Capacity of Multiple Unicast in Wireless Networks: A Polymatroidal Approach
A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper, the authors "Extend" the wireline result to the wireless context. Their main result is the approximate optimality of a simple layering principle: local physical-layer schemes combined with global routing. They use the reciprocity of the wireless channel critically in this result. They formal result is in the context of channel models for which "Good" local schemes, that achieve the cut-set bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks).