chacon,
D. Coudert,
and F. Tillerot.
A Note on Cycle Covering.
In ACM Symposium on Parallel Algorithms and Architectures  SPAA,
Crete island, Greece,
pages 310311,
46 July 2001.
[POSTSCRIPT
]
Abstract: 
This study considers the design of a survivable WDM network based on covering the initial network with subnetworks, which are protected independently from each other. 

J.C. Bermond,
L. Chacon,
D. Coudert,
and F. Tillerot.
Cycle Covering.
In International Colloquium on Structural Information and Communication Complexity  SIROCCO,
Proceedings in Informatics 11,
Vall de Nuria, Spain,
pages 2134,
2729 June 2001.
Carleton Scientific.
[PDF
] [POSTSCRIPT
]
Abstract: 
This paper considers the design of a survivable WDM network based on covering the initial network with subnetworks, which are protected independently from each other. We focus on the case where the optical WDM network is a ring, there are requests between any pair of vertices and the covering is done with small cycles. This problem can be modelled as follows: Find a covering of the edges of a logical graph $I$ (here the complete graph $K_n$) by subgraphs $I_k$ of a certain kind (here cycles $C_k$ of length $k$), such that, for each $I_k$, there exists in the physical graph $G$ (here $C_n$) a disjoint routing of the edges of $I_k$. The aim is to minimize the number of subgraphs $I_k$ in the covering. We give optimal solutions for that problem. 

J.C. Bermond,
F. Havet,
and D. Tóth.
Design of fault tolerant on board networks with priorities.
In $3^{e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2001),
SaintJeandeLuz , France,
pages 9598,
Mai 2001.

S. Bertrand,
A. Laugier,
and P. Mahey.
Routing flows in networks with heterogenous protocols and pathdependent edge costs.
In $3^{e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2001),
SaintJeandeLuz , France,
pages 5560,
Mai 2001.

A. Caminada,
A. Ferreira,
and L. Floriani.
Principal Component Analysis for data volume reduction in experimental analysis of heuristics.
In Proceedings of GECCO 2001 Workshop on Reallife Evolutionary Design Optimisation,
San Francisco (USA),
2001.

I. Caragianis,
A. Ferreira,
C. Kaklamanis,
S. Pérennes,
and H. Rivano.
Fractional path coloring on bounded degree trees.
In F. Orejas,
P. G. Spirakis,
and J. van Leeuwen, editors,
Proceedings of the 28th ICALP,
volume 2076 of Lecture Notes in Computer Science,
Crete, Greece,
pages 732743,
July 2001.
SpringerVerlag.
[PDF
]
Abstract: 
This paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexing (wdm) alloptical networks. 

I. Caragiannis,
A. Ferreira,
C. Kaklamanis,
S. Pérennes,
P. Persiano,
and H. Rivano.
Approximate Constrained Bipartite Edge Coloring.
In V.B. Le A. Branstädt, editor,
27th International Workshop on GraphTheoretic Concepts in Computer Science (WG'01),
volume 2204 of Lecture Notes in Computer Science,
Boltenhagen, Germany,
pages 2131,
June 2001.
SpringerVerlag.
[PDF
]
Abstract: 
We study the following Constrained Bipartite Edge Coloring (CBEC) problem: We are given a bipartite graph G(U,V,E) of maximum degree l with n vertices, in which some of the edges have been legally colored with c colors. We wish to complete the coloring of the edges of G minimizing the total number of colors used. The problem has been proved to be NPhard event for bipartite graphs of maximum degree three [5]. 

S. Choplin.
Virtual Path Layout in ATM Path with given hop count.
In International Conference on Networking, ICN01,
volume 2094, Part II of LNCS,
pages 527537,
2001.
Springer.

H. Cirstea,
C. Kirchner,
and L. Liquori.
Matching Power.
In RTA, International Conference on Rewriting Techniques and Applications,
volume 2051 of Lecture Notes in Computer Science,
pages 7792,
2001.
[POSTSCRIPT
]

H. Cirstea,
C. Kirchner,
and L. Liquori.
The Rho Cube.
In FoSSaCS, International Conference on Foundations of Software Science and Computation Structures,
volume 2030 of Lecture Notes in Computer Science,
pages 168183,
2001.
[POSTSCRIPT
]

M. Cosnard and L. Grigori.
A Parallel Algorithm for Sparse Symbolic LU Factorization without Pivoting on Out of Core Matrices.
In 15th ACM International Conference on Supercomputing (ICS'01),
2001.

D. Coudert.
Chemins disjoints de poids minimum pour la sécurisation de réseaux de télécommunications.
In Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications  AlgoTel,
StJean de Luz, France,
pages 4753,
2830 Mai 2001.
[POSTSCRIPT
]
Abstract: 
Cette \'etude s'int\'eresse \`a la planification de r\'eseaux WDM tol\'erants aux pannes. Nous cherchons \`a \'etablir, pour chaque couple de n{\oe}uds du r\'eseau, deux chemins de communication disjoints, l'un \'etant r\'eserv\'e \`a la protection de l'autre. Pour un r\'eseau \`a $n$ n{\oe}uds et $m$ liens de communications, nous donnons un algorithme en $O(n(m+n\log n))$, permettant de calculer depuis un n{\oe}ud donn\'e et vers chacun des autres n{\oe}uds deux chemins arcdisjoints dont la somme des poids est minimale. Ceci am\'eliore la complexit\'e des solutions bas\'ees sur les algorithmes de flot de poids minimum, qui est en temps $O(m(m+n\log n)\log n)$ pour un seul couple de sommets. 

D. Coudert and X. Muñoz.
How Graph Theory can help Communications Engineering.
In D.K.Gautam, editor,
Broad band optical fiber communications technology  BBOFCT,
Jalgaon, India,
pages 4761,
December 2001.
Nirtali Prakashan.
Note: Invited paper.
[POSTSCRIPT
]
Abstract: 
We give an overview of different aspects of graph theory which can be applied in communication engineering, not trying to present immediate results to be applied neither a complete survey of results, but to give a flavor of how graph theory can help this field. We deal in this paper with network topologies, resource competition, state transition diagrams and specific models for optical networks. 

