-
K.E. Avrachenkov and V.S. Borkar,
Whittle index based Q-learning
for restless bandits with average reward. Automatica, v.139, 2022.
-
K. Avrachenkov, V. Gaitsgory and L. Gamertsfelder,
LP Based Upper and Lower Bounds
for Cesaro and Abel Limits of the Optimal Values in Problems of Control
of Stochastic Discrete Time Systems.
Journal of Mathematical Analysis and Applications, v.512(1), 2022.
-
K. Avrachenkov, K. Patil and G. Thoppe,
Online Algorithms for Estimating
Change Rates of Web Pages. Performance Evaluation, v.153, 2022.
-
M. Hamidouche, L. Cottatellucci and K. Avrachenkov,
On the Normalized Laplacian Spectra of Random
Geometric Graphs. Journal of Theoretical Probability, 2022.
DOI 10.1007/s10959-022-01158-0
-
F. Robledo, V. Borkar, U. Ayesta and K. Avrachenkov,
QWI: Q-learning with Whittle Index.
ACM Sigmetrics Performance Evaluation Review, v.49(2), 2022.
Back to the top
-
K. Avrachenkov, A. Bobu and M. Dreveton,
Higher-Order Spectral Clustering
for Geometric Graphs. Journal of Fourier Analysis and Applications, 27:22, 2021.
DOI 10.1007/s00041-021-09825-2
-
K. Avrachenkov, M. Dreveton and L. Leskelä,
Recovering Communities in Temporal Networks
Using Persistent Edges, in Proceedings of the 10th International Conference on Computational Data
and Social Networks (CSoNet 2021), also Springer LNCS v.13116, pp.243-254.
-
K. Avrachenkov, V.S. Borkar, H.P. Dolhare and K. Patil,
Full Gradient DQN Reinforcement Learning:
A Provably Convergent Scheme. arXiv preprint 2103.05981.
In A.B. Piunovskiy and Y. Zhang (eds.), Modern Trends in Controlled Stochastic Processes:
Theory and Applications, Volume III. 2021.
-
K. Avrachenkov, V. Gaitsgory and L. Gamertsfelder,
LP Based Bounds for Cesaro and Abel Limits
of the Optimal Values in Non-ergodic Stochastic Systems, in Proceedings of European Control
Conference (ECC 2021).
-
K. Avrachenkov, V. Borkar and K. Patil,
Deep Reinforcement Learning for Web Crawling.
The Seventh Indian Control Conference 2021, Mumbai, India.
-
K. Avrachenkov, A. Boisbunon and M. Kamalov,
Graph Diffusion & PCA Framework for Semi-supervised
Learning, In Proceedings of the 15th Learning and Intelligent Optimization Conference (LION 2021),
also Springer LNCS v.12931, pp.25-39.
Back to the top
-
K. Avrachenkov, M. Dreveton and L. Leskelä,
Estimation of static community memberships from temporal network data.
arXiv preprint 2008.04790.
-
K. Avrachenkov, P. Brown and N. Litvak,
Red Light Green Light method for solving large Markov chains.
arXiv preprint arXiv:2008.02710.
-
K. Avrachenkov and M. Mironov,
Cluster-size constrained network partitioning.
Proceedings of ICPR 2020/2021.
-
K. Avrachenkov and A. Bobu,
Cliques
in high-dimensional random geometric graphs.
Applied Network Science, v.5(1), pp.1-24, 2020.
-
K. Avrachenkov, K. Patil and G. Thoppe,
Change rate estimation and optimal freshness in web page crawling.
Proceedings of ValueTools 2020, pp.3-10.
(A significantly extended version.)
-
A. Albrecht, K. Avrachenkov, P. Howlett and G. Verma.
Evolutionary dynamics in discrete time for
the perturbed positive definite replicator equation.
The ANZIAM Journal, v.62(2), pp.148-184, 2020.
-
Y. Chen, Y. Gel and K. Avrachenkov,
LFGCN: Levitating over graphs with Levy flights.
Proceedings of IEEE ICDM 2020.
Back to the top
-
K. Avrachenkov and M. Dreveton,
Almost exact recovery in label spreading.
Proceedings of WAW 2019.
-
K. Avrachenkov and V. Borkar,
Metastability in stochastic replicator dynamics.
Dynamic Games and Applications, v.9(2), pp.366-390, 2019.
-
K. Avrachenkov and V. Borkar,
A learning algorithm for the Whittle index policy for scheduling web crawlers.
Proceedings of Allerton 2019, pp.1001-1006.
-
K. Avrachenkov, V. Ejov, J. Filar and A. Moghaddam,
Zero-sum stochastic games over the field of real algebraic numbers.
Dynamic Games and Applications, v.9(4), pp.1026-1041, 2019.
-
K. Avrachenkov, P. Chebotarev and D. Rubanov,
Similarities on graphs: Kernels versus proximity measures.
European Journal of Combinatorics, v.80, pp.47-56, 2019.
-
K. Avrachenkov and A. Borodina,
On the escape probability estimation in large graphs.
Proceedings of IEEE FRUCT 2019.
-
K. Avrachenkov and V. Singh,
Stochastic coalitional better-response dynamics for finite games with application to network formation games.
Book chapter in Multilevel Strategic Interaction Game Models for Complex Networks,
(eds.) E. Altman et al, pp.185-199, 2019.
-
K. Avrachenkov and A. Bobu,
Cliques in high-dimensional random geometric graphs.
Proceedings of Complex Networks 2019.
-
K. Avrachenkov, L. Cottatellucci and M. Hamidouche,
Eigenvalues and spectral dimension of random geometric graphs
in thermodynamic regime.
Proceedings of Complex Networks 2019.
-
M. Hamidouche, L. Cottatellucci and K. Avrachenkov,
Spectral analysis of the adjacency matrix of random geometric graphs.
Proceedings of Allerton 2019.
-
K. Avrachenkov, J. Goseling and B. Serbetci,
Distributed cooperative caching for VoD with geographic constraints.
Proceedings of WiOpt 2019.
-
K. Avrachenkov, J. Goseling and B. Serbetci,
Distributed cooperative caching for utility maximization of VoD systems.
Proceedings of IEEE SPAWC 2019.
Back to the top
-
K. Avrachenkov and I. Bogdanov,
Analysis of relaxation time in random walk with jumps.
Proceedings of WAW 2018.
