Second-Order Methods for Distributed Approximate Single- and Multicommodity Flow

We study local-control algorithms for maximum flow and multicommodity flow problems in distributed networks. We propose a second-order method for accelerating the convergence of the “first-order” distributed algorithms recently proposed by Awerbuch and Leighton. Our experimental study shows that second-order methods are significantly faster than the first-order methods for approximate singleand multicommodity flow problems. Furthermore, our experimental study gives valuable insights into the diffusive processes that underly these local-control algorithms; this leads us to identify many open technical problems for theoretical study.