S. Céroi and F. Havet.
Trees with three leaves are (n + 1)unavoidable.
In Jayme Szwarcfiter and Siang Song, editors,
Electronic Notes in Discrete Mathematics,
volume 7,
2001.
Elsevier Science Publishers.

O. Dalle,
J. Radzik,
C. Rigal,
F. Rodière,
and C. Saroléa.
ASIMUT: An Environment for the Simulation of MultiMedia Satellite Telecommunication Networks.
In 19th International Communications Satellite Systems Conference (ICSSC),
Toulouse, France,
April 2001.
AIAA.

H. Everett,
C. M. H. de Figueiredo,
S. Klein,
and B. Reed.
Bullreducible Berge graphs are perfect.
In Comb01Euroconference on Combinatorics, Graph Theory and Applications,
volume 10 of Electron. Notes Discrete Math.,
Amsterdam,
pages 3 pp. (electronic),
2001.
Elsevier.

G. Fertin,
A. Raspaud,
and B. Reed.
On star coloring of graphs.
In Graphtheoretic concepts in computer science (Boltenhagen, 2001),
volume 2204 of Lecture Notes in Comput. Sci.,
Berlin,
pages 140153,
2001.
Springer.

J. Galtier.
SemiDefinite Programming as a Simple Extension to Linear Programming: Convex Optimization with Queueing, Equity and Other Telecom Functionals.
In $3^{e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2001),
SaintJeandeLuz,
pages 2128,
May 2001.

J. Galtier and A. Oliveira.
A proposal to study satellite constellation routing via classical linear programming methods.
In 43rd conference of the Canadian Operations Research Society,
2001.

C. Gavoille,
D. Peleg,
S. Pérennes,
and R. Raz.
Distance Labeling in Graphs.
In SODA'01,
pages 210219,
2001.

C. Gomes and A. H. Dominguez.
Modelagem e Implementação do módulo tutor do ambiente AVATA@ead.
In Anais XI Encontro de Iniciação Cientìfica da Universidade Federal de Alagoas,
2001.

F. Havet and M. Wennink.
The Push Tree Problem.
In SPAA'01: 13th ACM Symposium on Parallel Algorithms and Architectures,
Crète , Grèce,
pages 318319,
Juillet 2001.

C. McDiarmid and B. Reed.
Channel assignment on nearly bipartite and bounded treewidth graphs.
In Comb01Euroconference on Combinatorics, Graph Theory and Applications,
volume 10 of Electron. Notes Discrete Math.,
Amsterdam,
pages 4 pp. (electronic),
2001.
Elsevier.

M. Molloy and B. Reed.
Colouring graphs when the number of colours is nearly the maximum degree.
In Proceedings of the ThirtyThird Annual ACM Symposium on Theory of Computing,
New York,
pages 462470 (electronic),
2001.
ACM.

D. Rautenbach and B. Reed.
Approximately covering by cycles in planar graphs.
In Proceedings of the Twelfth Annual ACMSIAM Symposium on Discrete Algorithms (Washington, DC, 2001),
Philadelphia, PA,
pages 402406,
2001.
SIAM.

H. Rivano.
Planification de réseaux optiques WDM kfibres.
In AlgoTel'01  $3^{e}$ Rencontres Françaises sur les Aspects Algorithmiques des Télécommunications,
SaintJeandeLuz, France,
pages 4146,
mai 2001.
[WWW
] [PDF
]
Abstract: 
Cet article propose une modélisation en termes d'hypergraphe du problème d'affectation de longueurs d'onde à des chemins dans un réseau \wdm $k$fibres. La contrainte classique rencontrée dans les réseaux \wdm change de nature lorsque plusieurs fibres connectent physiquement deux noeuds du réseau. Nous montrons l'équivalence entre ce problème et la coloration $k${\em tolérante} de {\em l'hypergraphe des conflits} des chemins. Nous exploitons ensuite deux résultats d'algorithmique aléatoire de la littérature pour donner une première approximation du dimensionnement des réseaux $k$fibres. 

E. Altman,
E. Baçsar,
T. Jiménez,
and N. Shimkin.
Competitive Routing in Networks with Polynomial Cost.
In IEEE Infocom 2000,
pages 15861593,
mars 2000.

A. Andreev,
A. Clementi,
P. Penna,
and J. Rolim.
Parallel Read Operations Without Memory Contention.
In Electronic Colloquium on Computational Complexity,
volume TR0053,
2000.

B. Beauquier,
K.S. Candan,
A. Ferreira,
S. Pérennes,
and A. Sen.
On shortest path problems with ``nonMarkovian'' link contribution to path lengths.
In Proc. of IFIP/TC6 Networking 2000 Conference,
Paris, France,
mai 2000.

B. Beauquier and E. Darrot.
Arbitrary size Waksman networks and their vulnerability.
In Actes des $1^{res}$ Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'99),
2000.
World Scientific.

P. Bergé,
A. Ferreira,
J. Galtier,
and S. Petit.
A probabilistic study of intersatellite links load in polar orbit satellite constellations.
In $2^{e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2000),
La Rochelle, France,
pages 137142,
Mai 2000.

J.C. Bermond,
A. Bonnecaze,
T. Kodate,
S. Perennes,
and P. Sole.
Broadcasting in hypercubes in the circuit switched model.
In Proc. Conference IPDPS 2000, Cancun, Mexico,, May 2000,
pages 2126,
2000.
[PDF
]

JC. Bermond,
L. Chacon,
D. Coudert,
and F. Tillerot.
Conception d'un réseau WDM protégé par sousréseaux.
In 2ème Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'00),
La Rochelle, France,
pages 8388,
May 2000.
INRIA.
[WWW
] [PDF
]
Abstract: 
Nous proposons une modélisation de la construction d'un réseau WDM protégé comme l'extension du problème classique de couverture des arêtes d'un graphe. Un ensemble de résultats est donné pour la réalisation de l'instance AlltoAll sur un réseau en anneau. 