-
K. Avrachenkov and V. Borkar,
Whittle index policy for crawling ephemeral content.
IEEE Trans. on Control of Network Systems, v.5(1), pp.446-455, 2018.
-
K. Avrachenkov, A. Piunovskiy and Y. Zhang,
Impulsive control for G-AIMD dynamics with relaxed and hard constraints.
Proceedings of IEEE CDC 2018.
-
K. Avrachenkov, A. Kadavankandy and N. Litvak,
Mean field analysis of Personalized PageRank with implications for local graph clustering.
Journal of Statistical Physics, v.173(3-4), pp.895-916, 2018.
-
K. Avrachenkov, A. Piunovskiy and Y. Zhang,
Hitting times in Markov chains with restart and their application to network centrality.
Methodology and Computing in Applied Probability, v.20(4), pp.1173-1188, 2018.
-
Z. Allybokus, K. Avrachenkov, J. Leguay and L. Maggi,
Multi-path alpha-fair resource allocation at scale in distributed software defined networks.
IEEE Journal on Selected Areas in Communications, v.36(12), pp.2655-2666, 2018.
-
A. Kadavankandy, K. Avrachenkov, L. Cottatellucci and R. Sundaresan,
The power of side-information in subgraph detection.
IEEE Trans. on Signal Processing, v.66(7), pp.1905-1919, 2018.
-
K. Avrachenkov, A. Kondratev, V. Mazalov and D. Rubanov,
Network partitioning algorithms
as cooperative games. Computational Social Networks, v.5(11), 2018.
-
K. Avrachenkov and T. Bodas,
On the equivalence between multiclass processor sharing
and random order scheduling policies.
ACM SIGMETRICS Performance Evaluation Review, v.45(4), pp.2-6, 2018.
-
K. Avrachenkov, V. Borkar, A. Kadavankandy and J. Sreedharan,
Revisiting random walk based sampling
in networks: Evasion of burn-in period and frequent regenerations.
Computational Social Networks, v.5(4), 2018.
Back to the top
-
K. Avrachenkov, P. Chebotarev and A. Mishenin,
Semi-supervised Learning with Regularized Laplacian.
Optimization Methods and Software, 32(2), pp.222-236, 2017.
-
K. Avrachenkov, P. Chebotarev and D. Rubanov,
Kernels on graphs as proximity measures.
Proceedings of WAW 2017.
-
K. Avrachenkov, A. Kadavankandy, L. Ostroumova and A. Raigorodskii,
PageRank in undirected random graphs.
Internet Mathematics journal, doi.org/10.24166/im.09.2017, 2017.
-
K. Avrachenkov, X. Bai and J. Goseling,
Optimization of caching devices with geometric constraints.
Performance Evaluation, v.113, pp.68-82, 2017.
-
K. Avrachenkov, J. Goseling and B. Serbetci,
A low-complexity approach to distributed cooperative caching with
geographic constraints.
Proceedings of ACM SIGMETRICS 2017.
-
K. Avrachenkov, A. Kondratev and V. Mazalov,
Cooperative game theory approaches for network partitioning.
Proceedings of CSoNet 2017. Also, Springer LNCS v.10392, pp.591-602.
-
K. Avrachenkov, V. Borkar and S. Pattathil,
Controlling G-AIMD by index policy.
Proceedings of IEEE CDC 2017.
-
K. Avrachenkov, P. Jacquet and J. Sreedharan,
Hamiltonian system approach to distributed spectral decomposition in networks.
Proceedings of IEEE nDS 2017.
-
A. Kadavankandy, K. Avrachenkov, L. Cottatellucci and R. Sundaresan,
Belief propagation for subgraph detection with imperfect side-information.
Proceedings of IEEE ISIT 2017.
-
Z. Allybokus, K. Avrachenkov, J. Leguay and L. Maggi,
Real-time fair resource allocation in distributed software defined networks.
Proceedings of ITC 29 - 2017.
-
Z. Allybokus, K. Avrachenkov, J. Leguay and L. Maggi,
Lower bounds for the fair resource allocation problem.
Proceedings of IFIP Performance 2017.
-
S. de Nigris, E. Bautista, P. Abry, K. Avrachenkov and P. Goncalves,
Fractional graph-based semi-supervised learning.
Proceedings of EUSIPCO 2017.
Back to the top
-
K. Avrachenkov, X. Bai and J. Goseling,
Optimization of Caching Devices with Geometric Constraints.
Arxiv 1602.03635, 2016.
-
K. Avrachenkov, L. Iskhakov and M. Mironov,
On mixing in pairwise Markov random fields
with application to social networks, Proceedings of WAW 2016, also Springer LNCS v.10088, pp.127-139.
-
K. Avrachenkov, V. Borkar and K. Saboo,
Distributed and asynchronous methods for
semi-supervised learning, Proceedings of WAW 2016, also Springer LNCS v.10088, pp.34-46.
-
K. Avrachenkov, G. Neglia and A. Tuholukova,
Subsampling for chain-referral methods.
Proceedings of ASMTA, also Springer LNCS v.9845, pp.17-31, 2016.
-
K. Avrachenkov, V. Borkar, A. Kadavankandy and J.K. Sreedharan,
Comparison of random walk based techniques
for estimating network averages.
Proceedings of CSoNet 2016, also Springer LNCS v.9795, pp. 27-38, 2016.
-
K. Avrachenkov, B. Ribeiro and J.K. Sreedharan,
Inference in OSNs via lightweight partial crawls.
Proceedings of ACM SIGMETRICS 2016.
-
K. Avrachenkov, P. Jacquet and J.K. Sreedharan,
Distributed spectral decomposition in networks by
complex diffusion and quantum random walk,
Proceedings of IEEE Infocom 2016.
-
K. Avrachenkov, J. Filar, V. Gaitsgory and A. Stillman,
Singularly perturbed linear programs and Markov decision processes.
Operations Research Letters, v.44(3), pp.297-301, 2016.
-
K. Avrachenkov and V.V. Singh,
Stochastic coalitional better-response dynamics and stable equilibrium.
Mathematical Game Theory and Applications, v.8(1), pp.4-26, 2016.
Version in Russian.
-
K. Avrachenkov, G. Neglia and V.V. Singh,
Network formation games with teams,
Journal of Dynamics and Games, v.3(4), pp.303-318, 2016.
