. Le-nombre-de-paquets-en-transit-dans-b-est-borné-nous-montrons-ici-que-la-partition-b-de-la-coupe-(-a and . Vu-comme-un-s-d-réseau-r-généralisé-réalisable, que le nombre de paquets en transit dans B est borné. Nous construisons un S -D -réseau B qui se comporte comme B dans le réseau G. Soit X l'ensemble des sommets de B adjacents aux sommets de la partition A. Considérons alors le réseau B contenant un ensemble de sources R-généralisées S et un ensemble de destinations R-généralisées D , tels que

. Par-hypothèse-d-'induction,-si-le-s-d-réseau-r-généralisé-b-est-réalisable, En effet, par définition de B , nous pouvons choisir un [80207] IEEE Std 802.11-2007. IEEE Standard for Information technology- Telecommunications and information exchange between systems- Local and metropolitan area networks-Specific requirements -Part 11 : Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE Standard for Local and metropolitan area networks Part 16 : Air Interface for Broadband Wireless Access Systems, pp.9116-2009, 2007.

B. Awerbuch, P. Berenbrink, A. Brinkmann, and C. Scheideler, Simple routing strategies for adversarial systems, Proceedings 2001 IEEE International Conference on Cluster Computing, pp.158-167, 0102.
DOI : 10.1109/SFCS.2001.959890

B. Aoun, R. Boutaba, Y. Iraqi, and G. Kenward, Gateway Placement Optimization in Wireless Mesh Networks With QoS Constraints, IEEE Journal on Selected Areas in Communications, vol.24, issue.11, pp.2127-2136, 2006.
DOI : 10.1109/JSAC.2006.881606

R. [. Alicherry, L. Bhatia, and . Li, Joint channel assignment and routing for throughput optimization in multi-radio wireless mesh networks, Proceedings of the 11th annual international conference on Mobile computing and networking , MobiCom '05, pp.58-72, 2005.
DOI : 10.1145/1080829.1080836

E. Amaldi, A. Capone, M. Cesana, I. Filippini, F. K. Malucelliamo93-]-r et al., Optimization models and methods for planning wireless mesh networks, Computer Networks, vol.52, issue.11, pp.2159-2171, 1993.
DOI : 10.1016/j.comnet.2008.02.020

I. F. Akyildiz, X. Wang, and W. Wang, Wireless mesh networks: a survey, Computer Networks, vol.47, issue.4, pp.445-487, 2005.
DOI : 10.1016/j.comnet.2004.12.001

. Bgk-+-06-]-j-c, J. Bermond, R. Galtier, N. Klasing, S. Morales et al., Hardness and approximation of gathering in static radio networks, Parallel Processing Letters, vol.16, issue.33, pp.165-183, 2006.

V. Bonifaci, P. Korteweg, A. Marchetti-spaccamela, and L. Stougie, An approximation algorithm for the wireless gathering problem, 10th Scandinavian Workshop on Algorithm Theory (SWAT), pp.328-338, 2006.

]. A. Bkr-+-96, J. Borodin, P. Kleinberg, M. Raghavan, D. P. Sudan et al., Adversarial queuing theory, 28th ACM Symposium of Foundations of Computer Science (STOC) Birge and F. Louveaux. Introduction to Stochastic Programming . Springer Series in Operations Research, pp.376-385, 1996.

S. [. Bui, R. Sanghavi, and . Srikant, Distributed Link Scheduling With Constant Overhead, IEEE/ACM Transactions on Networking, vol.17, issue.5, pp.1467-1480267, 2003.
DOI : 10.1109/TNET.2009.2013621

C. , D. S. De-couto, D. Aguayo, B. A. Chambers, and R. Morris, Performance of multihop wireless networks : Shortest path in not enough Unit disk graphs, ACM SIGCOMM Computer Communication Review Discrete Mathematics, vol.33, issue.86, pp.83-881, 1925.

W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver, Combinatorial optimization, p.82, 1997.
DOI : 10.1002/9781118033142
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.8315

G. Carello, I. Filippini, S. Gualandi, and F. Malucelli, Scheduling and routing in wireless multi-hop networks by column generation, International Network Optimization Conference (INOC), Spa, Belgium, p.53, 2007.

