Minimum-cost multicast over coded packet networks

IEEE Transactions on Information Theory

Volumn 52, Issue 6, 2006, Pages 2608-2623

  Lun, Desmond S ^a   Ratnakar, Niranjan ^b   Médard, Muriel ^a   Koetter, Ralf ^b   Karger, David R ^c   Ho, Tracey ^d   Ahmed, Ebad ^a   Zhao, Fang ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d California Institute of Technology   (United States)

Author keywords

Ad hoc networks; Communication networks; Distributed algorithms; Dynamic multicast groups; Multicast; Network coding; Network optimization; Wireless networks

Indexed keywords

ALGORITHMS; COMPUTER NETWORKS; DYNAMIC PROGRAMMING; MULTICASTING; OPTIMIZATION; POLYNOMIALS; TELECOMMUNICATION NETWORKS; WIRELESS TELECOMMUNICATION SYSTEMS;

AD HOC NETWORKS; DISTRIBUTED ALGORITHMS; DYNAMIC MULTICAST GROUPS; NETWORK CODING; NETWORK OPTIMIZATION; WIRELESS NETWORKS;

PACKET NETWORKS;

EID: 33745149292     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.874523     Document Type: Article

References (59)

1. R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1204-1216, Jul. 2000.
2. S.-Y. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 371-381, Feb. 2003.
3. R. Koetter and M. Médard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol. 11, no. 5, pp. 782-795, Oct. 2003.
4. S. Jaggi, P. Sanders, P. A. Chou, M. Effros, S. Egner, K. Jain, and L. M. G. M. Tolhuizen, "Polynomial time algorithms for multicast network code construction," IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1973-1982, Jun. 2005.
5. T. Ho, M. Médard, R. Koetter, D. R. Karger, M. Effros, J. Shi, and B. Leong, "A random linear network coding approach to multicast," IEEE Trans. Inf. Theory. Available: [Online] at http://web.mit.edu/trace/www/itrandom-revision.pdf, submitted for publication.
6. D. S. Lun, M. Médard, R. Koetter, and M. Effros, "On coding for reliable communication over packet networks," IEEE Trans. Inf. Theory. Available: [Online] at http://arxiv.org/abs/cs.IT/0510070, submitted for publication.
7. K. Bharath-Kumar and J. M. Jaffe, "Routing to multiple destinations in computer networks," IEEE Trans. Commun., vol. COM-31, no. 3, pp. 343-351, Mar. 1983.
8. B. M. Waxman, "Routing of multicast connections," IEEE J. Select. Areas Commun., vol. 6, no. 9, pp. 1617-1622, Dec. 1988.
9. P. Winter, "Steiner problem in networks: A survey," Networks, vol. 17, pp. 129-167, 1987.
10. S. Ramanathan, "Multicast tree generation in networks with asymmetric links," IEEE/ACM Trans. Netw., vol. 4, no. 4, pp. 558-568, Aug. 1996.
11. M. Charikar, C. Chekuri, T.-y. Cheung, Z. Dai, A. Goel, S. Guha, and M. Li, "Approximation algorithms for directed Steiner problems," J. Algorithms, vol. 33, no. 1, pp. 73-91, Oct. 1999.
12. L. Zosin and S. Khuller, "On directed Steiner trees," in Proc. 13th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA 2002), San Francisco, CA, Jan. 2002, pp. 59-63.
13. J. E. Wieselthier, G. D. Nguyen, and A. Ephremides, "Energy-efficient broadcast and multicast trees in wireless networks," Mobile Netw. Applic., vol. 7, pp. 481-492, 2002.
14. M. Imase and B. M. Waxman, "Dynamic Steiner tree problem," SIAM J. Discr. Math., vol. 4, no. 3, pp. 369-384, Aug. 1991.
15. J. Westbrook and D. C. K. Yan, "Greedy algorithms for the on-line Steiner tree and generalized Steiner problems," in Proc. 3rd Workshop on Algorithms and Data Structures (WADS '93), Montreal, QC, Canada, Aug. 1993, pp. 622-633.
16. L. Song, R. W. Yeung, and N. Cai, "Zero-error network coding for acyclic networks," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3129-3139, Dec. 2003.