-
A. Kadavankandy, L. Cottatellucci and K. Avrachenkov,
Characterization of L1-norm statistic
for anomaly detection in Erdos-Renyi graphs.
Proceedings of IEEE CDC 2016.
-
K. Avrachenkov, A. Eshragh and J. Filar,
On transition matrices of Markov chains corresponding to Hamiltonian cycles.
Annals of Operations Research, v.243(1-2), pp.19-35, 2016.
-
K. Avrachenkov, E. Morozov and B. Steyaert,
Sufficient stability conditions
for multi-class constant retrial rate systems. Queueing Systems, v.82(1-2), pp.149-171, 2016.
-
K. Avrachenkov, E. Perel and U. Yechiali,
Finite-buffer polling systems with threshold-based switching policy.
TOP, v.24(3), pp.541-571, 2016.
-
V. Mazalov, K. Avrachenkov, L. Trukhina and B. Tsynguev,
Game-theoretic centrality measures
for weighted graphs.
Fundamenta Informaticae, v.145(3), pp.341-358, 2016.
-
K. Avrachenkov, E. Morozov, R. Nekrasova and B. Steyaert,
Stability of constant retrial rate systems with NBU input.
Journal of Mathematical Sciences, v.214(1), pp.22-33, 2016.
Back to the top
-
K. Avrachenkov and V.S. Borkar,
Whittle index policy for crawling ephemeral content,
Proceedings of IEEE CDC 2015, also Inria Research Report RR-8702, March 2015.
-
K. Avrachenkov, A. Kadavankandy, L.O. Prokhorenkova and A. Raigorodskii,
PageRank in undirected random graphs.
Proceedings of WAW 2015, pp.151-163, December 2015.
-
K. Avrachenkov, V. Mazalov and B. Tsynguev,
Beta current flow centrality for weighted networks,
Proceedings of the 4th International Conference on Computational Social Networks (CSoNet 2015),
Also LNCS v.9197, pp. 216-227, Springer, August 2015.
-
K. Avrachenkov, A. Piunovskiy and Y. Zhang,
Hitting with Restart: A Reason for Sisyphus Labour,
Inria Research Report RR-8581, March 2015.
-
K. Avrachenkov, V. Borkar and K. Saboo,
Parallel and distributed approaches
for graph based semi-supervised learning
Inria Research Report RR-8767, 2015.
-
K. Avrachenkov, P. Chebotarev and A. Mishenin,
Semi-supervised learning with regularized laplacian,
Inria Research Report RR-8765, 2015.
-
K. Avrachenkov, L. Cottatellucci and A. Kadavankandy,
Spectral properties of random matrices for stochastic block model,
In Proceedings of WiOpt Workshop PhysComNet 2015, May 2015.
-
A. Kadavankandy, L. Cottatellucci and K. Avrachenkov,
Characterization of Random Matrix Eigenvectors for Stochastic Block Model,
Proceedings of the 50th IEEE Asilomar Conference on Signals, Systems, and Computer, November 2015.
-
K. Avrachenkov, N.M. Markovich and J.K. Sreedharan,
Distribution and dependence
of extremes in network sampling processes,
Computational Social Networks, In Press, 2015.
-
K. Avrachenkov, B. Ribeiro and J.K. Sreedharan,
Bayesian inference of online social network statistics
via lightweight random walk crawls
Inria Research Report RR-8793, 2015.
-
K. Avrachenkov, O. Habachi, A. Piunovskiy and Y. Zhang,
Infinite horizon optimal impulsive control
with applications to Internet congestion control,
International Journal of Control, v.88(4), pp.703-716, 2015.
-
K. Avrachenkov and A. Varava,
Completely Mixed Stochastic Games with Small Unfixed Discount Factor,
Book chapter in Modern trends in controlled stochastic processes: Theory and applications,
Ed. A. Piunovskiy, v.2, pp.152-163, 2015.
-
K. Avrachenkov, E. Morozov, R. Nekrasova,
Optimal and equilibrium retrial rates in single-server multi-orbit retrial systems,
In Proceedings of MACOM 2015, pp.135-146, 2015.
-
M. El Chamie, G. Neglia and K. Avrachenkov,
Distributed weight selection in consensus protocols by Schatten norm minimization,
IEEE Trans. Automat. Contr., v.60(5), pp.1350-1355, 2015.
-
K. Avrachenkov, J. Elias, F. Martignon, G. Neglia and L. Petrosyan,
Cooperative network design: A Nash bargaining solution approach,
Computer Networks, v.83, pp.265-279, 2015.
Back to the top
-
K. Avrachenkov, N. Litvak, M. Sokol and D. Towsley,
Quick detection of nodes with large degrees,
Internet Mathematics, v.10(1-2), pp.1-19, 2014.
-
K. Avrachenkov, N. Litvak, L.O. Prokhorenkova and E. Suyargulova,
Quick detection of high-degree entities in large directed networks,
In Proceedings of IEEE ICDM 2014, pp.20-29, December 2014.
-
K. Avrachenkov, R. van der Hofstad and M. Sokol,
Personalized PageRank with Node-Dependent Restart,
In Proceedings of WAW 2014, pp.23-33, December 2014.
-
K. Avrachenkov, P. Basu, G. Neglia, B. Ribeiro and D. Towsley,
Pay few, influence most: Online myopic network covering,
INFOCOM NetSciCom Workshop 2014, pp.813-818, 2014.
-
K. Avrachenkov, P. Nain and U. Yechiali,
A retrial system with two input streams and two orbit queues,
Queueing Systems, v.77(1), pp.1-31, 2014.
-
E. Altman, K. Avrachenkov and J. Goseling,
Distributed storage in the plane. In Proceedings of IFIP Networking 2014,
pp. 1-9, June 2014.
-
K. Avrachenkov, L. Cottatellucci and L. Maggi,
Confidence intervals for the Shapley–Shubik power index in Markovian games,
Dynamic Games and Applications, v.4(1), pp.10-31, 2014.
-
K. Avrachenkov, A. Eshragh and J.A. Filar,
On transition matrices of Markov chains corresponding to Hamiltonian cycles,
Annals of Operations Research, pp.1-17, 2014.
-
K. Avrachenkov and E. Morozov,
Stability analysis of GI/GI/c/K retrial queue with constant retrial rate,
Math. Meth. OR, v.79(3), pp.273-291, 2014.