G. Bongiovanni,
A. Clementi,
and P. Penna.
A Note on Parallel Read Operations on Large Public Databases.
In Proc. of ARACNE00, International Workshop on Approximation and Randomized Algorithms in Communication Networks,
volume Carleton Scientific Press,
pages 123133,
2000.

A. Clementi,
A. Ferreira,
P. Penna,
S. Pérennes,
and R. Silvestri.
The Minimum Range Assignment Problem on Linear Radio Networks.
In Proc. of ESA00, 8th Annual European Symposium on Algorithms,
volume LNCS,
pages 143154,
2000.

A. Clementi,
P. Penna,
and R. Silvestri.
On The Power Assignment Problem in Radio Networks.
In Electronic Colloquium on Computational Complexity,
volume TR0054,
2000.

A. Clementi,
P. Penna,
and R. Silvestri.
The Power Range Assignment Problem in Radio Networks on the Plane.
In Proc. of STACS00, 17th Annual Symposium on Theoretical Aspects of Computer Science,
volume LNCS,
pages 651660,
2000.

D. Colnet and L. Liquori.
MatchO, a Statically Safe (?) Dialect of Eiffel.
In TOOLS, International Conference on Technology of ObjectOriented Languages and Systems,
pages 190201,
2000.
IEEE Computer Society.
[POSTSCRIPT
]

D. Coudert,
A. Ferreira,
and S. Perennes.
De Bruijn Isomorphisms and Free Space Optical Networks.
In IEEE International Parallel and Distributed Processing Symposium,
pages 769774,
2000.
IEEE Press.
[PDF
] [POSTSCRIPT
]
Abstract: 
The de Bruijn digraph $B(d,D)$ has degree $d$, diameter $D$, $d^D$ vertices and $d^{D+1}$ arcs. It is usually defined by words of size $D$ on an alphabet of cardinality $d$, through a cyclic left shift permutation on the words, after which the rightmost symbol is changed. In this paper, we show that any digraph defined on words of a given size, through an {\em arbitrary} permutation on the alphabet {\bf and} an {\em arbitrary} permutation on the word indices, is isomorphic to the de Bruijn digraph, provided that this latter permutation is {\em cyclic}. We use this result to improve from $O\left(d^{D+1}\right)$ to $\Theta\left(\sqrt{d^{D+1}}\right)$ the number of lenses required for the implementation of $B(d,D)$ by the Optical Transpose Interconnection System proposed by Marsden {\em et al.} (Optics Letters 18(13):10831085, July 1993). 

P. Crescenzi,
G. Gambosi,
and P. Penna.
OnLine Algorithms for the Channel Assignment Problem in Cellular Networks.
In Proc. of ACM DIALM2000, 4th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications,
pages 17,
2000.

O. Dalle,
P. Mussi,
and C. Rigal,
and V. Sutter.
ASIMUT: An Environment for the Simulation of MultiMedia Satellite Telecommunication Networks.
In Proc. 6th ESA Workshop on Simulation in European Space Pragrams,
ESTEC, Noordwijk, The Netherlands,
pages 285288,
October 2000.
European Space Agency.
[WWW
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A. Ferreira,
J. Galtier,
P. Mahey,
G. Mateus,
and A. Oliveira.
An Optimization Model for Routing in Low Earth Orbit Satellite Constellations.
In Proceedings of ISPAN,
Dallas, USA,
December 2000.

A. Ferreira,
J. Galtier,
and S. Pérennes.
Approximation of a straight line in a bounded lattice.
In $2^{e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2000),
La Rochelle, France,
pages 5358,
Mai 2000.

P. Fraigniaud,
A. Pelc,
D. Peleg,
and S. Pérennes.
Assigning labels in unknown anonymous networks.
In Proceedings of PODC 2000, (Nineteenth Annual ACM SIGACTSIGOPS Symposium on PRINCIPLES OF DISTRIBUTED COMPUTING),
pages 101112,
2000.

J. Galtier.
Routing issues for LEO satellite constellations.
In International Conference on Advances in Infrastructure for Electronic Business, Science, and Education on the Internet (SSGRR 2000),
L'Aquila, Italie,
juillet 2000.

J. Galtier and S. Lanteri.
On overlapping partitions.
In David J. Lilja, editor,
Proceedings of the 2000 International Conference on Parallel Processing,
Toronto, Canada,
pages 461468,
août 2000.

L. Gargano,
A. Pelc,
S. Pérennes,
and U. Vaccaro.
Efficient communication in unknown networks.
In Proc. of WG'2000  26th International Workshop on GraphTheoretic Concepts in Computer Science,
2000.
Note: A paraître.

S. Haddad,
A. Laugier,
and JeanFrancois Maurras.
Designing telecommunication networks with global capacities under survivability constraints.
In ECCO XIII,
2000.

S. Haddad,
A. Laugier,
and JeanFrancois Maurras.
Global designing of telecommunication networks.
In CO 2000,
2000.

M.C. Heydemann,
N. Marlin,
and S. Pérennes.
Rotational Cayley Graphs on Transposition Generated Groups (Extended Abstract).
In 6ème Colloque International de Théorie des Graphes,
Electronical Notes in Discrete Mathematics,
pages 187190,
2000.
Elsevier Science.

T. Jiménez.
Optimal Admission Control for High Speed Networks: A Dynamic Programming Approach.
In IEEE Conference on Decision and Control,
decembre 2000.

T. Jiménez,
P. Mussi,
and G. Siegel.
A road traffic simulator : carfollowing and lanechanging.
In European Simulation Multiconference 2000,
Gent, Belgium,
pages 241245,
Mai 2000.

