Abstract
Recent advances in network coding research dramatically changed the underlying structure of optimal multicast routing algorithms and made them efficiently computable. While most such algorithm design assumes a single file/layer being multicast, layered coding introduces new challenges into the paradigm due to its cumulative decoding nature. Layered coding is designed to handle heterogeneity in receiver capacities, and a node may decode layer k only if it successfully receives all layers in 1..k. We show that recently proposed optimization models for layered multicast do not correctly address this challenge. We argue that in order to achieve the absolute maximum throughput (or minimum cost), it is necessary to decouple the application-layer throughput from network-layer throughput. In particular, a node should be able to receive a nonconsecutive layer or a partial layer even if it cannot decode and utilize it (e.g., for playback in media streaming applications). The rationale is that nodes at critical network locations need to receive data just for helping other peers. We present a mathematical programming model that addresses these challenges and achieves absolute optimal performance. Simulation results show considerable throughput gain (cost reduction) compared with previous models, in a broad range of network scenarios. We then provide a formal proof that the layered multicast problem is NP-complete. We design a randomized rounding algorithm to approximate the optimal layered multicast, and show the efficacy of our technique using simulations. We then proceed to further generalize our model by studying the optimal progression of layer sizes. We show that such optimization is nonconvex, and apply a simulated annealing algorithm to solve it, with flexible trade-off between solution quality and running time. We verify the effectiveness of the new model and the simulated annealing algorithm through extensive simulations, and point out insights on the connection between optimal layer size progression and node capacity distribution.
- Ahlswede, R., Cai, N., Li, S. R., and Yeung, R. W. 2000. Network information flow. IEEE Trans. Inf. Theory 46, 4, 1204--1216. Google Scholar
Digital Library
- Banerjee, S., Bhattacharjee, B., and Kommareddy, C. 2002. Scalable application layer multicast. In Proceedings of the ACM SIGCOMM Data Communications Festival. Google Scholar
Digital Library
- BRITE. Boston university representative Internet topology generator. http://www.cs.bu.edu/brite/Google Scholar
- Chen, S., Günlük, O., and Yener, B. 2000. The multicast packing problem. IEEE/ACM Trans. Netw. 8, 3, 311--318. Google Scholar
Digital Library
- Dumitrescu, S., Shao, M., and Wu, X. 2009. Layered multicast with inter-layer network coding. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- Feigenbaum, J., Papadimitriou, C., and Shenker, S. 2001. Sharing the cost of multicast transmissions. J. Comput. Syst. Sci. 63, 21--41. Google Scholar
Digital Library
- Fletcher, R. and Leyffer, S. 1994. Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66, 327--349. Google Scholar
Digital Library
- Gamal, A. E. and Cover, T. M. 1982. Achievable rates for multiple descriptions. IEEE Trans. Inf. Theory 28, 851--857.Google Scholar
Digital Library
- Garey, M. and Johnson, D. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco, CA. Google Scholar
Digital Library
- Garg, N., Khandekar, R., Kunal, K., and Pandit, V. 2003. Bandwidth maximization in multicasting. In Proceedings of the 11th European Symposium on Algorithms (ESA).Google Scholar
- Geoffrion, A. M. 1972. Generalized benders decomposition. J. Optimiz. Theory Appl. 10, 237--260.Google Scholar
Cross Ref
- GLPK. GNU linear programming kit. http://www.gnu.org/software/glpk/Google Scholar
- Gupta, O. K. and Ravindran, A. 1985. Branch and bound experiments in convex nonlinear integer programming. Manag. Sci. 31, 1533--1546.Google Scholar
Digital Library
- Hajek, B. 1988. Cooling schedules for optimal annealing. Math. Oper. Res.13, 311--329. Google Scholar
Digital Library
- Ho, T., Medard, M., Koetter, R., Karger, D., Effros, M., Shi, J., and Leong, B. 2006. A random linear network coding approach to multicast. IEEE Trans. Inf. Theory 52, 10, 4413--4430. Google Scholar
Digital Library