-
K. Avrachenkov, E. Morozov, R. Nekrasova and B. Steyaert,
Stability Analysis and Simulation of n-class retrial System with Constant retrial rates and Poisson inputs,
Asia-Pacific Journal of Operational Research, v.31(2), 18p., 2014.
-
K. Avrachenkov, M. El Chamie and G. Neglia,
Graph clustering based on mixing time of random walks,
In Proceedings of IEEE ICC 2014, pp.4089-4094, June 2014.
-
K. Avrachenkov, K. De Turck, D. Fiems and B. Prabhu,
Information dissemination processes in directed social networks,
In Proceedings of International Workshop on Modeling, Analysis and Management
of Social Networks and their Applications (SOCNET), pp.35-43, March 2014.
Back to the top
-
K. Avrachenkov, J.A. Filar and P.G. Howlett,
Analytic Perturbation Theory and Its Applications, SIAM 2013, pp. I-XII, 1-372, SIAM 2013.
-
K. Avrachenkov, L. Cottatellucci and L. Maggi,
Cooperative Markov Decision Processes: Time Consistency, Greedy Players Satisfaction, and Cooperation Maintenance,
International Journal of Game Theory, v.42(1), pp.239-262, 2013.
-
K. Avrachenkov, U. Ayesta, J. Doncel and P. Jacko,
Congestion Control of TCP Flows in Internet Routers by Means of Index Policy,
Computer Networks, v.57(17), pp.3463-3478, 2013.
-
K. Avrachenkov, P. Goncalves and M. Sokol,
On the Choice of Kernel and Labelled Data in Semi-supervised Learning Methods,
In Proceedings of WAW 2013, also LNCS v.8305, pp.56-67, 2013.
-
K. Avrachenkov, N. Litvak, V. Medyanikov and M. Sokol,
Alpha Current Flow Betweenness Centrality,
In Proceedings of WAW 2013, also LNCS v.8305, pp.106-117, 2013.
-
K. Avrachenkov, L. Cottatellucci and L. Maggi,
Dynamic Rate Allocation in Markovian Quasi-static Multiple Access Channels:
A Game Theoretic Approach,
In Proceedings of WiOpt 2013, pp.162-169, 2013.
-
K. Avrachenkov, P. Goncalves, A. Legout and M. Sokol,
Classification of Content and Users
in BitTorrent by Semi-supervised Learning Methods,
In Proceedings of IEEE IWCMC/TRAC, 2012.
Back to the top
-
K. Avrachenkov, P. Goncalves, A. Legout and M. Sokol,
Classification of Content and Users
in BitTorrent by Semi-supervised Learning Methods,
In Proceedings of IEEE IWCMC/TRAC, 2012.
-
K. Avrachenkov, L. Cottatellucci and L. Maggi,
Dynamic
Rate Allocation in Markovian Quasi-Static Multiple Access Channels,
Eurecom Research Report RR-12-269, August 2012.
-
K. Avrachenkov and J.B. Lasserre, Analytic
Perturbation of Generalized Inverses,
Linear Algebra and its Applications, in press, 2012.
-
K. Avrachenkov, A. Piunovskiy and Y. Zhang,
Markov Processes with Restart, Inria Research Report no.8000, June 2012.
-
K. Avrachenkov, P. Nain and U. Yechiali,
A Retrial System with Two Input Streams and Two Orbit Queues,
Inria Research Report no.7999, June 2012.
-
K. Avrachenkov and P. Jacko,
CCN Interest Forwarding Strategy as Multi-Armed Bandit Model with Delays,
Inria Research Report no.7917, April 2012.
-
K. Avrachenkov, L. Cottatellucci and L. Maggi,
Cooperative
Markov Decision Processes: Time Consistency, Greedy Players Satisfaction, and Cooperation Maintenance,
accepted to International Journal of Game Theory, 2012, Also Eurecom
Research Report no.11-248.
-
K. Avrachenkov, N. Litvak, M. Sokol and D. Towsley,
Quick Detection of Nodes with Large Degrees,
in Proceedings of WAW 2012, Also in LNCS v.7323, pp.54-65, 2012.
-
K. Avrachenkov, P. Goncalves, A. Mishenin and M. Sokol,
Generalized
Optimization Framework for Graph-based Semi-supervised Learning,
in Proceeding of SIAM Conference on Data Mining (SDM'2012), pp.966-974, 2012.
-
K. Avrachenkov, R.S. Burachik, J.A. Filar and V. Gaitsgory,
Constraint augmentation in pseudo-singularly perturbed linear programs.
Mathematical Programming, v.132(1-2), pp.179-208, 2012.
-
K. Avrachenkov, L. Cottatellucci and L. Maggi,
Algorithms for Uniform
Optimal Strategies in Two-player Zero-sum Stochastic Games with Perfect Information,
Operations Research Letters, v.40(1), pp.56-60, 2012. Also
Inria Research Report no.7355, July 2010.
-
E. Altman, K. Avrachenkov and S. Ramanath,
Multiscale Fairness and its Application
to Resource Allocation in Wireless Networks,
Computer Communications, v.35(7), pp.820-828, 2012.
(An extended version of the IFIP Networking 2011 paper.)
Back to the top
-
K. Avrachenkov, A. Dudin, V. Klimenok, P. Nain, O. Semenova.
Optimal Threshold Control by the Robots of Web Search Engines
with Obsolescence of Documents, Computer Networks, v.55(8), pp.1880-1893, 2011.
-
K. Avrachenkov, N. Litvak, D. Nemirovsky, E. Smirnova and M. Sokol,
Quick Detection of Top-k Personalized PageRank Lists, In Proceedings of WAW'2011,
pp.50-61, 2011.
-
K. Avrachenkov, A. Piunovskiy and Y. Zhang,
Asymptotic Fluid Optimality and Efficiency of the Tracking Policy for Bandwidth-sharing
Networks, Journal of Applied Probability, v.48(1), 90-113, 2011.
-
K. Avrachenkov, M. El Chamie and G. Neglia,
A Local Average Consensus Algorithm for Wireless Sensor Networks,
in Proceedings of DCOSS'2011, pp.1-6, 2011.
-
K. Avrachenkov, J. Elias, F. Martignon, G. Neglia, L. Petrosyan,
"A Nash bargaining solution for Cooperative Network Formation Games"
In Proceedings of IFIP Networking 2011, May 2011.
-
E. Altman, K. Avrachenkov and S. Ramanath,
Multiscale Fairness and its Application to Resource Allocation in Wireless Networks,
In Proceedings of IFIP Networking 2011, May 2011.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Jamming in Wireless Networks Under Uncertainty, Mobile Networks and Applications,
v.16(2), pp.246-254, 2011.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Closed Form Solutions for Water-filling Problems in Optimization and Game Frameworks,
Telecommunication Systems, v.47(1-2), pp.153-164, 2011.
(An extended version of the GameComm'2007 paper.)
-
K. Avrachenkov, A. Eshragh and J.A. Filar,
Hamiltonian Transition Matrices, In Proceedings of ValueTools'11, pp.463-466, 2011.
-
K. Avrachenkov, P. Goncalves, A. Legout and M. Sokol,
Graph Based Classification of Content
and Users in BitTorrent, in Proceeding of NIPS Big Learning Workshop, December 2011.
-
J. Elias, F.Martignon, K. Avrachenkov, G. Neglia,
A Game Theoretic Analysis of Network Design with Socially-Aware Users,
Computer Networks, v.55, no.1, pp.106-118, 2011.
-
I. Lassoued, A. Krifa, C. Barakat, K. Avrachenkov,
Network-wide monitoring through self-configuring adaptive system,
In Proceedings of IEEE INFOCOM 2011, April 2011.
-
L. Xiao, L. Cottatelluci, K. Avrachenkov,
Equilibriums in slow fading interfering channels with partial knowledge
of the Channels,
In Proceedings of IEEE Infocom 2011, Mini Conference, April 2011.
Back to the top
-
K. Avrachenkov, B. Ribeiro, D. Towsley,
Improving Random Walk Estimation Accuracy with Uniform Restarts,
In Proceedings of WAW 2010, December 2010, Also
LNCS v.6516, pp.98-109, 2010.
-
K. Avrachenkov, V. Ejov, J. A. Filar,
Multivariate Polynomial Perturbations of Algebraic Equations,
Journal of Mathematical Analysis and Applications,
v.369, no.1, pp.214-221, 2010.
-
K. Avrachenkov, V. Borkar, D. Nemirovsky,
Quasi-Stationary Distributions as Centrality Measures
for the Giant Strongly Connected Component of a Reducible Graph,
Journal of Computational and Applied Mathematics, Special Volume on
Numerical Linear Algebra, Internet and Large Scale Applications,
v.234, no.11, pp.3075-3090, 2010.
-
K. Avrachenkov, U. Ayesta, N. Osipova,
Conditional sojourn time of optimal scheduling policy
in a multi-class single-server queue,
Chapter in Modern Trends in Controlled Stochastic Processes: Theory and Applications,
(ed.) A. B. Piunovskiy, Luniver Press, pp.284-303, 2010.
-
E. Smirnova, K. Avrachenkov, B. Trousse,
Using Web Graph Structure for Person Name Disambiguation,
In Proceedings of the Conference on Multilingual and Multimodal
Information Access Evaluation (CLEF 2010), September 2010.
-
K. Avrachenkov, U. Ayesta, A. Piunovskiy,
Convergence of Trajectories and Optimal Buffer Sizing for AIMD Congestion Control,
Performance Evaluation, v.67, no.7, pp.501-527, 2010.
-
X. Lei, K. Avrachenkov, L. Cottatellucci, A. Garnaev,
Competitive Unlicensed Spectrum Sharing with Partial Information
on Slow Fading Channels,
Wired/Wireless Internet Communications, (eds.) E. Osipov, A. Kassler,
T. Bohnert, X. Masip-Bruin, Springer LNCS v.6074, pp.158-169, 2010.
-
E. Altman, K. Avrachenkov, A. Garnaev.
Fair Resource Allocation in Wireless Networks in the Presence of a Jammer,
Performance Evaluation, v.67, no.4, pp.338-349, 2010.
-
E. Altman, K. Avrachenkov, A. Garnaev,
Taxation for Green Communication,
In Proceedings of WiOpt 2010, pp.108-112, June 2010.
-
K. Avrachenkov, N. Litvak, D. Nemirovsky, E. Smirnova and M. Sokol,
Monte Carlo Methods for Top-k Personalized PageRank Lists
and Name Disambiguation, Inria Research Report no.7367, August 2010.
-
D. Carra, K. Avrachenkov, S. Alouf, A. Blanc, P. Nain, G. Post,
Passive Online RTT Estimation for Flow-Aware Routers Using One-Way Traffic,
In Proceedings of IFIP Networking 2010, May 2010,
Also Springer LNCS v.6091, pp.109-121, 2010.
-
K. Avrachenkov, Stochatic Methods for TCP/IP Networks and the WWW,
University of Nice Sophia Antipolis, HDR thesis, April 29 2010 (available upon request).
-
J. Elias, F. Martignon, K. Avrachenkov, G. Neglia,
Socially-Aware Network Design Games,
In Proceedings of IEEE Infocom, Mini Conference, March 2010.
-
K. Avrachenkov and U. Yechiali,
On tandem blocking queues with a common retrial queue,
Computers and Operations Research, v.37, no.7, pp.1174-1180, 2010.
-
Y. Zhang, A. Piunovskiy, U. Ayesta and K. Avrachenkov,
Convergence of trajectories and optimal buffer sizing
for MIMD congestion control, Computer Communications, v.33, pp.149-159, 2010.
Back to the top
-
K. Avrachenkov, P. Brown and N. Osipova,
Optimal Choice of Threshold in Two Level Processor Sharing,
Annals of Operations Research, v.170, pp.21-39, 2009.
-
E. Altman, K. Avrachenkov, L. Cottatellucci, M. Debbah, G. He and A. Suarez,
Operating point selection in multiple access rate regions,
In Proceedings of the 21st International Teletraffic Congress (ITC-21), September 2009.
-
N. Osipova, U. Ayesta and K. Avrachenkov,
Optimal policy for multi-class scheduling in
a single server queue, In Proceedings of the 21st International Teletraffic Congress (ITC-21),
September 2009.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Alpha-Fair Resource Allocation under Incomplete Information
and Presence of a Jammer,
In Proceedings of NETCOOP'09, also in LNCS, v.5894, pp.219-233, 2009.
