M. Mézard and G. Parisi, The Bethe lattice spin glass revisited, The European Physical Journal B, vol.20, issue.2, pp.217-233, 2001.
DOI : 10.1007/PL00011099

M. Mézard and G. Parisi, The cavity method at zero temperature, Journal of Statistical Physics, vol.111, issue.1/2, pp.1-34, 2003.
DOI : 10.1023/A:1022221005097

M. Mézard, G. Parisi, and R. Zecchina, Analytic and Algorithmic Solution of Random Satisfiability Problems, Science, vol.297, issue.5582, pp.812-815, 2002.
DOI : 10.1126/science.1073287

A. Braunstein, M. Mézard, and R. Zecchina, Survey propagation: An algorithm for satisfiability, Random Structures and Algorithms, vol.13, issue.2, pp.201-226, 2005.
DOI : 10.1002/rsa.20057
URL : https://hal.archives-ouvertes.fr/hal-00008893

S. Jonathan, . Yedidia, T. William, Y. Freeman, and . Weiss, Understanding belief propagation and its generalizations. Exploring artificial intelligence in the new millennium, pp.236-239, 2003.

M. Mézard and A. Montanari, Information, physics, and computation, 2009.
DOI : 10.1093/acprof:oso/9780198570837.001.0001

R. Frank, . Kschischang, J. Brendan, H. Frey, and . Loeliger, Factor graphs and the sumproduct algorithm. Information Theory, IEEE Transactions on, vol.47, issue.2, pp.498-519, 2001.

A. Montanari and T. Rizzo, How to compute loop corrections to the Bethe approximation, Journal of Statistical Mechanics: Theory and Experiment, vol.2005, issue.10, p.10011, 2005.
DOI : 10.1088/1742-5468/2005/10/P10011

M. Mézard and G. Parisi, The cavity method at zero temperature, Journal of Statistical Physics, vol.111, issue.1/2, pp.1-34, 2003.
DOI : 10.1023/A:1022221005097

I. Neri and D. Bollé, The cavity approach to parallel dynamics of Ising spins on a graph, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.08, p.8009, 2009.
DOI : 10.1088/1742-5468/2009/08/P08009

E. Aurell and H. Mahmoudi, A message-passing scheme for non-equilibrium stationary states, Journal of Statistical Mechanics: Theory and Experiment, vol.2011, issue.04, pp.2011-04014, 2011.
DOI : 10.1088/1742-5468/2011/04/P04014

E. Aurell and H. Mahmoudi, Dynamic mean-field and cavity methods for diluted Ising systems, Physical Review E, vol.85, issue.3, p.31119, 2012.
DOI : 10.1103/PhysRevE.85.031119

H. Mahmoudi and D. Saad, Generalized mean field approximation for parallel dynamics of the Ising model, Journal of Statistical Mechanics: Theory and Experiment, vol.2014, issue.7, pp.2014-07001, 2014.
DOI : 10.1088/1742-5468/2014/07/P07001

W. Feller, An introduction to probability theory and its applications, 2008.

Y. Andrey, M. Lokhov, H. Mézard, L. Ohta, and . Zdeborová, Inferring the origin of an epidemic with a dynamic message-passing algorithm, Physical Review E, vol.90, issue.1, p.12801, 2014.

A. Fabrizio-altarelli, L. Braunstein, A. Dall-'asta, R. Lage-castellanos, and . Zecchina, Bayesian inference of epidemics on networks via belief propagation. Physical review letters, p.118701, 2014.

J. Roy and . Glauber, Time-dependent statistics of the ising model, Journal of mathematical physics, vol.4, issue.2, pp.294-307, 1963.

A. William and . Little, The existence of persistent states in the brain, From High- Temperature Superconductivity to Microminiature Refrigeration, pp.145-164, 1996.

P. Peretto, Collective properties of neural networks: A statistical physics approach, Biological Cybernetics, vol.24, issue.1, pp.51-62, 1984.
DOI : 10.1007/BF00317939

J. Daniel and . Amit, Modeling brain function: The world of attractor neural networks, 1992.

E. Goles, Y. Gérad, and . Vichniac, Lyapunov functions for parallel neural networks, AIP Conference Proceedings, pp.165-181, 1986.
DOI : 10.1063/1.36274

Y. Kanoria and A. Montanari, Majority dynamics on trees and the dynamic cavity method. The Annals of Applied Probability, pp.1694-1748, 2011.

