The Community for Technology Leaders
RSS Icon
Issue No.09 - September (2009 vol.20)
pp: 1299-1308
Zongpeng Li , University of Calgary, Calgary
Carey Williamson , University of Calgary, Calgary
We study multicast in a noncooperative environment where information flows selfishly route themselves through the cheapest paths available. The main challenge is to enforce such selfish multicast flows to stabilize at a socially optimal operating point incurring minimum total edge cost, through appropriate cost allocation and other economic measures, with replicable and encodable properties of information flows considered. We show that known cost allocation schemes are not sufficient. We provide a shadow-price-based cost allocation for networks without capacity limits and show that it enforces minimum-cost multicast. This improves previous result where a 2-approximate multicast flow is enforced. For capacitated networks, computing cost allocation by ignoring edge capacities will not yield correct results. We show that an edge tax scheme can be combined with a cost allocation to strictly enforce optimal multicast flows in this more realistic case. If taxes are not desirable, they can be returned to flows while maintaining weak enforcement of the optimal flow. We relate the taxes to VCG payment schemes and discuss an efficient primal-dual algorithm that simultaneously computes the taxes, the cost allocation, and the optimal multicast flow, with potential of fully distributed implementations.
Communication/networking, multicast, graph algorithms.
Zongpeng Li, Carey Williamson, "Enforcing Minimum-Cost Multicast Routing against Selfish Information Flows", IEEE Transactions on Parallel & Distributed Systems, vol.20, no. 9, pp. 1299-1308, September 2009, doi:10.1109/TPDS.2008.229
[1] R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993.
[2] D.P. Bertsekas, Network Optimization: Continuous and Discrete Models. Athena Scientific, 1998.
[3] R. Ahlswede, N. Cai, S.R. Li, and R.W. Yeung, “Network Information Flow,” IEEE Trans. Information Theory, vol. 46, no. 4, pp. 1204-1216, July 2000.
[4] R. Koetter and M. Médard, “An Algebraic Approach to Network Coding,” IEEE/ACM Trans. Networking, vol. 11, no. 5, pp. 782-795, Oct. 2003.
[5] K. Jain, M. Mahdian, and M.R. Salavatipour, “Packing Steiner Trees,” Proc. 10th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA), 2003.
[6] Z. Li, B. Li, and L.C. Lau, “On Achieving Optimal Multicast Throughput in Undirected Networks,” IEEE Trans. Information Theory, vol. 52, no. 6, pp. 2467-2485, June 2006.
[7] D.S. Lun, N. Ratnakar, R. Koetter, M. Médard, E. Ahmed, and H. Lee, “Achieving Minimum-Cost Multicast: a Decentralized Approach Based on Network Coding,” Proc. IEEE INFOCOM, 2005.
[8] Z. Li and B. Li, “Efficient and Distributed Computation of Maximum Multicast Rates,” Proc. IEEE INFOCOM, 2005.
[9] E. Koutsoupias and C. Papadimitriou, “Worst-Case Equilibria,” Lecture Notes in Computer Science, vol. 1563, pp. 404-413, 1999.
[10] T. Roughgarden and E. Tardos, “How Bad is Selfish Routing?” J. ACM, vol. 49, no. 2, pp. 236-259, 2002.
[11] H. Yang and H. Huang, “The Multi-Class, Multi-Criteria Traffic Network Equilibrium and Systems Optimum Problem,” Transportation Research, Part B, vol. 38, no. 1, pp. 1-15, Jan. 2004.
[12] L. Fleischer, K. Jain, and M. Mahdian, “Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games,” Proc. 45th IEEE Symp. Foundations of Computer Science (FOCS), 2004.
[13] G. Karakostas and S.G. Kolliopoulos, “Edge Pricing of Multicommodity Networks for Heterogeneous Selfish Users,” Proc. 45th IEEE Symp. Foundations of Computer Science (FOCS), 2004.