-
K. Avrachenkov, N. Litvak, K.S. Pham,
A Singular Perturbation Approach for
Choosing the PageRank Damping Factor,
Internet Mathematics, v.5, no.1-2, pp.47-69, 2009.
-
E. Altman, K. Avrachenkov, I. Menache, G. Miller, B.J. Prabhu and A. Shwartz,
Dynamic Discrete Power Control in Cellular Networks,
IEEE Trans. on Automatic Control, v.54, no.10, pp.2328-2340, 2009.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Jamming in wireless networks under uncertainty,
In Proceedings of WiOpt'09, Seoul, Korea, June 2009.
-
P. Howlett, K. Avrachenkov, C. Pearce and V. Ejov,
Inversion of analytically perturbed linear
operators that are singular at the origin,
Journal of Mathematical Analysis and Applications,
v.353, no.1, pp.68-84, 2009.
-
A. Blanc, K. Avrachenkov, D. Collange and G. Neglia,
Compound TCP with Random Losses,
Proceedings of Networking'09, also in LNCS v. 5550, pp.482-494, 2009.
Back to the top
-
K. Avrachenkov and U. Yechiali,
Retrial networks with finite buffers and their application
to Internet data traffic,
Probability in the Engineering and Informational Sciences, v.22, pp.519-536, 2008.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Generalized alpha-fair resource allocation in wireless networks,
Proceedings of IEEE CDC'08, pp.2414-2419, December 2008.
-
E. Altman, K. Avrachenkov, N. Bonneau, M. Debbah, R. El-Azouzi and D. Sadoc Menasche,
Constrained cost-coupled stochastic games with independent state processes,
Operations Research Letters, v.36, no.2, pp.160-164, 2008.
-
E. Altman, K. Avrachenkov, and A. Garnaev,
Closed form solutions for symmetric water filling games,
Proceedings of IEEE INFOCOM 2008.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Transmission power control game with SINR as objective function,
Proceedings of NETCOOP'08, also in LNCS v.5425, pp.112-120, 2009.
-
N. Osipova, A. Blanc and K. Avrachenkov,
Improving TCP Fairness with the MarkMax Policy,
Proceedings of ITC 2008.
-
K. Avrachenkov, V. Dobrynin, D. Nemirovsky, S.K. Pham and E. Smirnova,
PageRank Based Clustering of Hypertext Document Collections,
Proceedings of ACM SIGIR 2008.
Back to the top
-
K. Avrachenkov, N. Litvak, and K.S. Pham,
Distribution of PageRank Mass Among
Principle Components of the Web, Proceedings of the
5th Workshop on Algorithms and Models for the Web-Graph (WAW2007),
also Arxiv extended version,
September 2007.
-
K. Avrachenkov, D. Nemirovsky and S. Pham,
A survey on distributed approaches to graph based reputation measures,
Proceedings of International Workshop on Tools for Solving Structured Markov Chains:
SMCtools 2007.
-
K. Avrachenkov, N. Litvak, D. Nemirovsky and N. Osipova,
Monte Carlo methods in PageRank computation: When one iteration is sufficient,
SIAM Journal on Numerical Analysis, v.45, no.2, pp.890-904, 2007.
-
E. Altman, K. Avrachenkov and A. Garnaev,
Closed form solutions for water-filling problems in optimization and game frameworks,
Proceedings of GameComm2007.
-
E. Altman, K. Avrachenkov and A. Garnaev,
A jamming game in wireless networks with transmission cost,
Proceedings of NETCOOP07, also in LNCS v.4465, pp.1-12, 2007.
-
E. Altman, K. Avrachenkov, N. Bonneau, M. Debbah, R. El-Azouzi, and D. Sadoc Menasche,
Constrained Stochastic Games in Wireless Networks,
Proceedings of IEEE GLOBECOM 2007.
-
E. Altman, K. Avrachenkov, G. Miller and B. Prabhu,
Discrete Power Control: Cooperative and Non-Cooperative Optimization,
Proceedings of IEEE INFOCOM 2007.
- N. Moller, C. Barakat, K. Avrachenkov and E. Altman,
Inter-protocol fairness between TCP New Reno and TCP Westwood,
Proceedings of the 3rd EuroNGI Conference on Next Generation Internet
Networks, 2007.
Back to the top
-
K. Avrachenkov,
Discussion on ``A Gradient-Based Repetitive Control Algorithm
Combining ILC and Pole Palcement'' by
J.J. Hatonen, C.T. Freeman, D.H. Owens, P.L. Lawin and E. Rogers,
European Journal of Control, v.12(3), pp.293-295, 2006.
-
K. Avrachenkov, P. Brown and N. Osipova,
Optimal Choice of Threshold in Two Level
Processor Sharing, Proceedings of the EuroNGI Workshop on
Stochastic Performance Models for Resource Allocation in Communication
Systems (StoPeRa'06), Amsterdam, The Netherlands, November 2006.
-
E. Altman, K. Avrachenkov and U. Ayesta,
A survey on discriminatory processor sharing
Queueing Systems, v.53(1-2), pp.53-63, 2006.
-
K. Avrachenkov, D. Nemirovsky and N. Osipova,
Web Graph Analyzer Tool,
Proceedings of the 1-st International Conference on
Performance Evaluation Methodologies and Tools (ValueTools'06),
Pisa, Italy, October 2006.
-
K. Avrachenkov and D. Lebedev,
PageRank of Scale Free Growing
Networks, Internet Mathematics, v.3, no.2, pp.207-231, 2006, also
INRIA Research Report no. 5858, March 2006.
-
K.E. Avrachenkov and N. Litvak,
The effect of new links on Google PageRank, Stochastic Models,
v.22, no.2, pp.319 - 331, 2006. Also INRIA Research Report no. 5256,
July 2004.
-
K. Avrachenkov, L. Finlay and V. Gaitsgory,
Analysis of TCP-AQM Interaction Via Periodic Optimization
and Linear Programming: The Case of Sigmoidal Utility Function,
NEW2AN'2006 Proceedings, Also
Lecture Notes in Computer Science v.4003, pp.517-529, May 2006.
-
E. Altman, K.E. Avrachenkov, G.B. Miller, and B.J. Prabhu,
Uplink dynamic discrete power control
in cellular networks, INRIA Research Report no. 5818, January 2006.
Back to the top
-
K. Avrachenkov, U. Ayesta and P. Brown,
Batch arrival processor-sharing with application
to multi-level processor sharing scheduling,
Queueing Systems, v.50(4), pp.459-480, 2005.