M. Mézard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond, 1987.

R. Paulo, . Campos, M. Viviane, . Oliveira, and . Brady-moreira, Small-world effects in the majority-vote model, Physical Review E, vol.67, issue.2, p.26104, 2003.

F. Luiz, F. Pereira, and . Brady-moreira, Majority-vote model on random graphs, Physical Review E, vol.71, issue.1, p.16123, 2005.

C. Castellano and R. Pastor-satorras, Zero temperature Glauber dynamics on complex networks, Journal of Statistical Mechanics: Theory and Experiment, vol.2006, issue.05, p.5001, 2006.
DOI : 10.1088/1742-5468/2006/05/P05001

P. James and . Gleeson, Binary-state dynamics on complex networks: pair approximation and beyond, Physical Review X, vol.3, issue.2, p.21004, 2013.

R. Abou-chacra, D. Thouless, and P. Anderson, A selfconsistent theory of localization, Journal of Physics C: Solid State Physics, vol.6, issue.10, p.1734, 1973.
DOI : 10.1088/0022-3719/6/10/009

R. Karp, Reducibility among combinatorial problems, 1972.

C. H. Yeung, D. Saad, and K. M. Wong, From the physics of interacting polymers to optimizing routes on the London Underground, Proceedings of the National Academy of Sciences, vol.110, issue.34, pp.13717-13722, 2013.
DOI : 10.1073/pnas.1301111110

P. Erd?-os and A. Rényi, On the evolution of random graphs, Publications of the Mathematical Institute of the Hungarian Academy of Sciences, pp.17-61, 1960.

N. Robertson and P. Seymour, Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995.
DOI : 10.1006/jctb.1995.1006

A. Aggarwal, J. Kleinberg, and D. Williamson, Node-disjoint paths on the mesh and a new trade-off in vlsi layout, Proc. of the twenty-eighth annual ACM symposium on Theory of computing, pp.585-594, 1996.

C. Chekuri and A. Ene, Poly-logarithmic Approximation for Maximum Node Disjoint Paths with Constant Congestion, SODA, pp.326-341, 2013.
DOI : 10.1137/1.9781611973105.24

C. De-bacco, S. Franz, D. Saad, and C. Yeung, Shortest node-disjoint paths on random graphs, Journal of Statistical Mechanics: Theory and Experiment, vol.2014, issue.7, pp.2014-07009, 2014.
DOI : 10.1088/1742-5468/2014/07/P07009
URL : https://hal.archives-ouvertes.fr/hal-01070758

R. Albert and A. Barabási, Statistical mechanics of complex networks, Reviews of Modern Physics, vol.74, issue.1, p.47, 2002.
DOI : 10.1103/RevModPhys.74.47

N. Robertson and P. Seymour, Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995.
DOI : 10.1006/jctb.1995.1006

B. C. Chatterjee, N. Sarma, and P. P. Sahu, Review and Performance Analysis on Routing and Wavelength Assignment Approaches for Optical Networks, IETE Technical Review, vol.30, issue.1, p.12, 2013.
DOI : 10.4103/0256-4602.107335

A. Fabrizio-altarelli, L. Braunstein, C. D. Dall-'asta, S. Bacco, and . Franz, The edge-disjoint path problem on random graphs by message-passing. arXiv preprint, 2015.

Z. Galil, S. Micali, and H. Gabow, An $O(EV\log V)$ Algorithm for Finding a Maximal Weighted Matching in General Graphs, SIAM Journal on Computing, vol.15, issue.1, pp.120-130, 1986.
DOI : 10.1137/0215009

M. Blesa and C. Blum, Ant Colony Optimization for the Maximum Edge-Disjoint Paths Problem, pp.160-169, 2004.
DOI : 10.1007/978-3-540-24653-4_17

Q. D. Pham, Y. Deville, V. Hentenryck, and P. , LS(Graph): a constraint-based local search for constraint optimization on trees and paths, Constraints, vol.1, issue.1, pp.357-408, 2012.
DOI : 10.1007/s10601-012-9124-0

A. Braunstein and R. Zecchina, Learning by message passing in networks of discrete synapses. Physical review letters, p.30201, 2006.

