A Reduction Approach to the Multiple-Unicast Conjecture in Network Coding

Abstract

The multiple-unicast conjecture in network coding states that for multiple unicast sessions in an undirected network, network coding has no advantage over routing in improving the throughput or saving bandwidth. In this paper, we propose a reduction method to study the multiple-unicast conjecture, and prove the conjecture for a new class of networks that are characterized by relations between cut-sets and source-receiver paths. This class subsumes all the known types of networks with non-zero max-flow min-cut gaps but zero coding advantage. Combining this result with a computer-aided search, we derive as a corollary that network coding is unnecessary in networks with up to six coding nodes. We also prove the multiple-unicast conjecture for almost all unit-link-length networks with up to three sessions and seven nodes.