. Dans-ce-chapitre-nous-présentons-un-algorithme-décentralisé-qui-construit-et-maintient-une-forêt-couvrante-dans-un-graphe-dynamique, Notre contribution à ce problème est double. Nous présentons d'une part, une amélioration signigficative, en terme de performance, d'un algorithme décentralisé à jeton basé sur le modèle DA-GRS proposé A. CASTEIGTS et S. CHAUMETTE [CC06, Cas06, Cas07] pour la construction et le maintien d'un arbre couvrant dans les MANETs. D'autre part, nous proposons une analyse probabiliste de l'algorithme à jeton initial et de l'algorithme amélioré, Après avoir discuté des motivations de ce travail

. Enfin, la dernière section étudie les phénomènes observés en simulation à l'aide d'une analyse probabiliste

. Ada99, A. Lada, and . Adamic, The small world web, Proc. 3rd European Conf. Research and Advanced Technology for Digital Libraries, ECDL, number 1696, pp.443-452, 1999.

A. Barabási and R. Albert, Emergence of scaling in random networks, Science, vol.286, p.509, 1999.

J. Bicket, D. Aguayo, S. Biswas, and R. Morris, Architecture and evaluation of an unplanned 802.11 b mesh network, Proceedings of the 11th annual international conference on Mobile computing and networking, pp.31-42, 2005.

]. P. Bak96 and . Bak, How Nature works : the science of self-organized criticality, 1996.

C. Bertelle, A. Dutot, F. Guinand, and D. Olivier, Organization detection for dynamic load balancing in individual-based simulations . Multi-Agent and Grid Systems, p.42, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00430523

M. [. Bonabeau, G. Dorigo, and . Theraulaz, Swarm Intelligence : from natural to artificial systems, 1999.

]. H. Ber02 and . Bersini, And the winner is...not the fittest [coevolution], Evolutionary Computation CEC '02. Proceedings of the 2002 Congress on, pp.1510-1515, 2002.

[. Bersini, des réseaux et des sciences -Biologie, informatique, sociologie : l'omniprésence des réseaux. vuibert informatique. Vuibert Smooth is better than sharp : a random mobility model for simulation of wireless networks, Proceedings of the 4th ACM international workshop on Modeling, analysis and simulation of wireless and mobile systems, pp.19-27, 2001.

[. Bettstetter, Mobility modeling in wireless networks, ACM SIGMOBILE Mobile Computing and Communications Review, vol.5, issue.3, p.11, 2001.
DOI : 10.1145/584051.584056

J. Beal and S. Gilbert, Rambonodes for the metropolitan ad hoc network, 2003.

A. [. Bai and . Helmy, Wireless Ad Hoc and Sensor Networks, chapter A Survey of Mobility Modeling and Analysis in Wireless Adhoc Networks, 2004.

R. [. Bullnheimer, C. Hartl, and . Strauss, A new rank-based version of the ant system : a computational study, Central European Journal for Operations Research and Economics, vol.7, issue.1, pp.25-38, 1999.

Z. Andrei, R. Broder, F. Kumar, P. Maghoul, . Raghavan et al., Graph structure in the web, Computer Networks, vol.33, issue.16, pp.309-320, 2000.

]. S. Blm-+-06, V. Boccaletti, Y. Latora, M. Moreno, D. Chavez et al., Complex networks : Structure and dynamics, Physics Reports, vol.424, pp.175-308, 2006.

]. J. Bmj-+-98, D. A. Broch, D. B. Maltz, Y. C. Johnson, J. Hu et al., A performance comparison of multi-hop wireless ad hoc network routing protocols, Proceedings of the 4th annual ACM/IEEE international conference on Mobile computing and networking, pp.85-97, 1998.

G. [. Bettstetter, P. Resta, and . Santi, The node distribution of the random waypoint mobility model for wireless ad hoc networks, IEEE Transactions on Mobile Computing, vol.2, issue.3, pp.257-269, 2003.
DOI : 10.1109/TMC.2003.1233531

[. Barán and M. Schaerer, A multiobjective ant colony system for vehicle routing problem with time windows, Proceedings of the 21st IASTED International Conference, 2003.