F. Altarelli, A. Braunstein, J. Realpe-gomez, and R. Zecchina, Statistical mechanics of budget-constrained auctions, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.07, p.7002, 2009.
DOI : 10.1088/1742-5468/2009/07/P07002

C. H. Yeung and D. Saad, Competition for Shortest Paths on Sparse Graphs, Physical Review Letters, vol.108, issue.20, p.208701, 2012.
DOI : 10.1103/PhysRevLett.108.208701

W. Edsger and . Dijkstra, A note on two problems in connexion with graphs. Numerische mathematik, pp.269-271, 1959.

J. Nash, Non-cooperative games, Annals of mathematics, pp.286-295, 1951.

A. Fabrizio-altarelli, L. Braunstein, C. D. Dall-'asta, S. Bacco, D. Franz et al., The nash equilibrium in routing problems by message-passing, 2015.

W. Robert and . Rosenthal, A class of games possessing pure-strategy nash equilibria, International Journal of Game Theory, vol.2, issue.1, pp.65-67, 1973.

N. Nisan, T. Roughgarden, E. Tardos, V. Vijay, and . Vazirani, Algorithmic game theory, 2007.
DOI : 10.1017/CBO9780511800481

S. Kirkpatrick and . Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

A. Fabrikant, C. Papadimitriou, and K. Talwar, The complexity of pure Nash equilibria, Proceedings of the thirty-sixth annual ACM symposium on Theory of computing , STOC '04, pp.604-612, 2004.
DOI : 10.1145/1007352.1007445

S. David, C. H. Johnson, M. Papadimitriou, and . Yannakakis, How easy is local search? Journal of computer and system sciences, pp.79-100, 1988.

T. Barthel, C. D. Bacco, and S. Franz, The matrix-product representation of dynamic cavity equations, 2015.

U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics, vol.326, issue.1, pp.96-192, 2011.
DOI : 10.1016/j.aop.2010.09.012

A. Roger, . Horn, R. Charles, and . Johnson, Matrix analysis, 2012.

L. Lovász, Random walks on graphs: A survey. Combinatorics, Paul erdos is eighty, pp.1-46, 1993.

C. De-bacco, N. Satya, P. Majumdar, and . Sollich, The average number of distinct sites visited by a random walker on random graphs, Journal of Physics A: Mathematical and Theoretical, vol.48, issue.20, p.48205004, 2015.
DOI : 10.1088/1751-8113/48/20/205004
URL : https://hal.archives-ouvertes.fr/hal-01153635

C. De-bacco, A. Guggiola, K. Reimer, and P. Paga, Rare events statistics of random walks on networks: localisation and other dynamical phase transitions, Journal of Physics A: Mathematical and Theoretical, vol.49, issue.18, 2015.
DOI : 10.1088/1751-8113/49/18/184003

F. Chung and . Rk, Spectral graph theory, 1997.
DOI : 10.1090/cbms/092

P. Dirac, A new notation for quantum mechanics, Mathematical Proceedings of the Cambridge Philosophical Society, vol.35, issue.03, pp.416-418, 1939.
DOI : 10.1017/S0305004100021162

G. ¨. Frobenius, Uber matrizen aus nicht negativen elementen

O. Perron, Zur Theorie der Matrices, Mathematische Annalen, vol.64, issue.2, pp.248-263, 1907.
DOI : 10.1007/BF01449896

F. Jasch and A. Blumen, Target problem on small-world networks, Physical Review E, vol.63, issue.4, p.41108, 2001.
DOI : 10.1103/PhysRevE.63.041108

F. Jasch and A. Blumen, Trapping of random walks on small-world networks. Physical review. E, Statistical, nonlinear, and soft matter physics, pp.66104-066104, 2001.