T. Jiménez,
P. Mussi,
and G. Siegel.
The distribution and partitioning scheme of the HIPERTRANS traffic simulator.
In European Simulation Symposium 2000,
Hamburg, Allemagne,
pages 462466,
September 2000.

A. Laugier and P. Mahey.
Design of multilevelprotocol data networks.
In $2^{e}$ rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2000),
La Rochelle, France,
pages 107111,
Mai
2000.

M. Molloy and B. Reed.
$k$colouring when $k$ is close to $\Delta$.
In 6th International Conference on Graph Theory (Marseille, 2000),
volume 5 of Electron. Notes Discrete Math.,
Amsterdam,
pages 4 pp. (electronic),
2000.
Elsevier.

M. Molloy and B. Reed.
Nearoptimal list colorings.
In Proceedings of the Ninth International Conference ``Random Structures and Algorithms'' (Poznan, 1999),
volume 17,
pages 376402,
2000.

P. Penna.
Succinct Representations of Model Based Belief Revision.
In Proc. of STACS00, 17th Annual Symposium on Theoretical Aspects of Computer Science,
volume LNCS,
pages 205216,
2000.

B. Reed.
How tall is a tree?.
In Proceedings of the ThirySecond Annual ACM Symposium on Theory of Computing,
New York,
pages 479483 (electronic),
2000.
ACM.

E. Altman,
G. Koole,
and T. Jiménez.
Comparing tandem queueing systems and their fluid limits.
In 37th Annual Allerton Conference on Communication, Control, and Computing,
September 1999.

F. Baude,
D. Caromel,
N. Furmento,
and D. Sagnol.
Overlapping Communication with Computation in Distributed Object Systems.
In Peter Sloot,
Marian Bubak,
Alfons Hoekstra,
and Bob Hertzberger, editors,
Proceedings of the 7th International Conference  High Performance Computing Networking'99 (HPCN Europe 1999),
volume 1593 of Lecture Notes in Computer Science,
Amsterdam, The Netherlands,
pages 744753,
April 1999.

B. Beauquier and E. Darrot.
Arbitrary size Waksman networks.
In Actes des 1ères Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel'99),
Roscoff, France,
pages 95100,
May 1999.

B. Beauquier,
S. Pérennes,
and D. Tóth.
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Abstract: 
Many results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be done in linking those results together. In this paper, we propose a step in this direction, by giving optical layouts for several graphtheoretical topologies studied in the literature, using the Optical Transpose Interconnection System (OTIS) architecture. These topologies include the family of Partitioned Optical Passive Star (POPS) and stackKautz networks as well as a generalization of the Kautz and de Bruijn digraphs. 

D. Coudert,
A. Ferreira,
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T. Jiménez,
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Gruia Calinescu,
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Abstract: 
In this paper we study the design of regular multicast networks implemented with Optical Passive Star (OPS) couplers. We focus on an architecture based on both Kautz graphs and stackgraphs, and show that it is very costeffective with respect to its resources requirements, namely the number of OPS couplers, power budget, scalability and number of transceivers, and presents a large ratio numberofnodes/diameter. The important issue of medium access control is also addressed and control protocols for accessing the optical couplers are given and analyzed. Finally, we show through simulation that these control protocols efficiently implement shortest path routing on these networks. 

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M. Molloy and B. Reed.
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A. Goldman,
and S. Song.
Comunicação em hipergrades e hipertoros usando barramentos.
In Proceedings of the 5th Simpósio Brasileiro de Arquitetura de Computadores e Proc. de Alto Desempenho, SBC,
Florianópolis (Br),
pages 1732,
September 1993.
Brazilian Society of Computer Science.

A. Ferreira and S. Ubéda.
Ultrafast parallel contour tracking, with applications to thinning.
In G.R. Joubert,
D. Trystram,
F.J. Peters,
and D.J. Evans, editors,
Parallel Computing: Trends and Applications (ParCo'93),
volume 9 of Advances in Parallel Computing,
pages 97104,
1993.
Elsevier Science B.V., Amsterdam.

L. Mallet and P. Mussi.
Object Oriented Parallel Discrete Event Simulation: The PROSIT Approach.
In Modelling and Simulation FSM 93, june 79, LYON,
June 1993.
SCS.

H. Rakotoarisoa and P. Mussi.
PARSEVAL: A Workbench for Queueing Networks Parallel Simulation.
In Modelling and Simulation FSM 93, june 79, LYON,
June 1993.
SCS.

S. Akl,
M. Cosnard,
and A. Ferreira.
Revisiting parallel speedup complexity.
In W.W. Koczkodaj,
P.L. Lauer,
and A.A. Toptsis, editors,
Proceedings of the IEEE International Conference on Computing and Information  ICCI'92,
pages 179182,
1992.
IEEE Press.

J.C. Bermond and P. Fraigniaud.
Broadcasting and NPCompleteness.
In Graph Theory Notes of New York,
volume XXII,
pages 814,
1992.
[PDF
]

J. C. Bermond and M. Syska.
Routage wormhole et canaux virtuels.
In M. Nivat M. Cosnard and Y. Robert, editors,
Algorithmique Parallèle,
pages 149158,
1992.
Masson.
[PDF
]

P. Berthomé and A. Ferreira.
Efficiently solving geometric problems on large hypercube multiprocessors.
In S. Tzafestas,
P. Borne,
and L. Grandinetti, editors,
Parallel and Distributed Computing in Engineering Systems,
pages 123128,
1992.
IMACS  North Holland.

M. Cosnard and A. Ferreira.
Designing nonnumerical parallel algorithms.
In D.J. Evans,
G.R. Joubert,
and H. Liddell, editors,
invited paper, Proceedings of the International Conference on Parallel Computing  ParCo'91,
London (UK),
pages 318,
1992.
Elsevier Science Publishers B.V..