A. [. Bui-xuan, A. Ferreira, and . Jarry, COMPUTING SHORTEST, FASTEST, AND FOREMOST JOURNEYS IN DYNAMIC NETWORKS, International Journal of Foundations of Computer Science, vol.14, issue.02, pp.267-285, 2003.
DOI : 10.1142/S0129054103001728
URL : https://hal.archives-ouvertes.fr/inria-00071996

A. Casteigts, Model Driven capabilities of the DA-GRS model, International Conference on Autonomic and Autonomous Systems (ICAS'06), 2006.
DOI : 10.1109/ICAS.2006.35
URL : https://hal.archives-ouvertes.fr/hal-00305752

A. Casteigts, Contribution à l'algorithmique distribuée dans les réseaux mobiles ad hoc -Calculs locaux et réétiquetages de graphes dynamiques, 2007.

S. [. Casteigts and . Chaumette, Dynamicity Aware Graph Relabeling Systems and the Constraint Based Synchronization: A Unifying Approach to Deal with Dynamic Networks, International Conference on Wireless Algorithms, pp.688-697, 2006.
DOI : 10.1007/11814856_64

M. [. Chlamtac, J. J. Conti, and . Liu, Mobile ad hoc networking: imperatives and challenges, Ad Hoc Networks, pp.13-64, 2003.
DOI : 10.1016/S1570-8705(03)00013-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.4069

A. Cardon, A. Dutot, F. Guinand, and D. Olivier, Emergent Properties in Natural and Artificial Dynamical Systems, chapter Competing Ants for Organization Detection : application to Dynamic Distribution complexity : Understanding Complex Systems, pp.25-52, 2006.

]. O. Cdvhm00, I. F. Cordon, F. De-viana, L. Herrera, and . Moreno, A new aco model integrating evolutionary computation concepts : the best-worst ant system, Abstract proceedings of ANTS 2000 ? From Ant Colonies to Artificial Ants : Second International Workshops on Ant Algorithms, pp.22-29, 2000.

M. Conti, S. Giordano, G. Maselli, and G. Turi, MobileMAN: Mobile Metropolitan Ad Hoc Networks, Proc. Eight International IFIP- TC6 Conference Lecture Notes in Computer Science LNCS 2775, pp.173-178, 2003.
DOI : 10.1007/978-3-540-39867-7_15
URL : http://puma.isti.cnr.it/rmydownload.php?filename=cnr.iit/cnr.iit/2003-A0-007/2003-A0-007.pdf

A. [. Costa and . Hertz, Ants can colour graphs, Journal of the Operational Research Society, vol.48, issue.3, pp.295-305, 1997.
DOI : 10.1057/palgrave.jors.2600357

P. T. Clausen, A. Jacquet, and . Laouiti, Optimized link state routing protocol, IEEE INMIC Pakistan, 2001.
DOI : 10.17487/rfc3626
URL : https://hal.archives-ouvertes.fr/inria-00471712

[. Cortes, D. Pregibon, and C. Volinsky, Computational Methods for Dynamic Graphs, Journal of Computational and Graphical Statistics, vol.12, issue.4, pp.950-970, 2003.
DOI : 10.1198/1061860032742

]. M. Den-besten, T. Stutzle, and M. Dorigo, Ant Colony Optimization for the Total Weighted Tardiness Problem, Proceedings of PPSN-VI, Sixth International Conference on Parallel Problem Solving from Nature, pp.611-620, 1917.
DOI : 10.1007/3-540-45356-3_60

G. [. Dorigo and . Caro, New Ideas in Optimization. D. Corne and M. Dorigo and F. Glover eds, chapter The Ant Colony Optimization Meta- Heuristic, pp.11-32, 1997.

[. Deo and A. Cami, Preferential deletion in dynamic models of web-like networks, Information Processing Letters, vol.102, issue.4, pp.156-162, 2007.
DOI : 10.1016/j.ipl.2006.12.009

[. Caro, F. Ducatelle, and L. M. Gambardella, Anthocnet : an ant-based hybrid routing algorithm for mobile ad hoc networks, Proceedings of Parallel Problem Solving from Nature (PPSN VIII), pp.461-470, 2004.

G. Dicaro and M. Dorigo, Antnet : Distributed stigmergetic control for communications networks, Journal of Artificial Intelligence Research, vol.9, pp.317-365, 1998.