J. Beeler-jr, Distribution Functions for the Number of Distinct Sites Visited in a Random Walk on Cubic Lattices: Relation to Defect Annealing, Physical Review, vol.134, issue.5A, p.1396, 1964.
DOI : 10.1103/PhysRev.134.A1396

J. Klafter and A. Blumen, Models for dynamically controlled relaxation, Chemical Physics Letters, vol.119, issue.5, pp.377-382, 1985.
DOI : 10.1016/0009-2614(85)80438-3

C. Cattuto, A. Barrat, A. Baldassarri, G. Schehr, and V. Loreto, Collective dynamics of social annotation, Proceedings of the National Academy of Sciences, pp.10511-10515, 2009.
DOI : 10.1073/pnas.0901136106
URL : https://hal.archives-ouvertes.fr/hal-00361199

C. H. Yeung and D. Saad, Networking???a statistical physics perspective, Journal of Physics A: Mathematical and Theoretical, vol.46, issue.10, p.103001, 2013.
DOI : 10.1088/1751-8113/46/10/103001

G. H. Vineyard, The Number of Distinct Sites Visited in a Random Walk on a Lattice, Journal of Mathematical Physics, vol.4, issue.9, pp.1191-1193, 1963.
DOI : 10.1063/1.1704049

E. W. Montroll and G. Weiss, Random Walks on Lattices. II, Journal of Mathematical Physics, vol.6, issue.2, pp.167-181, 1965.
DOI : 10.1063/1.1704269

A. Dvoretzky and P. Erdös, Proceedings of the second berkeley symposium, 1951.

H. Larralde, P. Trunfio, S. Havlin, H. E. Stanley, and G. Weiss, Number of distinct sites visited by n random walkers, Physical Review A, issue.10, p.457128, 1992.

A. Kundu, S. N. Majumdar, and G. Schehr, Exact distributions of the number of distinct and common sites visited by n independent random walkers. Physical review letters, p.220602, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00832957

H. Barry, D. Sahimi, and M. , Random walks on the bethe lattice, Journal of Statistical Physics, vol.29, issue.4, pp.781-794, 1982.

R. Burioni and C. D. , Random walks on graphs: ideas, techniques and results, Journal of Physics A: Mathematical and General, vol.38, issue.8, p.45, 2005.
DOI : 10.1088/0305-4470/38/8/R01

S. Redner, A guide to first-passage processes, 2001.

D. J. Watts and S. Strogatz, Collective dynamics of 'small-world' networks, Nature, vol.393, issue.6684, pp.440-442, 1998.
DOI : 10.1038/30918

A. Barabási and A. R. , Emergence of scaling in random networks, Science, vol.286, issue.5439, pp.509-512, 1999.

J. Friedman, On the second eigenvalue and random walks in randomd-regular graphs, Combinatorica, vol.62, issue.3, pp.331-362, 1991.
DOI : 10.1007/BF01275669

A. Broder and E. Shamir, On the second eigenvalue of random regular graphs, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987), pp.286-294, 1987.
DOI : 10.1109/SFCS.1987.45

I. J. Farkas, I. Derényi, A. Barabási, and T. Vicsek, Spectra of ???real-world??? graphs: Beyond the semicircle law, Physical Review E, vol.64, issue.2, p.26704, 2001.
DOI : 10.1103/PhysRevE.64.026704

Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices, Combinatorica, vol.67, issue.3, pp.233-241, 1981.
DOI : 10.1007/BF02579329

F. Chung, L. Lu, and V. Vu, Spectra of random graphs with given expected degrees, Proceedings of the National Academy of Sciences, pp.6313-6318, 2003.

T. Rogers, I. P. Castillo, R. Kühn, and K. Takeda, Cavity approach to the spectral density of sparse symmetric random matrices, Physical Review E, vol.78, issue.3, p.31116, 2008.
DOI : 10.1103/PhysRevE.78.031116

S. F. Edwards and R. Jones, The eigenvalue spectrum of a large symmetric random matrix, Journal of Physics A: Mathematical and General, vol.9, issue.10, p.1595, 1976.
DOI : 10.1088/0305-4470/9/10/011

M. J. Urry and P. Sollich, Random walk kernels and learning curves for Gaussian process regression on random graphs, The Journal of Machine Learning Research, vol.14, issue.1, pp.1801-1835, 2013.