17. M. Médard, M. Effros, D. Karger, and T. Ho, "On coding for nonmulticast networks," in Proc. 41st Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Oct. 2003.
18. A. R. Lehman and E. Lehman, "Complexity classification of network information flow problems," in Proc. 41st Annu. Allerton Conf. Communication, Control, and Computing, Princeton, NJ, Oct. 2003.
19. S. Riis, "Linear versus nonlinear Boolean functions in network flow," in Proc. 2004 Conf. Information Sciences and Systems (CISS 2004), Princeton, NJ, Mar. 2004.
20. R. Dougherty, C. Freiling, and K. Zeger, "Insufficiency of linear coding in network information flow," IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2745-2759, Aug. 2005.
21. R.W. Yeung, "Multilevel diversity coding with distortion," IEEE Trans. Inf. Theory, vol. 41, no. 2, pp. 412-422, Mar. 1995.
22. Y. Cui, Y. Xue, and K. Nahrstedt, "Optimal distributed multicast routing using network coding: Theory and applications, SIGMETRICS Perform. Eval. Rev., vol. 32, no. 2, pp. 47-49, 2004.
23. D. S. Lun, M. Médard, T. Ho, and R. Koetter, "Network coding with a cost criterion," in Proc. 2004 Int. Symp. Information Theory and Its Applications (ISITA 2004), Parma, Italy, Oct. 2004, pp. 1232-1237.
24. Z. Li, B. Li, D. Jiang, and L. C. Lau, "On achieving optimal throughput with network coding," in Proc. IEEE INFOCOM 2005, vol. 3, Miami, FL, Mar. 2005, pp. 2184-2194.
25. Z. Li and B. Li, "Efficient and distributed computation of maximum multicast rates," in Proc. IEEE INFOCOM 2005, vol. 3, Miami, FL, Mar. 2005, pp. 1618-1628.
26. Y. Wu, P. A. Chou, and S.-Y. Kung, "Minimum-energy multicast in mobile ad hoc networks using network coding," IEEE Trans. Commun., vol. 53, no. 11, pp. 1906-1918, Nov. 2005.
27. P. A. Chou, Y. Wu, and K. Jain, "Practical network coding," in Proc. 41st Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Oct. 2003.
28. D. P. Bertsekas and R. Gallager, Data Networks, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1992.
29. D. P. Bertsekas, Network Optimization: Continuous and Discrete Models. Belmont, MA: Athena Scientific, 1998.
30. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications. Upper Saddle River, NJ: Prentice-Hall, 1993.
31. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods. Englewood Cliffs, NJ: Prentice-Hall, 1989.
32. D. P. Bertsekas, Nonlinear Programming. Belmont, MA: Athena Scientific, 1995.
33. G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization. New York: Wiley, 1999.
34. H. D. Sherali and G. Choi, "Recovery of primal solutions when using subgradient optimization methods to solve Lagrangian duals of linear programs," Oper. Res. Lett., vol. 19, pp. 105-113, 1996.
35. D. P. Bertsekas, L. C. Polymenakos, and P. Tseng, "An ε-relaxation method for separable convex cost network flow problems," SIAM J. Optimiz., vol. 7, no. 3, pp. 853-870, Aug. 1997.
36. R. de Leone, R. R. Meyer, and A. Zakarian, "A partitioned ε-relaxation algorithm for separable convex network flow problems," Computa. Optimiz, Applic., vol. 12, no. 1-3, pp. 107-126, Jan. 1999.
37. S. Deb and R. Srikant, "Congestion control for fair resource allocation in networks with multicast flows," IEEE/ACM Trans. Netw., vol. 12, no. 2, pp. 274-285, Apr. 2004.
38. A. Ouorou, P. Mahey, and J.-P. Vial, "A survey of algorithms for convex multicommodity flow problems," Manage. Sci., vol. 46, no. 1, pp. 126-147, Jan. 2000.
39. D. P. Bertsekas, "A class of optimal routing algorithms for communication networks," in Proc. 5th Int. Conf. Computer Communication (ICCC '80), Atlanta, GA, Oct. 1980, pp. 71-76.