]. M. Dg97a, L. M. Dorigo, and . Gambardella, Ant colony system : a cooperative learning approach to the travelingsalesman problem, Evolutionary Computation IEEE Transactions on, vol.1, issue.1, pp.53-66, 1997.

M. Dorigo and L. M. Gambardella, Ant colonies for the travelling salesman problem, Biosystems, vol.43, issue.2, pp.73-81, 1997.
DOI : 10.1016/S0303-2647(97)01708-5

. Dgh-+-01-]-k, W. Doerner, R. Gutjahr, C. Hartl, C. Strauss et al., Ant colony optimization in multiobjective portfolio selection, Proceedings of the 4th Metaheuristics Intl. Conf, pp.243-248, 2001.

K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, and C. Stummer, Pareto Ant Colony Optimization: A Metaheuristic Approach to Multiobjective Portfolio Selection, Annals of Operations Research, vol.131, issue.1-4, pp.1-479, 2004.
DOI : 10.1023/B:ANOR.0000039513.99038.c6

G. F. Demetrescu and . Italiano, Fully dynamic all pairs shortest paths with real edge weights Algorithmic techniques for maintaining shortest routes in dynamic networks, DI07] Camil Demetrescu and Giuseppe F. Italiano, pp.813-8373, 2006.

[. Dijkstra, A note on two problems in connexion with graphs, Numerische Mathematik, vol.4, issue.1, pp.269-271, 1959.
DOI : 10.1007/BF01386390

V. [. Dorigo, A. Maniezzo, and . Colorni, Positive feedback as a search strategy, 1991.

V. [. Dorigo, A. Maniezzo, and . Colorni, Ant system : optimization by a colony of cooperating agents. Systems, Man and Cybernetics, Part B IEEE Transactions on, vol.26, issue.1, pp.29-41, 1996.

A. Dutot, Distribution dynamique adaptative par des mécanismes d'intelligence collective, détection d'organisations par des techniques de collaboration et de compétition, 2005.

E. [. Levine and . Ben-jacob, Des fleurs de bactéries. Pour la Science -Les formes de la vie, pp.4478-83, 2004.

J. [. Eberhart and . Kennedy, A new optimizer using particle swarm theory. Micro Machine and Human Science, MHS'95 Proceedings of the Sixth International Symposium on, pp.39-43, 1995.

A. [. Erdös and . Rényi, On the evolution of random graphs, Bulletin of the Institute of International Statistics, vol.38, pp.343-347, 1961.

C. Eyckelhof and M. Snoek, Ant Systems for a Dynamic TSP, ANTS '02 : Proceedings of the Third International Workshop on Ant Algorithms, pp.88-99, 2002.
DOI : 10.1007/3-540-45724-0_8

A. Ferreira, On models and algorithms for dynamic communication networks : The case for evolving graphs, 4e rencontres francophones sur les Aspects Algorithmiques des Telecommunications (ALGOTEL'2002), 2002.

D. Frigioni, A. Marchetti-spaccamela, and U. Nanni, Fully dynamic output bounded single source shortest path problem (extended abstract), SODA : ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms ), 1996.

C. [. Fenet and . Solnon, Searching for maximum cliques with ant colony optimization. Applications of Evolutionary Computing, Proceedings of Evo- Workshops, pp.236-245, 2003.

[. , M. Gambardella, and M. Dorigo, Ant-q : A reinforcement learning approach to the traveling salesman problem, International Conference on Machine Learning, pp.252-260, 1995.

[. Gambardella, É. Taillard, and G. Agazzi, MACS- VRPTW : A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows, New Ideas in Optimization, pp.63-76, 1999.

F. Glover and M. Laguna, Tabu search, Modern Heuristic Techniques for Combinatorial Problems, 1993.
URL : https://hal.archives-ouvertes.fr/hal-01389283

[. Gerla, C. Lindemann, and A. Rowstron, P2p manet's -new research issues Perspectives Workshop : Peer-to-Peer Mobile Ad Hoc Networks -New Research Issues, Dagstuhl Seminar Proceedings. Internationales Begegnungs-und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, pp.213-2005, 2005.

]. M. Gm02a, M. Guntsch, and . Middendorf, Applying population based aco to dynamic optimization problems [GM02b] Michael Guntsch and Martin Middendorf. A population based approach for ACO, Applications of Evolutionary Computing , Proceedings of EvoWorkshops2002 : EvoCOP, pp.71-80, 2002.