-
E. Altman, K. Avrachenkov, C. Barakat, A. Kherani, and B. Prabhu,
Analysis of MIMD congestion control
algorithm for high speed networks,
Computer Networks, v.48, pp.972-989, 2005.
An earlier version appeared in Proceedings of IEEE HSNMC'04,
Toulouse, France.
-
E. Altman, K. Avrachenkov, R. Marquez , and G. Miller,
Zero-sum constrained stochastic games with independent state processes
Math. Meth. Oper. Res., v.62, pp.375-386, 2005.
-
K. Avrachenkov, N. Litvak, D. Nemirovsky, and N. Osipova,
Monte Carlo methods in PageRank computation: When one iteration
is sufficient,
University of Twente Research Report, February 2005.
-
K. Avrachenkov, U. Ayesta, P. Brown, and R. Nunez-Queija,
Discriminatory processor sharing revisited,
Proceedings of IEEE INFOCOM 2005, Miami, March 2005.
-
E. Altman, K.E. Avrachenkov, and B. J. Prabhu,
Fairness in MIMD congestion control algorithms,
Proceedings of IEEE INFOCOM 2005, Miami,
March 2005. An extended version has appeared in
Telecommunication Systems, v.30(4), pp.387-415,
2005.
-
E. Altman, K. Avrachenkov, A. A. Kherani, and B. J. Prabhu,
Analysis of Scalable TCP
in the presence of Markovian Losses,
Proceedings of PFLDnet 2005 workshop, Lyon, France,
February 2005.
-
E. Altman, K. Avrachenkov, C. Barakat, A. A. Kherani, and B. J. Prabhu,
Analysis of MIMD Congestion Control Algorithm
for High Speed Networks,
Accepted for publication in Computer Networks.
An earlier version appeared in Proceedings of HSNMC'04,
Toulouse, France.
-
E. Altman, K.E. Avrachenkov, A. A. Kherani, and B.J. Prabhu,
Performance Analysis and Stochastic
Stability of Congestion Control Protocols,
Proceedings of IEEE INFOCOM 2005, Miami, March 2005,
For an extended version see
INRIA Research Report
no. 5262.
-
B. Miller, K. Avrachenkov, K. Stepanyan, and G. Miller,
Flow control as stochastic optimal
control problem with incomplete information,
Proceedings of IEEE INFOCOM 2005, Miami, March 2005,
For an extended version see
INRIA Research Report
no. 5239.
-
K.E. Avrachenkov, N.O. Vilchevsky, and G.L. Shevlyakov,
The priority queueing with finite buffer size and
randomized push-out mechanism,
Performance Evaluation, v.61(1), pp.1-16, 2005.
Back to the top
-
E. Altman, K.E. Avrachenkov, and R. Nunez-Queija,
Perturbation analysis for denumerable Markov chains
with application to queueing models,
Advances in Applied Probability, v.36, no.3, pp.839-853, September 2004.
-
E. Altman, K. Avrachenkov, and B. J. Prabhu,
A Singular Perturbation Approach to Analysing a RED Queue,
Proceedings of HET-NETs 2004, Ilkley, UK, July 2004.
-
K.E. Avrachenkov, A.A. Kherani, N.O. Vilchevsky, and V.S. Zaborovski,
"Optimal tuning of the TCP retransmission TimeOut for small-BDP lossy
wireless networks",
Proceedings of the 16-th ITC Specialist Seminar on Performance
Evaluation of Wireless and Mobile Systems, Antwerp, Belgium,
September 2004.
-
K.E. Avrachenkov and M. Haviv,
The first Laurent series coefficients
for singularly perturbed stochastic matrices.
Linear Algebra and its Applications, v.386, pp.243-259, July 2004.
-
E. Altman, K.E. Avrachenkov, C. Barakat, A. A. Kherani and B. J. Prabhu,
Analysis of Scalable TCP,
Proceedings of IEEE International Conference on High Speed Networks and
Multimedia Communications 2004 (HSNMC'04), Toulouse, France.
-
K.E. Avrachenkov and N. Litvak,
Decomposition of the Google PageRank
and optimal linking strategy,
INRIA Research Report no. 5101,
January 2004.
-
K.E. Avrachenkov, U. Ayesta, P. Brown, and E. Nyberg,
Differentiation between short and long TCP flows:
Predictability of the response time,
Proceedings of IEEE INFOCOM 2004, Hong Kong.
Back to the top
-
M. Allman, K. Avrachenkov, U. Ayesta, and J. Blanton,
Early
Retransmit for TCP and SCTP,
Internet-Draft (work in progress), December 2003.
-
U. Ayesta, K. Avrachenkov, E. Altman, C. Barakat, and P. Dube,
Multilevel Approach for Modeling Short TCP Sessions,
Proceedings of ITC-18, Berlin, September 2003.
Also extended version is available as
INRIA Research Report no. 4605.
-
U. Ayesta, K. Avrachenkov, E. Altman, C. Barakat, and P. Dube,
Simulation Analysis and
Fixed Point Approach for Multiplexed TCP flows,
INRIA Research Report no. 4749,
Also in Proceedings of The First Workshop on Protocols for Fast
Long-Distance Networks (PFLDnet'03), CERN-Geneva, Switzerland,
February 2003.
-
B.J. Prabhu, E. Altman, K. Avrachenkov, and J. Abadia Dominguez,
A Simulation Study of TCP Performance over UMTS,
Proceedings of IEEE VTC 2003-fall, Orlando, Florida,
October 2003.
-
K.E. Avrachenkov and M. Haviv, Perturbation of null spaces
with application to the eigenvalue problem and generalized inverses,
Linear Algebra and its Applications, v.369, pp.1-25, 2003.
-
P.G. Howlett, V. Ejov, and K.E. Avrachenkov,
Inversion of perturbed linear operators
that are singular at the origin,
Proceedings of IEEE CDC'03 conference, December 2003.
-
K.E. Avrachenkov and R.W. Longman,
Iterative learning control for over-determined,
under-determined, and ill conditioned systems,
Int. J. Appl. Math. Comput. Sci., v.13, no.1, pp.113-122, 2003.
Back to the top
-
E. Altman, K.E. Avrachenkov and C. Barakat,
TCP network calculus: The case of large delay-bandwidth product,
Proceedings of IEEE INFOCOM 2002, July 2002.
