On the multiple unicast network coding, conjecture

In this paper, we study the multiple unicast network communication problem on undirected graphs. It has been conjectured by Li and Li [CISS 2004] that, for the problem at hand, the use of network coding does not allow any advantage over standard routing. Loosely speaking, we show that under certain (strong) connectivity requirements the advantage of network coding is indeed bounded by 3.

[1]  Baochun Li,et al.  Network Coding : The Case of Multiple Unicast Sessions , 2004 .

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[4]  Shuo-Yen Robert Li,et al.  Linear network coding , 2003, IEEE Trans. Inf. Theory.

[5]  Peter Sanders,et al.  Polynomial time algorithms for multicast network code construction , 2005, IEEE Transactions on Information Theory.

[6]  Zongpeng Li,et al.  Network Coding in Undirected Networks , 2004 .

[7]  R. Koetter,et al.  An algebraic approach to network coding , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[8]  Tracey Ho,et al.  A Random Linear Network Coding Approach to Multicast , 2006, IEEE Transactions on Information Theory.

[9]  Thomas M. Cover,et al.  Elements of Information Theory: Cover/Elements of Information Theory, Second Edition , 2005 .

[10]  Randall Dougherty,et al.  Nonreversibility and Equivalent Constructions of Multiple-Unicast Networks , 2006, IEEE Transactions on Information Theory.

[11]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[12]  Robert D. Kleinberg,et al.  On the capacity of information networks , 2006, IEEE Transactions on Information Theory.

[13]  Vijay V. Vazirani,et al.  On the capacity of multiple unicast sessions in undirected graphs , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[14]  R. Yeung,et al.  Network coding theory , 2006 .

[15]  Amit Agarwal,et al.  On the advantage of network coding for improving network throughput , 2004, ITW.

[16]  Sae-Young Chung,et al.  Network coding , 2008, Journal of Communications and Networks.