T. Duboux,
A. Ferreira,
and M. Gastaldo.
MIMD Dictionary Machines: from theory to practice.
In L. Bougé et al., editor,
Parallel Processing: CONPAR 92  VAPP V,
volume 634 of Lecture Notes in Computer Science,
pages 545550,
1992.
SpringerVerlag.

A. Ferreira.
Parallel search in sorted multisets, and NPComplete problems.
In R. BaezaYates and U. Manber, editors,
Computer Science  Research and Applications,
Santiago  Chile,
pages 383394,
1992.
Plenum Press.

A. Ferreira and S. Song.
Achieving optimality for gate matrix layout and PLA folding: a graph theoretic approach.
In I. Simon, editor,
LATIN '92,
volume 384 of Lecture Notes in Computer Science,
São Paulo (Br),
pages 139153,
1992.
SpringerVerlag.

C. McDiarmid,
B. Reed,
A. Schrijver,
and B. Shepherd.
Noninterfering network flows.
In Algorithm theorySWAT '92 (Helsinki, 1992),
volume 621 of Lecture Notes in Comput. Sci.,
Berlin,
pages 245257,
1992.
Springer.

M. Cosnard and A. Ferreira.
A tight bound for selection in X+Y.
In F. Dehne et al., editor,
Advances in Computing and Information  ICCI '91,
volume 497 of Lecture Notes in Computer Science,
pages 134138,
1991.
SpringerVerlag.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Efficient parallel construction and manipulation of pointer based quadtrees.
In Proceedings of the International Conference on Parallel Processing  ICPP'91,
St. Charles (USA),
pages 255262,
1991.

A. Ferreira and J. Peters.
Finding the smallest path in a rectilinear polygon on a hypercube multiprocessor.
In Proceedings of the Third Canadian Conference on Computational Geometry  CCCG'91,
Vancouver (Ca),
pages 162165,
1991.

B. Alspach,
J.C. Bermond,
and D. Sotteau.
Decomposition into cycles I: Hamilton decompositions.
In Proceedings of 1987 Cycles and Rays Colloquium, Montréal,
pages 918,
1990.
NATO ASI Ser. C, Kluwer Academic Publishers, Dordrech PDF = ftp://ftpsop.inria.fr/mascotte/personnel/JeanClaude.Bermond/PUBLIS/ABS90.pdf.

J.C. Bermond and J. Bond.
Combinatorial designs and hypergraphs of diameter one.
In Proceedings of the firts ChinaUS International Conference, Jinan, China, June 1986,
volume 576,
pages 5162,
1990.
Annals of the New York Academy of Sciences.

B. Braschi,
A. Ferreira,
and J. Zerovnik.
On the asymptotic behaviour of parallel simulated annealing.
In D.J. Evans,
G.R. Joubert,
and F.J. Peters, editors,
Proceedings of the International Conference on Parallel Computing  ParCo'89,
pages 263268,
1990.
NorthHolland.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
A massively parallel knowledgebase server using a hypercube multiprocessor.
In Proceedings of the IEEE International Conference on Tools for AI,
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pages 660666,
1990.
IEEE Press.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Parallel AI algorithms for finegrained hypercube multiprocessors.
In G. Wolf et al., editor,
invited paper, Proceedings of the International Workshop on Parallel Processing by Cellular Automata and Arrrays (PARCELLA),
volume 2,
EastBerlin,
pages 5165,
1990.

J.C. Bermond,
G. Illiades,
and C. Peyrat.
An optimization problem in distributed loop computer networks.
In Combinatorial Mathematics: Proceedings of the Third International Conference (New York, 1985),
volume 555 of Ann. New York Acad. Sci.,
New York,
pages 4555,
1989.
New York Acad. Sci..

J.C. Bermond and J.C. Konig.
General and efficient decentralized consensus protocols II.
In Proc. of the International Workshop on Parallel and distributed algorithms, Bonas, France,
pages 199210,
1989.
NorthHolland.

J.C. Bermond and C. Peyrat.
De Bruijn and Kautz networks: a competitor for the hypercube?.
In F. André and JP. Verjus, editors,
Proceedings of the 1st European Workshop on Hypercubes and Distributed Computers, Rennes,
pages 279293,
1989.
North Holland.

M. Cosnard and A. Ferreira.
Parallel algorithms for searching in X+Y.
In F.Ris and P.M.Kogge, editors,
Proceedings of the International Conference on Parallel Processing  ICPP'89,
volume 3,
pages 1619,
1989.
Penn State University Press.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Parallel branch and bound on fine grained hypercube multiprocessors.
In Proceedings of the IEEE Workshop on Tools for AI,
Herndon, VA (USA),
pages 616622,
1989.
IEEE Press.

F. Dehne,
A. Ferreira,
and A. RauChaplin.
Parallel fractional cascading on a hypercube multiprocessor.
In Proceedings of the 27th Annual Allerton Conference on Communication, Control and Computing,
pages 10841093,
October 1989.

A. Ferreira.
The Knapsack Problem on Parallel Architectures.
In M. Cosnard et al., editor,
Parallel and Distributed Algorithms,
pages 145152,
1989.
NorthHolland.

A. Ferreira and M. Gastaldo.
Implementing sorting on a hypercube.
In F. André et J.P. Verjus, editor,
Hypercube and Distributed Computers,
pages 359360,
1989.
INRIANorthHolland.

Z. Liu and P. Mussi.
Performance evaluation of a deadlock free protocol for blocking rings.
In International Conference on Super Computing,
June 1989.

J.C. Bermond and J.M. Fourneau.
Independent connections: an easy characterization of baseline equivalent multistage interconnection networks.
In Int. Conf. on Parallel Processing,
August 1988.

J.C. Bermond,
J.C. König,
and M. Raynal.
General and efficient decentralized consensus protocols.
In Distributed algorithms (Amsterdam, 1987),
volume 312 of Lecture Notes in Comput. Sci.,
Berlin,
pages 4156,
1988.
Springer.