M. J. Urry and P. Sollich, Replica theory for learning curves for Gaussian processes on random graphs, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.42, p.45425005, 2012.
DOI : 10.1088/1751-8113/45/42/425005

P. Sollich, D. Tantari, A. Annibale, and A. Barra, Extensive load in multitasking associative networks, 2014.

R. Kühn, Spectra of sparse random matrices, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.29, p.295002, 2008.
DOI : 10.1088/1751-8113/41/29/295002

N. Alon, Eigenvalues and expanders, Combinatorica, vol.67, issue.2, pp.83-96, 1986.
DOI : 10.1007/BF02579166

A. Nilli, On the second eigenvalue of a graph, Discrete Mathematics, vol.91, issue.2, pp.207-210, 1991.
DOI : 10.1016/0012-365X(91)90112-F

V. Kishore, M. S. Santhanam, and R. E. Amritkar, Extreme events and event size fluctuations in biased random walks on networks, Physical Review E, vol.85, issue.5, p.56120, 2012.
DOI : 10.1103/PhysRevE.85.056120

J. P. Garrahan, R. L. Jack, V. Lecomte, E. Pitard, K. Van-duijvendijk et al., First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.7, p.75007, 2009.
DOI : 10.1088/1751-8113/42/7/075007
URL : https://hal.archives-ouvertes.fr/hal-00364938

R. L. Jack and P. Sollich, Large Deviations and Ensembles of Trajectories in Stochastic Models, Progress of Theoretical Physics Supplement, vol.184, pp.304-317, 2010.
DOI : 10.1143/PTPS.184.304

A. Dembo and O. Zeitouni, Large deviations techniques and applications, 2009.

H. Touchette, The large deviation approach to statistical mechanics, Physics Reports, vol.478, issue.1-3, pp.1-69, 2009.
DOI : 10.1016/j.physrep.2009.05.002

H. Touchette, Legendre-fenchel transforms in a nutshell, 2005.

R. Tyrrell and R. , Convex analysis. Number 28, 1970.

C. Cornelius and . Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, 1950.

Y. Kabashima, H. Takahashi, and O. Watanabe, Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices, Journal of Physics: Conference Series, p.12001, 2010.
DOI : 10.1088/1742-6596/233/1/012001

E. Mark and . Newman, Random graphs as models of networks. arXiv preprint cond- mat, 2002.

R. Pastor-satorras, C. Castellano, P. Van-mieghem, and A. Vespignani, Epidemic processes in complex networks, Reviews of Modern Physics, vol.87, issue.3, 2014.
DOI : 10.1103/RevModPhys.87.925

T. Guhr, A. Müller-groeling, A. Hans, and . Weidenmüller, Random-matrix theories in quantum physics: common concepts, Physics Reports, vol.299, issue.4-6, pp.189-425, 1998.
DOI : 10.1016/S0370-1573(97)00088-4

E. Mark and . Newman, Modularity and community structure in networks, Proceedings of the National Academy of Sciences, vol.103, issue.23, pp.8577-8582, 2006.

S. Fortunato, Community detection in graphs, Physics Reports, vol.486, issue.3-5, pp.75-174, 2010.
DOI : 10.1016/j.physrep.2009.11.002

C. De-bacco, F. Baldovin, E. Orlandini, and K. Sekimoto, Nonequilibrium statistical mechanics of the heat bath for two brownian particles. Physical review letters, p.180605, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01006581

R. Zwanzig, Nonlinear generalized Langevin equations, Journal of Statistical Physics, vol.3, issue.3, pp.215-220, 1973.
DOI : 10.1007/BF01008729

H. Mori, Transport, collective motion, and brownian motion. Progress of theoretical physics, pp.423-455, 1965.

R. Zwanzig, Ensemble Method in the Theory of Irreversibility, The Journal of Chemical Physics, vol.33, issue.5, pp.1338-1341, 1960.
DOI : 10.1063/1.1731409

R. Zwanzig, Memory Effects in Irreversible Thermodynamics, Physical Review, vol.124, issue.4, p.983, 1961.
DOI : 10.1103/PhysRev.124.983

K. Sekimoto, Stochastic energetics, 2010.
DOI : 10.1007/978-3-642-05411-2
URL : https://hal.archives-ouvertes.fr/hal-00345077

R. Huang, I. Chavez, M. Katja, B. Taute, S. Luki´cluki´c et al., Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid, Nature Physics, vol.23, issue.7, pp.576-580, 2011.
DOI : 10.1063/1.457480

L. Bocquet, . Jaros?, and . Piasecki, Microscopic derivation of non-Markovian thermalization of a Brownian particle, Journal of Statistical Physics, vol.44, issue.5-6, pp.5-61005, 1997.
DOI : 10.1007/BF02181268

R. Monasson, Diffusion, localization and dispersion relations on " small-world " lattices. The European Physical Journal B-Condensed Matter and Complex Systems, pp.555-567, 1999.