C. , T. H. Cormen, C. E. Leiserson, R. L. Rivest-costa, L. Létocart et al., Introduction to algorithms , Second Edition Minimal multicut and maximal integer multiflow : A survey, European Journal of Operational Research, vol.57, issue.1621, pp.55-69, 1983.

R. Chandra, L. Qiu, K. Jain, and M. Mahdian, Optimizing the placement of integration points in multi-hop wireless networks Dual decomposition in stochastic integer programming, 12th IEEE International Conference on Network Protocols (ICNP), pp.271-282, 0130.

J. [. Desaulniers, M. M. Desrosiers, and . Solomon, Column generation, p.46, 2005.
DOI : 10.1007/b135457

O. Dousse, M. Franceschetti, D. Tse, and P. Thiran, Closing the gap in the capacity of random wireless networks, IEEE International Symposium on Information Theory (ISIT), p.438, 2004.

K. [. Durocher, A. Jampani, L. Lubiw, and . Narayanan, Modelling gateway placement in wireless networks, Proceedings of the fifth international workshop on Foundations of mobile computing, DIAL M-POMC '08, pp.79-86, 2008.
DOI : 10.1145/1400863.1400879

]. P. Dju07 and . Djukic, Scheduling Algorithms for TDMA Wireless Multihop Networks Djukic and S. Valaee. Link scheduling for minimum delay in spatial re-use TDMA, IEEE Conference on Computer Communications (Infocom), pp.28-36, 1927.

S. [. Djukic, . Valaeedv09-]-p, S. Djukic, and . Valaee, Delay Aware Link Scheduling for Multi-Hop TDMA Wireless Networks, IEEE/ACM Transactions on Networking, vol.17, issue.3, pp.870-883, 0100.
DOI : 10.1109/TNET.2008.2005219

. B. Bibliographie-[-dw60-]-g, P. Dantzig, and . Wolfe, Decomposition principles for linear programs Ergen and Varaiya. TDMA scheduling algorithms for sensor networks, Operation Research, vol.8, issue.1, pp.101-111, 1927.

A. [. Ferreira, J. Goldman, ]. S. Monteirogdp05, M. Gandham, R. Dawande et al., Performance evaluation of routing protocols for manets with known connectivity patterns using evolving graphs Wireless Networks Link scheduling in sensor networks : distributed edge coloring revisited, IEEE Conference on Computer Communications (Infocom), pp.2492-2501, 2005.

P. [. Gupta and . Kumar, The capacity of wireless networks, IEEE Transactions on Information Theory, vol.46, issue.2, pp.388-404, 2000.
DOI : 10.1109/18.825799

G. M. Grotschel, L. Lovasz, and A. Schrijver, Tdma Versus Cdma The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, vol.27, issue.16, pp.169-197, 1981.

C. [. Gomes, P. Molle, and . Reyes, Optimal design of wireless mesh networks, 9` emes Journées Doctorales en Informatique et Réseaux (JDIR), pp.67-76, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00375991

]. C. Gmrr07a, C. Gomes, P. Molle, H. Reyes, and . Rivano, Models for optimal wireless mesh network design, 22nd European Conference on Operational Research (EURO XXII), pp.43-60, 2007.

]. C. Gmrr07b, C. Gomes, P. Molle, H. Reyes, and . Rivano, Placement optimal de points d'accès dans les réseaux radio maillés, 9` emes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (AlgoTel), pp.117-120, 2007.

C. Gomes, S. Pérennes, P. Reyes, H. V. Rivanogt88-]-a, R. E. Goldberg et al., Bandwidth allocation in radio grid networks A new approach to the maximumflow problem, 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), pp.41-44921, 1988.

P. [. Hsu, J. P. Hung, and . Sheu, Scheduling of broadcasts in multihop wireless networks, The handbook of ad hoc wireless networks, pp.483-495, 2003.

T. Huovila, P. Lassila, J. Manner, and A. Penttinen, State of the art analysis of wireless mesh technologies 2006, 2005.

P. [. Hekmat and . Van-mieghem, Connectivity in wireless ad-hoc networks with an improved radio model, Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), 1924.

C. [. Iyer, A. Rosenberg, and . Karnik, What is the right model for wireless channel interference?, IEEE Transactions on Wireless Communications, vol.8, issue.5, pp.2662-2671, 1927.
DOI : 10.1109/TWC.2009.080720

J. [. Jain, V. Padhye, L. Padhamanabhan, M. L. Qiu, and . Sichitiu, Impact of interference on multi-hop wireless network performance The nominal capacity of wireless mesh networks Throughput-optimal configuration of fixed wireless networks, 9th Annual ACM International Conference on Mobile Computing and Networking (MobiCom) Kave, R. Khalili, and K. Salamatian. Evaluation of packet error rate in wireless networks, pp.66-80, 2003.