[14] J. Feigenbaum, C. Papadimitriou, and S. Shenker, “Sharing the Cost of Multicast Transmissions,” J. Computer and System Sciences, vol. 63, pp. 21-41, 2001.
[15] S. Bhadra, S. Shakkottai, and P. Gupta, “Min-Cost Selfish Multicast with Network Coding,” IEEE Trans. Information Theory, vol. 52, no. 11, pp. 5077-5087, Nov. 2006.
[16] L.S. Shapley, “A Value for $n$ -Person Games,” Contributions to the Theory of Games. Princeton Univ. Press, pp. 31-40, 1953.
[17] W. Wang, X. Li, and Y. Wang, “Truthful Multicast in Selfish Wireless Networks,” Proc. ACM MobiCom, 2004.
[18] Z. Li, B. Li, D. Jiang, and L.C. Lau, “On Achieving Optimal Throughput with Network Coding,” Proc. IEEE INFOCOM, 2005.
[19] Y. Wu, P.A. Chou, Q. Zhang, K. Jain, W. Zhu, and S.Y. Kung, “Network Planning in Wireless Ad Hoc Networks: A Cross-Layer Approach,” J. Selected Areas in Comm., vol. 23, no. 1, pp. 136-150, Jan. 2005.
[20] J. Yuan, Z. Li, W. Yu, and B. Li, “A Cross-Layer Optimization Framework for Multihop Multicast in Wireless Mesh Networks,” J. Selected Areas in Comm., special issue on multi-hop wireless mesh networks, 2006.
[21] H.W. Kuhn and A.W. Tucker, “Nonlinear Programming,” Proc. Second Berkeley Symp. Math. Statistics and Probability, 1951.
[22] W. Wang, X.-Y. Li, Y. Wang, and Z. Sun, “Designing Multicast Protocols for Non-Cooperative Networks,” IEEE J. Selected Areas in Comm., vol. 26, no. 7, pp. 1238-1249, Sept. 2008.
[23] K. Jain and V.V. Vazirani, “Applications of Approximation Algorithms to Cooperative Games,” Proc. 33rd ACM Symp. Theory of Computing (STOC), 2001.
[24] N. Immorlica, D. Karger, E. Nikolova, and R. Sami, “First-Price Path Auctions,” Proc. Sixth ACM Conf. Electronic Commerce (EC), 2005.
[25] Z. Li, “Cross-Monotonic Multicast,” Proc. IEEE INFOCOM, 2008.
[26] S. Jaggi, P. Sanders, P.A. Chou, M. Effros, S. Egner, K. Jain, and L. Tolhuizen, “Polynomial Time Algorithms for Multicast Network Code Construction,” IEEE Trans. Information Theory, vol. 51, no. 6, pp. 1973-1982, June 2005.
[27] G. Dantzig, Linear Programming and Extensions. Princeton Univ. Press, 1998.
[28] M.J. Osborne and A. Rubinstein, A Course in Game Theory. MITPress, 1994.
[29] E. Anshelevich, A. Dasgupta, J. Kleinberg, E. Tardos, T. Wexler, and T. Roughgarden, “The Price of Stability for Network Design with Fair Cost Allocation,” Proc. 45th IEEE Symp. Foundations of Computer Science (FOCS), 2004.
[30] C. Papadimitriou, “Algorithms, Games, and the Internet,” Proc. 33rd ACM Symp. the Theory of Computing (STOC), 2001.
[31] E. Altman and L. Wynter, “Euilibrium, Games, and Pricing in Transportation and Telecommunication Networks,” Networks and Spatial Economics, vol. 4, no. 1, pp. 7-21, Mar. 2004.
[32] H.D. Sherali and G. Choi, “Recovery of Primal Solutions When Using Subgradient Optimization Methods to Solve Lagrangian Duals of Linear Programs,” Operations Research Letters, vol. 19, 1996.
19 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool