Network capacity under traffic symmetry: Wireline and wireless networks

The problem of designing near optimal strategies for multiple unicast traffic in wireline networks is wide open; however, channel symmetry or traffic symmetry can be leveraged to show that routing can achieve with a polylogarithmic approximation factor of the edge-cut bound. For the same problem, the edge-cut bound is known to only upper bound rates of routing flows and unlike the information theoretic cut-set bound, it does not upper bound (capacity-achieving) information rates with general strategies. In this paper, we demonstrate that under channel or traffic symmetry, the edge-cut bound upper-bounds general information rates, thus providing a capacity approximation result. The key technique is a combinatorial result relating edge-cut bounds to generalized network sharing bounds. Finally, we generalize the results to wireless networks via an intermediary class of combinatorial graphs known as polymatroidal networks - our main result is that a natural architecture separating the physical and networking layers is near optimal when the traffic is symmetric among source-destination pairs, even when the channel is asymmetric (due to asymmetric power constraints, or prior frequency allocation like frequency division duplexing). This result is complementary to an earlier work of two of the authors proving a similar result under channel symmetry.