M. Cosnard and A. Ferreira.
A processor network for generating all the permutations.
In E. Chiricozzi and A. D'Amico, editors,
Parallel Processing and Applications,
pages 141147,
1988.
NorthHolland.

A. Ferreira.
An optimal ${O(n^2)}$ algorithm to fold special PLA's.
In H.A.Eiselt and G.Pederzoli, editors,
Advances in Optimization and Control,
volume 302 of Lecture Notes in Economics and Math. Systems,
pages 92102,
1988.
SpringerVerlag.

A. Ferreira.
Efficient parallel algorithms for the knapsack problem.
In M. Cosnard et al., editor,
Parallel Processing,
pages 169179,
1988.
IFIPNorth Holland.

J.C. Bermond,
J. Bond,
and C. Peyrat.
Interconnection networks with each node on two buses in Parallel Algorithms and Architectures.
In Proceedings InTernational Workshop on Parallel Algorithms and Architectures,
pages 155167,
April 1986.
North Holland.

A. Ferreira.
O problema do dobramento optimal de PLA's: uma nova abordagem e seu algoritmo.
In Proceedings of the 6th Brazilian Congress on Computer Science,
1986.
University of Pernambuco Press.

C. L. Monma,
B. Reed,
and W. T. Trotter, Jr..
A generalization of threshold graphs with tolerances.
In Proceedings of the seventeenth Southeastern international conference on combinatorics, graph theory, and computing (Boca Raton, Fla., 1986),
volume 55,
pages 187197,
1986.

J.C. Bermond and G. Memmi.
A graph theoretical characterization of minimal deadlocks in Petri nets.
In Graph theory with applications to algorithms and computer science (Kalamazoo, Mich., 1984),
WileyIntersci. Publ.,
New York,
pages 7387,
1985.
Wiley.

A. Ferreira.
Algoritmos heurìsticos para otimização de PLA's.
In Proceedings of the 5th Brazilian Symposium of Microelectronics,
1985.
University of São Paulo Press.

W. Jalby,
J. Maillard,
and P. Mussi.
Evaluation of Parallel Execution of Program Tree Structures.
In Parallel Computing 85,
pages 279285,
1985.

J.C. Bermond,
J. Bond,
and J.F. Saclé.
Large hypergraphs of diameter $1$.
In Graph theory and combinatorics (Cambridge, 1983),
London,
pages 1928,
1984.
Academic Press.

P. Mussi and P. Nain.
Evaluation of Parallel Execution of Program Tree Structures.
In ACM SIGMETRICS Conference on Measurement and Modeling,
volume 12,
August 1984.
ACM.

J.C. Bermond,
C. Delorme,
and J.J. Quisquater.
Grands graphes de degré et diamètre fixés.
In Combinatorial mathematics (MarseilleLuminy, 1981),
volume 75 of NorthHolland Math. Stud.,
Amsterdam,
pages 6573,
1983.
NorthHolland.

J.C. Bermond and B. Bollobás.
The diameter of graphsa survey.
In Proceedings of the Twelfth Southeastern Conference on Combinatorics, Graph Theory and Computing, Vol. I (Baton Rouge, La., 1981),
volume 32,
pages 327,
1981.

J.C. Bermond.
Graceful graphs, radio antennae and French windmills.
In Graph theory and combinatorics (Proc. Conf., Open Univ., Milton Keynes, 1978),
volume 34 of Res. Notes in Math.,
Boston, Mass.,
pages 1837,
1979.
Pitman.

J.C. Bermond.
Le problème des ``ouvroirs''.
In Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976),
volume 260 of Colloq. Internat. CNRS,
Paris,
pages 3134,
1978.
CNRS.

J.C. Bermond,
A. E. Brouwer,
and A. Germa.
Systèmes de triplets et différences associées.
In Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976),
volume 260 of Colloq. Internat. CNRS,
Paris,
pages 3538,
1978.
CNRS.

J.C. Bermond,
A. Germa,
M.C. Heydemann,
and D. Sotteau.
Hypergraphes hamiltoniens.
In Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976),
volume 260 of Colloq. Internat. CNRS,
Paris,
pages 3943,
1978.
CNRS.
[PDF
]

J.C. Bermond,
A. Kotzig,
and J. Turgeon.
On a combinatorial problem of antennas in radioastronomy.
In Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I,
volume 18 of Colloq. Math. Soc. János Bolyai,
Amsterdam,
pages 135149,
1978.
NorthHolland.

J.C. Bermond and D. Sotteau.
Cycle and circuit designs odd case.
In Contributions to graph theory and its applications (Internat. Colloq., Oberhof, 1977) (Germany),
Ilmenau,
pages 1132,
1977.
Tech. Hochschule Ilmenau.
[PDF
]

J.C. Bermond.
On Hamiltonian walks.
In Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975),
Winnipeg, Man.,
pages 4151. Congressus Numerantium, No. XV,
1976.
Utilitas Math..

J.C. Bermond and D. Sotteau.
Graph decompositions and $G$designs.
In Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975),
Winnipeg, Man.,
pages 5372. Congressus Numerantium, No. XV,
1976.
Utilitas Math..
[PDF
]

J.C. Bermond.
Decomposition of $K\sp*\sb{n}$ into $k$circuits and balanced $G$designs.
In Recent advances in graph theory (Proc. Second Czechoslovak Sympos., Prague, 1974),
Prague,
pages 5768,
1975.
Academia.

J.C. Bermond.
The circuithypergraph of a tournament.
In Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdos on his 60th birthday), Vol. I,
Amsterdam,
pages 165180. Colloq. Math. Soc. János Bolyai, Vol. 10,
1975.
NorthHolland.

J.C. Bermond.
Graphe représentatif de l'hypergraphe $h$parti complet.
In Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Columbus, Ohio, 1972; dedicated to Arnold Ross),
Berlin,
pages 3453. Lecture Notes in Math., Vol. 411,
1974.
Springer.