. [. Bibliographie, N. Klasing, S. Morales, and . Pérennes, On the complexity of bandwidth allocation in radio networks, Theoretical Computer Science, vol.406, issue.43, pp.225-239, 1931.

A. Kumar, M. Marathe, S. Parthasarathy, and A. Srinivasan, Algorithmic aspects of capacity in wireless networks Characterizing achievable rates in multi-hop wireless networks : the joint routing and scheduling problem On the capacity region of multiradio multi-channel wireless mesh networks, ACM International Conference on Measurements and Modeling of Computer Systems (SIGMETRICS) 9th Annual ACM International Conference on Mobile Computing and Networking (MobiCom) First IEEE Workshop on Wireless Mesh Networks (WiMesh), pp.133-144, 2003.

[. E. Lalandeld05-]-m, J. Lubbecke, and . Desrosiers, Conception de réseaux de télécommunications : optimisation et expérimentations Selected topics in column generation Efficient algorithms to solve a class of resource allocation problems in large wireless networks, 7th International Symposium on Modeling and Optimization in Mobile , Ad Hoc, and Wireless Networks (WiOpt), pp.1007-1023, 2004.

[. Li, X. Huang, Y. Fang, P. Linlss09, ]. S. Lakshmanan et al., Optimal placement of gateways in vehicular networks Multigateway association in wireless mesh networks Ad-Hoc Networks Mascopt -a network optimization library : Graph manipulation Optimal scheduling for link assignment in traffic-sensitive stdma wireless ad-hoc networks, International Conference on Computer Network and Mobile Computing (ICCNMC), pp.3421-3430622, 2004.

E. [. Miorandi and . Altman, Coverage and connectivity of ad hoc networks in presence of channel randomness, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies., pp.491-502, 1924.
DOI : 10.1109/INFCOM.2005.1497917
URL : https://hal.archives-ouvertes.fr/inria-00070626

]. N. Mor07, C. Morales, F. Molle, S. Peix, H. Pérennes et al., Algorithmique des réseaux de communication radio modélisés par des graphes Formulation en coupe/rounds pour le routage dans les réseaux radio maillés, 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel), pp.100-97, 2007.

]. C. Mppr08b, F. Molle, S. Peix, H. Pérennes, and . Rivano, Optimal routing and call scheduling in wireless mesh networks with localized information, 4th International Symposium on Trustworthy Global Computing (TGC) Meheut, S. Perennes, and H. Rivano. Evaluation stochastique et simulation des réseaux radio. Research report 5989, pp.171-185, 2006.

C. Molle, F. Peix, and H. Rivano, Génération de colonnes pour le routage et l'ordonnancement dans les réseaux radio maillés, Colloque francophone sur l'ingénierie des protocoles (CFIP), pp.119-130, 2008.

]. C. Mpr08b, F. Molle, H. Peix, and . Rivano, An optimization framework for the joint routing and scheduling in wireless mesh networks, 19th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), pp.2792-2796, 2008.

C. [. Muthaiah and . Rosenberg, Single gateway placement in wireless mesh networks, 8th International IEEE Symposium on Computer Networks (ISCN), p.11, 2008.

S. Max, L. Stibor, G. Hiertz, and D. Denteneer, IEEE 802.11s mesh network deployment concepts, 13th European Wireless Conference (EW), p.7, 2007.

H. [. Mukherjee, C. Viswanathanmv08, M. Molle, and . Voge, Throughput-range tradeoff of wireless mesh backhaul networks Influence des acquittements sur la capacité des réseaux radio maillés, 10èmes Rencontres Francophones sur les Aspects Algorithmiques de Télécommunications (AlgoTel) Voge. Effects of the acknowledgment traffic on the capacity of wireless mesh networks 69th IEEE Vehicular Technology Conference (VTC) Spring, pp.593-602, 2006.