R. Karp, Reducibility among combinatorial problems, 1972.

N. Robertson and P. Seymour, Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995.
DOI : 10.1006/jctb.1995.1006

C. Chen and S. Banerjee, A new model for optimal routing and wavelength assignment in wavelength division multiplexed optical networks, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications, pp.164-171, 1996.
DOI : 10.1109/INFCOM.1996.497890

P. Manohar, D. Manjunath, and R. Shevgaonkar, Routing and wavelength assignment in optical networks from edge disjoint path algorithms, IEEE Communications Letters, vol.6, issue.5, pp.211-213, 2002.
DOI : 10.1109/4234.1001667

D. Banerjee and B. Mukherjee, A practical approach for routing and wavelength assignment in large wavelength-routed optical networks, IEEE Journal on Selected Areas in Communications, vol.14, issue.5, pp.903-908, 1996.
DOI : 10.1109/49.510913

S. Kolliopoulos, C. Stein, R. E. Bixby, E. A. Boyd, R. et al., Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs, Integer Programming and Combinatorial Optimization, pp.153-168
DOI : 10.1007/3-540-69346-7_12

L. Belgacem, I. Charon, and O. Hudry, A post-optimization method for the routing and wavelength assignment problem applied to scheduled lightpath demands, European Journal of Operational Research, vol.232, issue.2, pp.298-306, 2014.
DOI : 10.1016/j.ejor.2013.06.050

N. Skorin-kapov, Routing and wavelength assignment in optical networks using bin packing based algorithms, European Journal of Operational Research, vol.177, issue.2, pp.1167-1179, 2007.
DOI : 10.1016/j.ejor.2006.01.003

M. Blesa and C. Blum, Ant Colony Optimization for the Maximum Edge-Disjoint Paths Problem, pp.160-169, 2004.
DOI : 10.1007/978-3-540-24653-4_17

R. Storn and K. Price, Differential evolution?a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, vol.11, issue.4, pp.341-359, 1997.
DOI : 10.1023/A:1008202821328

Z. Sumpter, L. Burson, B. Tang, and C. X. , Maximizing number of satisfiable routing requests in static ad hoc networks, 2013 IEEE Global Communications Conference (GLOBECOM), 2013.
DOI : 10.1109/GLOCOM.2013.6831041

A. Srinivas and E. Modiano, Minimum energy disjoint path routing in wireless ad-hoc networks, Proceedings of the 9th annual international conference on Mobile computing and networking , MobiCom '03, pp.122-133, 2003.
DOI : 10.1145/938985.938999

K. Akkaya and M. Younis, A survey on routing protocols for wireless sensor networks, Ad hoc networks, pp.325-349, 2005.
DOI : 10.1016/j.adhoc.2003.09.010

X. Li and L. Cuthbert, Stable node-disjoint multipath routing with low overhead in mobile ad hoc networks In Modeling, Analysis, and Simulation of Computer and Telecommunications Systems, Proceedings. The IEEE Computer Society's 12th Annual International Symposium on, pp.184-191, 2004.

S. Jain and S. Das, Exploiting path diversity in the link layer in wireless ad hoc networks, Ad Hoc Networks, vol.6, issue.5, pp.805-825, 2008.
DOI : 10.1016/j.adhoc.2007.07.002

A. Tanenbaum, Computer Networks 4th Edition, 2003.

C. Chekuri and A. Ene, Poly-logarithmic Approximation for Maximum Node Disjoint Paths with Constant Congestion, SODA, pp.326-341, 2013.
DOI : 10.1137/1.9781611973105.24

P. Erd?-os and A. Rényi, On the evolution of random graphs, Publications of the Mathematical Institute of the Hungarian Academy of Sciences, pp.17-61, 1960.

