On the Solvability of 2-pair Unicast Networks --- A Cut-based Characterization

In this paper, we propose a subnetwork decomposition/combination approach to investigate the single rate 2-pair unicast problem. It is shown that the solvability of a 2-pair unicast problem is completely determined by four specific link subsets, namely, A1,1, A2,2, A1,2 and A2,1 of its underlying network. As a result, an efficient cut-based algorithm to determine the solvability of a 2-pair unicast problem is presented. Index Terms Network coding, Capacity, 2-pair unicast problem, A-set.