G. D'Angelo,
G. Di Stefano,
A. Navarra,
N. Nisse,
and N. Suchan.
A unified approach for different tasks on rings in robotbased computing systems.
In 15th Workshop on Advances in Parallel and Distributed Computational Models (APDCM),
.
IEEE.
Note: To appear.
[WWW
] [PDF
]
Abstract: 
A set of autonomous robots have to collaborate in order to accomplish a common task in a ringtopology where neither nodes nor edges are labeled. We present a unified approach to solve three important problems in the field: the exclusive perpetual exploration, the exclusive perpetual graph searching and the 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 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 LookComputeMove asynchronous cycles. Moreover, robots are anonymous, oblivious, uniform and have no common sense of orientation. For the first two problems, the exclusivity constraint must also be satisfied, i.e., a node can be occupied by at most one robot. 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 ringtopologies. Besides being a unified approach for three different tasks, the given algorithms solve some open problems. Moreover, we provide some impossibility results for the perpetual graph searching problem. 

N. Nisse and R. Soares.
On The Monotonicity of Process Number.
In proceedings of the LatinAmerican Algorithms, Graphs and Optimization Symposium (LAGOS'13),
Electronic Notes in Discrete Mathematics,
Playa del Carmen, Mexico,
April.
[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 pathdecomposition 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. 

J. Araujo,
F. Giroire,
Y. Liu,
R. Modrzejewski,
and J. Moulierac.
Energy Efficient Content Distribution.
Technical report RR8091,
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 innetwork caches and CDN cooperation on an energyefficient 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\27775643210f power in the backbone, while 16\§an be gained solely thanks to caches. 

J. Araujo,
G. Morel,
L. Sampaio,
R. Soares,
and V. Weber.
Hull number: $P_5$free graphs and reduction rules.
Technical report RR8045,
INRIA,
August 2012.
[WWW
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]
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 polynomialtime algorithm to compute the hull number of any $P\_5$free trianglefree 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. 

J. BangJensen,
F. Havet,
and A. K. Maia.
Finding a subdivision of a digraph.
Technical report RR8024,
INRIA,
July 2012.
[WWW
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]
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 NPcompleteness proofs as well as a number of conjectures and open problems. 

JC. Bermond,
D. Coudert,
G. D'Angelo,
and F. Z. Moataz.
Diverse Routing with the star property.
Technical report RR8071,
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 SRLGdisjoint 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 counterexamples to the polynomial time algorithm proposed in\~\cite{LW05} for computing pairs of SRLGdisjoint 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 SRLGdisjoint 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. 

L. Blin,
J. Burman,
and N. Nisse.
Perpetual Graph Searching.
Technical report RR7897,
INRIA,
February 2012.
[WWW
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]
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 LookComputeMove} 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 faulttolerant 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. 

V. Campos,
F. Havet,
R. Sampaio,
and A. Silva.
Backbone colouring: tree backbones with small diameter in planar graphs.
Technical report RR8151,
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. 

N. Cohen,
D. Coudert,
and A. Lancin.
Exact and approximate algorithms for computing the hyperbolicity of largescale graphs.
Technical report RR8074,
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 biconnected 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 largescale graphs. 

G. D'Angelo,
G. Di Stefano,
and A. Navarra.
How to gather asynchronous oblivious robots on anonymous rings.
Technical report RR7963,
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 LookComputeMove 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 nongatherable configurations.
It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration. 

G. D'Angelo,
G. Di Stefano,
A. Navarra,
N. Nisse,
and K. Suchan.
A unified approach for different tasks on rings in robotbased computing systems.
Technical report RR8013,
INRIA,
2012.
[WWW
] [PDF
]
Abstract: 
A set of autonomous robots have to collaborate in order to accomplish a common task in a ringtopology 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 LookComputeMove} 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 ringtopologies.
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 $(k=5,n=10)$. 

G. Ducoffe.
Eulerian and Hamiltonian Directed Hypergraphs.
Technical report RR7893,
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 NPcomplete.
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. 

F. Havet and A. D. King.
List circular backbone colouring.
Technical report RR8159,
INRIA,
November 2012.
[WWW
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]
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. 

F. Havet,
A. D. King,
M. Liedloff,
and I. Todinca.
(Circular) backbone colouring: tree backbones in planar graphs.
Technical report RR8152,
INRIA,
November 2012.
[WWW
] [PDF
]
Abstract: 
Consider an undirected graph G and a subgraph H of G, on the same vertex set.
The qbackbone 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 NPhardness 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. 

F. Havet,
A. K. Maia,
and M. Yu.
Complexity of greedy edgecolouring.
Technical report RR8171,
INRIA,
December 2012.
[WWW
] [PDF
]
Abstract: 
The Grundy index of a graph G = (V,E) is the greatest number of colours that the greedy edgecolouring algorithm can use on G.
We prove that the problem of determining the Grundy index of a graph G = (V,E) is NPhard for general graphs.
We also show that this problem is polynomialtime solvable for caterpillars.
More specifically, we prove that the Grundy index of a caterpillar is $\Delta(G)$ or $\Delta(G)+1$ and present a polynomialtime algorithm to determine it exactly. 

F. Havet,
N. Paramaguru,
and R. Sampathkumar.
Detection number of bipartite graphs and cubic graphs.
Technical report RR8115,
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 NPcomplete 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 $3.$ 

A. Kosowski,
B. Li,
N. Nisse,
and K. Suchan.
kChordal Graphs: from Cops and Robber to Compact Routing via Treewidth.
Technical report RR7888,
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 $k1$ 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 treedecomposition} of $G$, each {\it bag} of which contains a dominating path with at most $k1$ vertices.
This allows us to prove that any $k$chordal graph with maximum degree $\Delta$ has treewidth at most $(k1)(\Delta1)+2$, improving the $O(\Delta (\Delta1)^{k3})$ bound of Bodlaender and Thilikos (1997).
Moreover, any graph admitting such a treedecomposition has hyperbolicity $\leq\lfloor \frac{3}{2}k\rfloor$. As an application, for any $n$node graph admitting such a treedecomposition, 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. 