[. Giraud, J. Pedersen, and L. Keller, Evolution of supercolonies: The Argentine ants of southern Europe, Proceedings of the National Academy of Sciences, vol.99, issue.9, pp.6075-6079, 2002.
DOI : 10.1073/pnas.092694199

[. Guidec and H. Roussain, Parallel and Distributed Processing and Applications, of Lecture Notes in Computer Science, chapter Asynchronous Document Dissemination in Dynamic Ad Hoc Networks, pp.44-48, 2005.

]. Gra59, E. Gambardella, M. Taillard, and . Dorigo, La reconstruction du nid et les coordinations interindividuelles chez belicositermes natalensis et cubitermes s.p. la théorie de la stigmergie : essai d'interprétation du comportement des termites constructeurs Ant colonies for the quadratic assignment problem, Insectes sociaux Journal of the Operational Research Society, vol.6, issue.502, pp.41-80167, 1959.

C. Felix and . Gärtner, A survey of self-stabilizing spanning-tree construction algorithms, 2003.

Z. Haas, A new routing protocol for the reconfigurable wireless networks, Proceedings of the 6th IEEE International Conference on Universal Person Communications Record, ICUPC '97, pp.562-566, 1997.

H. [. Grégoire and . Chaté, La forme des groupements animaux. Pour la Science -Les formes de la vie, pp.4457-61, 2004.

M. [. Hong, G. Gerla, C. C. Pei, and . Chiang, A group mobility model for ad hoc wireless networks, Proceedings of the 2nd ACM international workshop on Modeling, analysis and simulation of wireless and mobile systems , MSWiM '99, pp.53-60, 1999.
DOI : 10.1145/313237.313248

L. Hogie, Mobile Ad Hoc Networks : Modelling, Simulation and Broadcastbased Applications, 2007.

P. Amit, E. M. Jardosh, K. C. Belding-royer, S. Almeroth, and . Suri, Real-world environment models for mobile network evaluation, IEEE Journal on Selected Areas in Communications, vol.23, issue.3, pp.622-632, 2005.

J. [. Eberhart and . Kennedy, Swarm Intelligence, 2001.

R. Kumar, P. Raghavan, S. Rajagopalan, and D. Sivakumar, Stochastic models for the Web graph, Proceedings 41st Annual Symposium on Foundations of Computer Science, pp.57-65, 2000.
DOI : 10.1109/SFCS.2000.892065

L. [. Kazantzidis, M. Wang, and . Gerla, On fairness and efficiency of adaptive audio application layers for multihop wireless networks, 1999 IEEE International Workshop on Mobile Multimedia Communications (MoMuC'99) (Cat. No.99EX384), pp.357-362, 1999.
DOI : 10.1109/MOMUC.1999.819511

Z. [. Liang and . Haas, Predictive distance-based mobility management for PCS networks, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320), 1999.
DOI : 10.1109/INFCOM.1999.752157

Z. [. Leguizamon and . Michalewicz, A new version of ant system for subset problems, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), pp.6-9, 1999.
DOI : 10.1109/CEC.1999.782655

Z. [. Leguizamon and . Michalewicz, An ant system for the maximum independent set problem, Proceedings of the 2001 Argentinian Congress on Computer Science, pp.1027-1040, 2001.

M. Latapy and C. Magnien, Measuring fundamental properties of real-world complex networks, 2006.

]. V. Man99 and . Maniezzo, Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem, INFORMS Journal on Computing, vol.11, issue.4, pp.358-369, 1999.

A. [. Maniezzo and . Colorni, The ant system applied to the quadratic assignment problem, IEEE Transactions on Knowledge and Data Engineering, vol.11, issue.5, pp.769-778, 1999.
DOI : 10.1109/69.806935

[. Mao, S. Lin, S. S. Panwar, and Y. Wang, A multipath video streaming testbed for ad hoc networks, Vehicular Technology Conference, pp.2961-2965, 2003.

N. Pubudu and . Pathirana, Node localization using mobile robots in delaytolerant sensor networks, IEEE Transactions on Mobile Computing, vol.4, issue.3, pp.285-296, 2005.