40. D. P. Bertsekas, E. M. Gafni, and R. G. Gallager, "Second derivative algorithms for minimum delay distributed routing in networks," IEEE Trans. Commun., vol. COM-32, no. 8, pp. 911-919, Aug. 1984.
41. R. Srikant, The Mathematics of Internet Congestion Control. Boston, MA: Brikhäuser, 2004.
42. R. L. Cruz and A. V. Santhanam, "Optimal routing, link scheduling and power control in multi-hop wireless networks," in Proc. IEEE INFOCOM 2003, vol. 1, San Francisco, CA, Mar./Apr. 2003, pp. 702-711.
43. K. Jain, J. Padhye, V. N. Padmanabhan, and L. Qiu, "Impact of interference on multi-hop wireless network performance," in MobiCom '03: Proc. 9th Annu. Int. Conf. Mobile Computing and Networking, San Diego, CA, 2003, pp. 66-80.
44. M. Johansson, L. Xiao, and S. Boyd, "Simultaneous routing and power allocation in CDMA wireless data networks," in Proc. 2003 IEEE Int. Conf. Communications (ICC 2003), vol. 1, Anchorage, AK, May 2003, pp. 51-55.
45. L. Xiao, M. Johansson, and S. Boyd, "Simultaneous routing and resource allocation via dual decomposition," IEEE Trans. Commun., vol. 52, no. 7, pp. 1136-1144, Jul. 2004.
46. M. Kodialam and T. Nandagopal, "Characterizing achievable rates in multi-hop wireless mesh networks with orthogonal channels," IEEE/ACM Trans. Netw., vol. 13, no. 4, pp. 868-880, Aug. 2005.
47. 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," IEEE J. Select. Areas Commun., vol. 23, no. 1, pp. 136-150, Jan. 2005.
48. R. Mahajan, N. Spring, D. Wetherall, and T. Anderson, "Inferring link weights using end-to-end measurements," in Proc. 2nd ACM SIGCOMM Workshop on Internet Measurement, Marseille, France, Nov. 2002, pp. 231-236.
49. W. Liang, "Constructing minimum-energy broadcast trees in wireless ad hoc networks," in Proc. 3rd ACM Int. Symp. Mobile Ad Hoc Networking and Computing (MOBIHOC '02), Lausanne, Switzerland, Jun. 2002, pp. 112-122.
50. A. Ahluwalia, E. Modiano, and L. Shu, "On the complexity and distributed construction of energy-efficient broadcast trees in static ad hoc wireless networks," in Proc. 2002 Conf. Information Sciences and Systems (CISS 2002), Princeton, NJ, Mar. 2002.
51. M. Luby, "LT codes," in Proc. 43rd Annu. IEEE Symp. Foundations of Computer Science, Vancouver, BC, Canada, Nov. 2002, pp. 271-280.
52. A. Shokrollahi, "Raptor codes," IEEE Trans. Inf. Theory, vol. 52, no. 6, pp. 2551-2567, Jun 2006.
53. P. Pakzad, C. Fragouli, and A. Shokrollahi, "Coding schemes for line networks," in Proc. 2005 IEEE Int. Symp. Information Theory (ISIT 2005), Adelaide, Australia, Sep. 2005, pp. 1853-1857.
54. Y. Wu, P. A. Chou, and K. Jain, "A comparison of network coding and tree packing," in Proc. 2004 IEEE Int. Symp. Information Theory (ISIT 2004), Chicago, IL, Jun./Jul. 2004, p. 143.
55. D. P. Bertsekas, Dynamic Programming and Optimal Control, 2nd ed. Belmont, MA: Athena Scientific, 2001, vol. 2.
56. T. Ho and H. Viswanathan, "Dynamic algorithms for multicast with intra-session network coding," in Proc. 43rd Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sep. 2005.
57. Y. Xi and E. M. Yeh, "Distributed algorithms for minimum cost multicast with network coding," in Proc. 43rd Annu. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sep. 2005.
58. Y. Xi and E. M. Yeh, "Distributed algorithms for minimum cost multicast with network coding in wireless networks," in Proc. 4th Int. Symp. Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt '06), Boston, MA, Apr. 2006.
59. Y. Wu, M. Chiang, and S.-Y. Kung, "Distributed utility maximization for network coding based multicasting: A critical cut approach," Proc. 4th Int. Symp. Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt '06), Apr. 2006.