J. Mao, Z. Wu, X. Wu, M. Nassiri, M. Heusse et al., A TDMA scheduling scheme for many-to-one communications in wireless sensor networks, 27th IEEE Conference on Computer Communications (Infocom), pp.863-872, 2007.
DOI : 10.1016/j.comcom.2006.10.006

N. [. Gore, A. Kumar, and . Karandikar, Link scheduling in stdma wireless networks : A line graph approach, 14th National Conference on Communications (NCC), pp.108-111, 2008.

C. Laboratoire and I. Lyon, php/Main_Page. 100 [Oun08] A. Ouni. Capacity of wireless mesh networks : how to improve it ? [Pel87] D. Peleg. Distributed computing : a locality-sensitive approach, Society for Industrial and Applied Mathematics (SIAM), p.64, 0101.

T. L. Pham, I. Lavallee, M. Bui, S. H. Dopr90-]-m, G. Padberg et al., A distributed algorithm for the maximum flow problem An efficient algorithm for the minimum capacity cut problem, 4th International Symposium on Parallel and Distributed Computing (ISPDC) and I. Guerin-Lassous. Increasing fairness and efficiency using the madmac protocol in ad hoc networks. Ad-Hoc Networks Journal, pp.131-13819, 1990.

]. H. Riv03, ]. S. Rivanorl93, E. L. Ramanathan, M. Lloyd, A. J. Riis et al., Algorithmique et Télécommunications : Coloration et multiflot approchés et applications aux réseaux d'infrastructure Scheduling algorithms for multihop radio networks Deployment of mobile switching centers in a telecommunications network : a stochastic programming approach, IEEE/ACM Transactions on Networking Telecommunication Systems, vol.1, issue.261, pp.45166-17793, 0130.

F. [. Rivano, F. Theoleyre, and . Valois, Capacity evaluation framework and validation of self-organized routing schemes Wiley - Interscience series in discrete mathematics and optimization, IEEE International Workshop on Wireless Ad-hoc and Sensor Networks (IWWAN) Theory of Linear and Integer ProgrammingSny06] L. V. Snyder. Facility address under uncertainty : a review, pp.779-785, 1998.

M. Pearson-education, F. Stoer, and . Wagner, A simple min-cut algorithm 76 [TE92] L. Tassiulas and A. Ephremides. Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks Rc-mac : reduced collision mac for bandwidth optimization in wireless local area networks, Na¨?tNa¨?t-Abdesselam, and D. Simplot-Ryl ACS/IEEE International Conference on Computer Systems and Applications (AICCSA), pp.585-5911936, 1992.

]. P. Tsa97 and . Tsaparas, Stability in adversarial queueing theory, p.102, 1997.

Y. [. Tam and . Tseng, Joint Multi-Channel Link Layer and Multi-Path Routing Design for Wireless Mesh Networks, IEEE INFOCOM 2007, 26th IEEE International Conference on Computer Communications, pp.2081-2089, 1933.
DOI : 10.1109/INFCOM.2007.241

]. A. Vit95, . Viterbiwb07-]-p, S. Wang, . Bohacek, R. Wu et al., CDMA : Principles of Spread Spectrum Communication Approximation Algorithms for Facility address Problems (Lecture Notes) Technical Report 05950-OR, Research Institute for Discrete Mathematics Toward tractable computation of the capacity of multihop wireless networks Regulated maximal matching : A distributed scheduling algorithm for multi-hop wireless networks with nodeexclusive spectrum sharing, IEEE Conference on Computer Communications (Infocom) 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC), pp.35-2099, 0101.

Y. Xue, L. Dai, B. Chang, Y. Cui, H. K. Wu et al., Throughput optimization routing under uncertain demand for wireless mesh networks Maximum bandwidth routing in csma/ca-based wireless multi-hop wireless mesh networks Intelligent gateways placement for reduced data latency in wireless sensor networks, IEEE Internatonal Conference on Mobile Adhoc and Sensor Systems (MASS) IEEE International Conference on Communications (ICC), pp.1-11, 2006.

X. [. Zhou, R. Wang, and . Rao, Asymptotic Capacity of Infrastructure Wireless Mesh Networks, IEEE Transactions on Mobile Computing, vol.7, issue.8, pp.1011-1024, 2008.
DOI : 10.1109/TMC.2007.70778

J. Zhang, H. Wu, Q. Zhang, and B. Li, Joint routing and scheduling in multi-radio multi-channel multi-hop wireless networks, IEEE International Conference on Broadband Networks (BROADNETS), pp.678-687, 2005.