A. Piyatumrong, P. Bouvry, F. Guinand, and K. , Trusted Spanning Tree for Delay Tolerant MANETs, 2008 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing, 2008.
DOI : 10.1109/EUC.2008.45
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.7100

[. Pelusi, A. Passarella, M. Conti, and I. Networks, Beyond manets : dissertation on opportunistic networking, 2006.

[. Perkins and E. Royer, Ad-hoc on-demand distance vector routing, Mobile Computing Systems and Applications, 1999. Proceedings. WMCSA'99. Second IEEE Workshop on, pp.90-100, 1999.

C. Perkins and E. Royer, Ad-hoc on-demand distance vector routing, WMCSA '99 : Proceedings of the Second IEEE Workshop on Mobile Computer Systems and Applications, page 90, 1999.

M. [. Pallottino and . Scutellà, Shortest Path Algorithms In Transportation Models: Classical and Innovative Aspects, 1997.
DOI : 10.1007/978-1-4615-5757-9_11

]. C. Rey87 and . Reynolds, Flocks, Herds, and Schools : A Distributed Behavioral Model, Computer Graphics, vol.2187, issue.4, pp.25-34, 1987.

T. [. Ramalingam and . Reps, An Incremental Algorithm for a Generalization of the Shortest-Path Problem, Journal of Algorithms, vol.21, issue.2, pp.267-305, 1996.
DOI : 10.1006/jagm.1996.0046

. Sh-+-00-]-t, H. H. Stutzle, and . Hoos, Max-min ant system, Future Generation Computer Systems, vol.16, issue.8, pp.889-914, 2000.

O. [. Schoonderwoerd, J. L. Holland, L. J. Bruten, and . Rothkrantz, Ant-Based Load Balancing in Telecommunications Networks, Adaptive Behavior, vol.269, issue.1, p.169, 1997.
DOI : 10.1177/105971239700500203

P. [. Sánchez and . Manzoni, ANEJOS: a Java based simulator for ad hoc networks, Future Generation Computer Systems, vol.17, issue.5, pp.573-583, 2001.
DOI : 10.1016/S0167-739X(00)00040-6

J. [. Shawe-taylor and . Zerovnik, Ants and Graph Coloring, Proceedings of the International Conference on Artificial Neural Nets and Genetic Algorithms , ICANNGA'01, pp.276-279, 2001.
DOI : 10.1007/978-3-7091-6230-9_68

J. Jing-tian, C. Haehner, I. Becker, K. Stepanov, and . Rothermel, Graph-based mobility model for mobile ad hoc network simulation, Proceedings 35th Annual Simulation Symposium. SS 2002, p.337, 2002.
DOI : 10.1109/SIMSYM.2002.1000171

]. G. The97 and . Theraulaz, Auto-organisation et comportement, Collection Systèmes Complexes. Hermès, 1997.

]. S. Van-der-zwaan and C. Marques, Ant colony optimisation for job shop scheduling, Proceedings of the Third Workshop on Genetic Algorithms and Artificial Life (GAAL 99), 1999.

]. H. Wal94 and . Walter, L'aventure des langues en occident, 1994.

]. M. Wdv-+-97, C. Werner, H. J. Delucchi, G. Vogel, J. J. Maral et al., Atm-based routing in leo/meo satellite networks with intersatellitelinks. Selected Areas in Communications, IEEE Journal on, vol.15, issue.1, pp.69-82, 1997.

]. S. Wol84 and . Wolfram, Universality and complexity in cellular automata, Physica D, vol.10, pp.1-35, 1984.

T. Xu and Y. Cai, Streaming in MANET: Proactive Link Protection and Receiver-Oriented Adaptation, 2007 IEEE International Performance, Computing, and Communications Conference, pp.178-185, 2007.
DOI : 10.1109/PCCC.2007.358893

]. H. Zwi03 and . Zwirn, La complexité, science du xxi e siècle ? Pour la Science -La complexité, pp.28-29, 2003.

P. Guinand, An Ant-Based Model for Multiple Sequence Alignment, Large- Scale Scientific Computing, pp.553-560, 2008.
DOI : 10.1093/nar/22.22.4673
URL : https://hal.archives-ouvertes.fr/hal-00264040

N. Chromatique and .. , 58, 61 P Particle Swarm Optimization, p.45