Local phy + global flow: A layering principle for wireless networks

A classical result in undirected wireline networks is the near 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. Wireless channels differ from wireline ones in two primary ways: the signal out of a transmitting node is broadcast and the signals at a receiving node superpose. In this paper we focus on “extending” the wireline result to the wireless context, by separately considering the broadcast and superposition constraints. 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 both Gaussian networks and packet erasure networks. The key technical contribution is an approximation of min cut in a bidirected graph with submodular constraints on the edge capacities by max flow.