skip to main content
article

On the capacity of multiple unicast sessions in undirected graphs

Published:01 June 2006Publication History
Skip Abstract Section

Abstract

Li and Li conjectured that in an undirected network with multiple unicast sessions, network coding does not lead to any coding gain. Surprisingly enough, this conjecture could not so far be verified even for the simple network consisting of K 3, 2 with four source-sink pairs. Using entropy calculus, we provide the first verification of the Li-Li conjecture for this network. We extend our bound to the case of an arbitrary directed bipartite network.

References

  1. {1} M. Adler, N. J. A. Harvey, K. Jain, R. D. Kleinberg, and A. R. Lehman, "On the capacity of information networks, "in Proc. SODA 2006, 2006. Google ScholarGoogle Scholar
  2. {2} R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow, " IEEE Trans. Inf. Theory, vol. 46, pp. 1204-1216, 2000. Google ScholarGoogle Scholar
  3. {3} M. Charikar and A. Argawal, "On the advantage of network coding for improving network throughput, "in Proc. 2004 IEEE Inf. Theory Workshop , San Antonio, TX, 2004.Google ScholarGoogle Scholar
  4. {4} N. J. A. Harvey, R. D. Kleinberg, and A. R. Lehman, "On the capacity of information networks, " IEEE Trans. Inf. Theory, vol. 52, no. 6, pp. 2345-2364, Jun. 2006. Google ScholarGoogle Scholar
  5. {5} T. Ho, R. Koetter, M. Médard, M. Effros, J. Shi, and D. Karger, "A random linear network coding approach to multicast," IEEE Trans. Inf. Theory, 2005, submitted for publication. Google ScholarGoogle Scholar
  6. {6} K. Jain, "Security based on network topology against the wiretapping attack, " IEEE Magazine, Special Issue on Topics in Wireless Security, 2004. Google ScholarGoogle Scholar
  7. {7} R. Koetter and M. Medard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw.. Google ScholarGoogle Scholar
  8. {8} G. Kramer and S. A. Savari, "Progressive d -separating edge set bounds on network coding rates, "in Proc. IEEE Int. Symp. Information Theory, Adelaide, Australia, Sep. 2005, pp. 1588-1592.Google ScholarGoogle Scholar
  9. {9} Z. Li and B. Li, "Network coding in undirected networks, "in Proc. CISS, 2004.Google ScholarGoogle Scholar
  10. {10} F. T. Leighton and S. Rao, "An approximate max-flow min-cut theorem for uniform multicommodity flow problems with application to approximation algorithms, "in Proc. 29th Annu. IEEE Symp. Found. Comput. Sci., 1988, pp. 422-431.Google ScholarGoogle Scholar
  11. {11} D. Slepian and J. K. Wolf, "Noiseless coding of correlated information sources," IEEE Trans. Inf. Theory., vol. IT-19, pp. 471-480, Mar. 1973.Google ScholarGoogle Scholar
  12. {12} V. V. Vazirani, Approximation Algorithms. New york: Springer-Verlag, 2001. Google ScholarGoogle Scholar

Index Terms

  1. On the capacity of multiple unicast sessions in undirected graphs

                    Recommendations

                    Comments

                    Login options

                    Check if you have access through your login credentials or your institution to get full access on this article.

                    Sign in

                    Full Access

                    PDF Format

                    View or Download as a PDF file.

                    PDF

                    eReader

                    View online with eReader.

                    eReader