-
U. Ayesta and K. Avrachenkov,
The effect of the initial window size and
limited transmit algorithm on the transient behaviour of TCP transfers,
Proceedings of the 15th ITC Specialist Seminar on Internet Traffic Engineering and
Traffic Management, Wurzburg, Germany, July 2002.
-
K.E. Avrachenkov, U. Ayesta, E. Altman, P. Nain, C. Barakat,
The effect of router buffer size on the TCP performance,
Proceedings of LONIIS workshop on Telecommunication
Networks and Teletraffic Theory, St.Petersburg, Russia,
pp.116-121, January 2002.
-
N. Hegde and K. Avrachenkov,
Service Differentiation and Guarantees for
TCP-based Elastic Traffic,
Proceedings of International Workshop on Quality of future Internet
Services (QofIS'02), v.2511 in Lecture Notes in Computer Science,
October 2002, Zurich, Switzerland.
-
K.E. Avrachenkov, M. Haviv and P.G. Howlett,
Inversion of analytic matrix functions
that are singular at the origin,
SIAM Journal on Matrix Analysis and Applications, v.22, no.4, pp.1175-1189, 2001.
-
E. Altman, K.E. Avrachenkov and J.A. Filar,
An asymptotic simplex method
and Markov decision processes,
Proceedings of the 10-th International Symposium on Dynamic Games,
St. Petersburg, Russia, July 2002.
-
K.E. Avrachenkov, J.A. Filar and M. Haviv,
Singular perturbations of Markov chains
and decision processes. A Survey,
a chapter in Handbook of Markov Decision Processes: Methods and Applications,
(eds) E.A. Feinberg, A. Shwartz, v.40 in the series "International Series in
Operations Research and Management Science", Kluwer Academic Publishers,
pp.113-153, January 2002.
-
J.A. Filar, E. Altman and K.E. Avrachenkov,
An asymptotic simplex
method for singularly perturbed linear programs,
Operations Research Letters, v.30, no.5, pp.295-307, October 2002.
-
K.E. Avrachenkov, H.S.M. Beigi, and R.W. Longman,
Updating procedures for
iterative learning control in Hilbert space,
Intelligent Automation and Soft Computing,
v.8, no.2, pp.183-189, 2002.
Back to the top
-
E. Altman, K.E. Avrachenkov, C. Barakat and R. Nunez-Queija,
State-dependent M/G/1 Type Queueing Analysis
for Congestion Control in Data Networks, Proceedings of
IEEE INFOCOM 2001, Anchorage, Alaska, pp.1350-1359. A more detailed
version: CWI report PNA-R0005.
-
E. Altman, K.E. Avrachenkov, C. Barakat and R. Nunez-Queija,
TCP modeling in the presence of nonlinear window growth,
Proceedings of ITC-17, Salvador da Bahia, Brazil,
September 2001.
Back to the top
-
E. Altman, K.E. Avrachenkov and C. Barakat,
A stochastic model of TCP/IP with
stationary random losses,
ACM SIGCOMM 2000, Stockholm, Sweden, also in Computer
Communication Review, v.30, no.4, October 2000, pp.231-242.
A more detail version has appeared in IEEE/ACM Transactions on Networking,
v.13(2), pp.356-369, 2005.
-
E. Altman, K.E. Avrachenkov and C. Barakat,
Impact of bursty losses on TCP performance,
Performance Evaluation, v.42, no.2-3, pp.129-147, October 2000.
-
E. Altman, K.E. Avrachenkov and C. Barakat,
TCP in Presence of Bursty Losses,
Proceedings of ACM SIGMETRICS, Santa Clara, California, June 2000.
-
E. Altman, K.E. Avrachenkov, C. Barakat and P. Dube,
TCP over a multi-state Markovian path,
Performance and QoS of Next Generation Networking,
K. Goto, T. Hasegawa, H. Takagi and Y. Takahashi (Eds), Springer, 2000,
pp. 103-122.
-
P.G. Howlett and K.E. Avrachenkov,
Laurent series for the inversion of perturbed
linear operators on Hilbert space,
a book chapter in Progress in Optimization: Contributions from Australasia III,
Kluwer, 2000.
-
K.E. Avrachenkov and J.B. Lasserre,
Analytic perturbation of Sylvester and Lyapunov
matrix equations,
IEEE CDC 2000, Sydney, Australia, pp.1968-1973. An extended version is
appeared in IEEE Trans. Auto. Contr., v.47, no.7, pp.1116-1119, 2002.
-
K.E. Avrachenkov,
Singularly perturbed finite Markov chains with general
ergodic structure,
in Discrete Event Systems: Analysis and Control, R. Boel and
G. Stremersch (Eds.), pp.429-432, Kluwer, 2000.
Back to the top
-
K.E. Avrachenkov, Analytic Perturbation Theory and
its Applications,
(compressed postscript file),
University of South Australia, 1999.
-
K.E. Avrachenkov and J.B. Lasserre,
The fundamental matrix of
singularly perturbed Markov chains,
Advances in Applied Probability, v.31, pp.679-697, 1999.
-
E. Altman, K.E. Avrachenkov and J.A. Filar,
Asymptotic linear
programming and policy improvement for singularly perturbed
Markov decision processes,
ZOR: Mathematical Methods of Operations Research, v.49, no.1,
pp.97-109, 1999.
-
K.E. Avrachenkov and E. Altman,
Sensitive discount optimality via
nested linear programs for ergodic Markov decision processes,
IDC'99 Proceedings, pp.53-58, 1999.
Back to the top
-
K.E. Avrachenkov and J.B. Lasserre,
Perturbation analysis of reduced
resolvents and generalized inverses,
CNRS-LAAS Research Report No.98520, December 1998.
-
K.E. Avrachenkov and A.A. Pervozvanskii,
Regularization and
robustness of learning-based control algorithms,
Journal of computer and systems sciences, v.37, no.2,
pp.338-340, 1998.
-
K.E. Avrachenkov,
Iterative learning control based on quasi-Newton
methods, IEEE CDC'98 Proceedings, 1998.
-
K.E. Avrachenkov and A.A. Pervozvanskii,
Iterative learning control
for singularly perturbed systems,
(extended version),
Proceedings of ILC workshop, 1998.
Back to the top
Back to the top
Back to the front page