M. Mézard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond, 1987.

M. Mézard and A. Montanari, Information, physics, and computation, 2009.
DOI : 10.1093/acprof:oso/9780198570837.001.0001

M. Mézard and G. Parisi, The cavity method at zero temperature, Journal of Statistical Physics, vol.111, issue.1/2, pp.1-34, 2003.
DOI : 10.1023/A:1022221005097

C. H. Yeung and D. Saad, Competition for Shortest Paths on Sparse Graphs, Physical Review Letters, vol.108, issue.20, p.208701, 2012.
DOI : 10.1103/PhysRevLett.108.208701

M. Mézard and G. Parisi, The Bethe lattice spin glass revisited, The European Physical Journal B, vol.20, issue.2, pp.217-233, 2001.
DOI : 10.1007/PL00011099

R. Albert and A. Barabási, Statistical mechanics of complex networks, Reviews of Modern Physics, vol.74, issue.1, p.47, 2002.
DOI : 10.1103/RevModPhys.74.47

A. Tanenbaum, Computer Networks 4th Edition, 2003.

R. Gerald and . Ash, Traffic Engineering and QoS Optimization of Integrated Voice & Data Networks, 2006.

N. Robertson, D. Paul, and . Seymour, Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995.
DOI : 10.1006/jctb.1995.1006

H. Sabih and . Gerez, Algorithms for VLSI design automation, 1999.

. Wun-tat-chan, Y. Francis, H. Chin, and . Ting, Escaping a Grid by Edge-Disjoint Paths, Algorithmica, vol.36, issue.4, pp.343-359, 2003.
DOI : 10.1007/s00453-003-1023-8

B. Awerbuch, R. Gawlick, T. Leighton, and Y. Rabani, On-line admission control and circuit routing for high performance computing and communication, Proceedings 35th Annual Symposium on Foundations of Computer Science, pp.412-423, 1994.
DOI : 10.1109/SFCS.1994.365675

M. Gerla and J. Tsai, Multicluster, mobile, multimedia radio network, Wireless networks, pp.255-265, 1995.
DOI : 10.1007/BF01200845

K. Akkaya and M. Younis, A survey on routing protocols for wireless sensor networks, Ad hoc networks, pp.325-349, 2005.
DOI : 10.1016/j.adhoc.2003.09.010

G. Kang, P. Shin, and . Ramanathan, Real-time computing: A new discipline of computer science and engineering, Proceedings of the IEEE, vol.82, issue.1, pp.6-24, 1994.

A. Mahapatra, K. Anand, P. Dharma, and . Agrawal, QoS and energy aware routing for real-time traffic in wireless sensor networks, Computer Communications, vol.29, issue.4, pp.437-445, 2006.
DOI : 10.1016/j.comcom.2004.12.028

F. Hussein, . Salama, S. Douglas, Y. Reeves, and . Viniotis, Evaluation of multicast routing algorithms for real-time communication on high-speed networks. Selected Areas in Communications, IEEE Journal on, vol.15, issue.3, pp.332-345, 1997.

S. Jain and S. Das, Exploiting path diversity in the link layer in wireless ad hoc networks, Ad Hoc Networks, vol.6, issue.5, pp.805-825, 2008.
DOI : 10.1016/j.adhoc.2007.07.002

X. Li and L. Cuthbert, Node-disjointness-based multipath routing for mobile ad hoc networks, Proceedings of the 1st ACM international workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks , PE-WASUN '04, pp.23-29, 2004.
DOI : 10.1145/1023756.1023761

C. Hsu, H. Cho, and S. Fang, Routing and wavelength assignment in optical networks from maximum edgedisjoint paths, Genetic and Evolutionary Computing, pp.95-103, 2014.

R. Karp, Reducibility among combinatorial problems, 1972.

M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of books in the mathematical sciences, 1979.

C. Chekuri and S. Khanna, Edge-disjoint paths revisited, Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pp.628-637, 2003.
DOI : 10.1145/1290672.1290683

T. Erlebach, Approximation Algorithms for Edge-Disjoint Paths and Unsplittable Flow, Efficient Approximation and Online Algorithms, pp.97-134, 2006.
DOI : 10.1007/11671541_4

G. Stavros, C. Kolliopoulos, and . Stein, Approximating disjoint-path problems using packing integer programs, Mathematical Programming, pp.63-87, 2004.

