On the solvability of single rate 2-pair networks — A cut-based characterization

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