Multiple-unicast in fading wireless networks: A separation scheme is approximately optimal

A classical result in undirected wireline networks is the approximate optimality of routing (flow) for multiple-unicast: the min-cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we focus on extending this result to the wireless context. Our main result is the approximate optimality of a simple layering principle: local physical-layer schemes combined with global routing. We show this in the context of wireless networks, in which links are either absent or undergo i.i.d. fast fading. We also show an approximation result on the degrees-of-freedom, when the channels are fixed, but are chosen from a continuous ensemble. The key technical contribution is an approximation of min-cut in a bidirected graph with submodular constraints on the edge capacities by max flow.