E. Asuman, . Ozdaglar, P. Dimitri, and . Bertsekas, Routing and wavelength assignment in optical networks, IEEE/ACM Transactions on Networking (TON), vol.11, issue.2, pp.259-272, 2003.

A. Baveja and A. Srinivasan, Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems, Mathematics of Operations Research, vol.25, issue.2, pp.255-280, 2000.
DOI : 10.1287/moor.25.2.255.12228
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.149

D. Quang, Y. Pham, P. Deville, and . Van-hentenryck, Ls (graph): a constraint-based local search for constraint optimization on trees and paths, Constraints, vol.17, issue.4, pp.357-408, 2012.

F. Thiago, . Noronha, G. Mauricio, . Resende, C. Celso et al., A biased random-key genetic algorithm for routing and wavelength assignment, Journal of Global Optimization, vol.50, issue.3, pp.503-518, 2011.

M. Gen, R. Cheng, and L. Lin, Network models and optimization: Multiobjective genetic algorithm approach, 2008.

A. Hassan, C. Phillips, and J. Pitts, Dynamic routing and wavelength assignment using hybrid particle swarm optimization for wdm networks, EPSRC PostGraduate Network Symposium (PGNet), 2007.

M. Blesa and C. Blum, Ant Colony Optimization for the Maximum Edge-Disjoint Paths Problem, pp.160-169, 2004.
DOI : 10.1007/978-3-540-24653-4_17

M. Mézard and G. Parisi, The cavity method at zero temperature, Journal of Statistical Physics, vol.111, issue.1/2, pp.1-34, 2003.
DOI : 10.1023/A:1022221005097

M. Mézard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond, 1987.

M. Mézard and A. Montanari, Information, physics, and computation, 2009.
DOI : 10.1093/acprof:oso/9780198570837.001.0001

M. Mézard and G. Parisi, The Bethe lattice spin glass revisited, The European Physical Journal B, vol.20, issue.2, pp.217-233, 2001.
DOI : 10.1007/PL00011099

M. Mézard, G. Parisi, and R. Zecchina, Analytic and Algorithmic Solution of Random Satisfiability Problems, Science, vol.297, issue.5582, pp.812-815, 2002.
DOI : 10.1126/science.1073287

C. H. Yeung and D. Saad, Competition for Shortest Paths on Sparse Graphs, Physical Review Letters, vol.108, issue.20, p.208701, 2012.
DOI : 10.1103/PhysRevLett.108.208701

M. Bayati, C. Borgs, A. Braunstein, A. Chayes, R. Ramezanpour et al., Statistical mechanics of steiner trees. Physical review letters, p.37208, 2008.

C. De-bacco, S. Franz, D. Saad, and C. H. Yeung, Shortest node-disjoint paths on random graphs, Journal of Statistical Mechanics: Theory and Experiment, vol.2014, issue.7, pp.2014-07009, 2014.
DOI : 10.1088/1742-5468/2014/07/P07009
URL : https://hal.archives-ouvertes.fr/hal-01070758

L. Lovász and D. Plummer, Matching Theory, 2009.
DOI : 10.1090/chel/367

A. Braunstein and R. Zecchina, Learning by message passing in networks of discrete synapses. Physical review letters, p.30201, 2006.

A. Fabrizio-altarelli, J. Braunstein, R. Realpe-gomez, and . Zecchina, Statistical mechanics of budget-constrained auctions, Journal of Statistical Mechanics: Theory and Experiment, issue.07, p.7002, 2009.

P. Erd?-os and A. Rényi, On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, pp.17-61, 1960.

E. Mark, . Newman, H. Steven, . Strogatz, J. Duncan et al., Random graphs with arbitrary degree distributions and their applications, Physical Review E, vol.64, issue.2, p.26118, 2001.

J. Michael and K. , Approximation algorithms for disjoint paths problems, 1996.

A. Medina, A. Lakhina, I. Matta, and J. Byers, Brite: An approach to universal topology generation In Modeling, Analysis and Simulation of Computer and Telecommunication Systems, Proceedings. Ninth International Symposium on, pp.346-353, 2001.

C. Hsu and H. Cho, A genetic algorithm for the maximum edge-disjoint paths problem, Neurocomputing, vol.148, 2014.
DOI : 10.1016/j.neucom.2012.10.046