N. Nisse and R. Soares.
On The Monotonicity of Process Number.
Technical report RR7003,
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 pathdecomposition 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. 

P. Aboulker,
F. Havet,
and N. Trotignon.
On wheelfree graphs.
Research Report RR7651,
INRIA,
June 2011.
[WWW
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]
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 3connected graph that does not contain a wheel as a subgraph is in fact minimally 3connected. We prove that every graph that does not contain a wheel as a subgraph is 3colorable. 

L. AddarioBerry,
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 $f(k)\leq (k1)^2$ and conjectured $f(k)=2n2$.
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 $f(k)\leq k^2/2k/2+1$.
Finally, we consider the existence of antidirected trees in digraphs.
We prove that every antidirected tree of order $k$ is contained in every $(5k9)$chromatic digraph.
We conjecture that if $E(D) > (k2) V(D)$,
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}sS\'os Conjecture.
We give some evidences for our conjecture to be true. 

J. Araujo,
JC. Bermond,
F. Giroire,
F. Havet,
D. Mazauric,
and R. Modrzejewski.
Weighted Improper Colouring.
Research Report RR7590,
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 reallife 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 celllike graphs, namely the {P}oisson {V}oronoi tessellations. 

J. Araujo,
V. Campos,
F. Giroire,
N. Nisse,
L. Sampaio,
and R. Soares.
On the hull number of some graph classes.
Technical report RR7567,
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 inclusionminimum 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 NPcomplete 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 NPhard 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 $(q,q4)$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 $1+\lceil \frac{3(n1)}{5}\rceil$ in general, at most $1+\lceil \frac{n1}{2}\rceil$ if $G$ is regular or has no triangle, and at most $1+\lceil \frac{n1}{3}\rceil$ if $G$ has girth at least $6$. 

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 RR7746,
INRIA,
2011.
[WWW
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]
Abstract: 
In this work we study the computational power of graphbased 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 BFStree in our different models. 

S. Belhareth,
D. Coudert,
D. Mazauric,
N. Nisse,
and I. Tahiri.
Reconfiguration with physical constraints in WDM networks.
Research Report RR7850,
INRIA,
2011.
[WWW
] [PDF
]
Keywords:
Reconfiguration,
WDM,
NPcomplete,
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 nonlinear function depending on the load of the links used by the new lightpath. We prove that determining the optimal rerouting order is NPcomplete 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. 

JC. Bermond,
A. JeanMarie,
D. Mazauric,
and J. 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 jelement 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 $b$. 

S. Bessy and F. Havet.
Enumerating the edgecolourings and total colourings of a regular graph.
Research Report RR7652,
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 $k$edgecolourings of a $k$regular graph on $n$ vertices is $k\cdot(k1!)^{n/2}$. Our proof is constructible and leads to a branching algorithm enumerating all the $k$edgecolourings of a $k$regular graph using a time $O^*((k1!)^{n/2})$ 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 $4$totalcolourings of a connected cubic graph is at most $3.2^{3n/2}$. Again, our proof yields a branching algorithm to enumerate all the $4$totalcolourings of a connected cubic graph. 

V. Campos and F. Havet.
5choosability of graphs with 2 crossings.
Research Report RR7618,
INRIA,
05 2011.
[WWW
] [PDF
]
Abstract: 
{W}e show that every graph with two crossings is 5choosable. {W}e also prove that every graph which can be made planar by removing one edge is 5choosable. 

J. G. Chang,
F. Havet,
M. Montassier,
and A. Raspaud.
Steinberg's Conjecture and nearcolorings.
Rapport de recherche RR7669,
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 3colorable 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 sousclasses de ${\cal F}$. Par exemple, Borodin {\it et al.}~ont prouv\'e
que tout graphe planaire sans cycles de longueur 4 \`a 7 est
3colorable. 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 quasicolorations}.
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. 

F. Fomin,
F. Giroire,
A. JeanMarie,
D. Mazauric,
and N. Nisse.
To Satisfy Impatient Web surfers is Hard.
Technical report RR7740,
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 NPhard. Deciding if the surveillance number of a DAG equals 4 is PSPACEcomplete. Moreover, computing the surveillance number is NPhard 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. 

F. Giroire,
S. K. Gupta,
R. Modrzejewski,
J. Monteiro,
and S. Pérennes.
Analysis of the Repair Time in Distributed Storage Systems.
Research Report RR7538,
INRIA,
02 2011.
[WWW
] [PDF
]
Keywords:
P2P storage systems,
data lifetime,
queuing model,
regenerating codes per formance evaluation.
Abstract: 
{D}istributed or peertopeer storage systems introduce redundancy to preserve the data in case of peer failures or departures. {T}o ensure longterm fault tolerance, the storage system must have a selfrepair 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 testbed platform. 

F. Havet and X. Zhu.
The game Grundy number of graphs.
Rapport de recherche RR7646,
INRIA,
June 2011.
[WWW
] [PDF
]
Keywords:
colouring game,
game Grundy number,
trees,
partial 2trees.
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 2tree is at most 7. 

F. Maffray and G. Morel.
On 3colorable $P_5$free graphs.
Technical report 191,
Les Cahiers Leibniz, Laboratoire GSCOP,
2011.
[PDF
]

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 RR7784,
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 endhost 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. 

J. BangJensen,
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 2cycles. We give a number of examples of polynomial instances as well as several NPcompleteness proofs. 

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. nonaccessible 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 nonconnected one is $O(\log n)$ while for trees this ratio is always at most 2. We also conjecture that this constantratio 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 forbiddengraph 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 compu  