- ISO/IEC. 1995. Generic coding of moving pictures and association audio information. ISO/IEC, 13818--2.Google Scholar
- ITU. 1998. Video coding for low bit rate communication. ITU-T recommendation H.263.Google Scholar
- Jain, K., Mahdian, M., and Salavatipour, M. R. 2003. Packing Steiner trees. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Google Scholar
Digital Library
- Kar, K., Sarkar, S., and Tassiulas, L. 2001. Optimization based rate control for multirate multicast sessions. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- Karp, R. 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations. E. Miller and J.W. Thatcher, New York.Google Scholar
- Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. 1983. Optimization by simulated annealing. Sci. 220, 4598, 671.Google Scholar
Cross Ref
- Koetter, R. and Médard, M. 2003. An algebraic approach to network coding. IEEE/ACM Trans. Netw. 11, 5, 782--795. Google Scholar
Digital Library
- Li, B. and Liu, J. 2003. Multirate video multicast over the Internet: An overview. IEEE Netw. 17, 1, 24--29. Google Scholar
Digital Library
- Li, X., Paul, S., Pancha, P., and Ammar, M. 1997. Layered video multicast with retransmission (LVMR): Evaluation of error recovery schemes. In Proceedings of the 6th International Workshop on Network and Operating System Support for Digital Audio and Video.Google Scholar
- Li, Z. 2007. Min-Cost multicast of selfish information flows. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
Digital Library
- Li, Z. and Li, B. 2005. Efficient and distributed computation of maximum multicast rates. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- Li, Z., Li, B., Jiang, D., and Lau, L. C. 2005. On achieving optimal throughput with network coding. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- Li, Z., Li, B., and Lau, L. C. 2006. On achieving optimal multicast throughput in undirected networks. IEEE Trans. Inf. Theory 52, 6, 2467--2485. Google Scholar
Digital Library
- Lun, D. S., Ratnakar, N., Koetter, R., Médard, M., Ahmed, E., and Lee, H. 2005. Achieving minimum-cost multicast: A decentralized approach based on network coding. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom).Google Scholar
- McCanne, S., Jacobson, V., and Vetterli, M. 1996. Receiver-Driven layered multicast. In Proceedings of the ACM SIGCOMM Data Communications Festival. Vol. 26. 117--130. Google Scholar
Digital Library
- Papadimitriou, C. and Steiglitz, K. 1998. Combinatorial Optimization: Algorithms and Complexity. Dover Publications.Google Scholar
Digital Library
- Quesada, I. and Grossmann, I. 1992. An lp/nlp based branch and bound algorithm for convex minlp optimization problems. Comput. Chem. Engin. 16, 937--947.Google Scholar
Cross Ref
- Sacham, N. 1992. Multipoint communication by hierarchically encoded data. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom). Google Scholar
Digital Library
- Sundaram, N., Ramanathan, P., and Banerjee, S. 2007. Multirate media stream using network coding. In Proceedings of 43rd Annual Allerton Conference on Communication, Control, and Computing.Google Scholar
- Thimm, M. 2001. On the approximability of the Steiner tree problem. In Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 2136. Springer, 678--689. Google Scholar
Digital Library
- Wang, W., Li, X.-Y., and Sun, Z. 2005. Sharing the multicast payment fairly. In Proceedings of the 11th International Computing and Combinatorics Conference (COCOON). Google Scholar
Digital Library
- Wu, Y., Chou, P. A., Zhang, Q., Jain, K., Zhu, W., and Kung, S. Y. 2005. Network planning in wireless ad hoc networks: A cross-layer approach. J. Select. Areas Comm. 23, 1, 136--150. Google Scholar
Digital Library
- Xi, C., Xu, Y., Zhan, C., Wu, R., and Wang, Q. 2007. On network coding based multirate video streaming in directed networks. In Proceedings of IEEE Professional Communication Conference.Google Scholar
- Yuan, J., Li, Z., Yu, W., and Li, B. 2006. A cross-layer optimization framework for multihop multicast in wireless mesh networks. J. Select. Areas Comm. 24, 11, 2092--2103. Google Scholar
Digital Library
- Zhao, J., Yang, F., Zhang, Q., Zhang, Z., and Zhang, F. 2006. Lion: Layered overlay multicast with network coding. IEEE Trans. Multimedia 8, 1021. Google Scholar
Digital Library
Index Terms
Optimal layered multicast
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