Faster approximate multicommodity flow using quadratically coupled flows

Jonathan A. Kelner, Gary L. Miller, Richard Peng
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1 − ǫ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate
more » ... specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with m edges and k commodities, we give algorithms that find 1 − ǫ approximate solutions to the maximum concurrent flow problem and the maximum weighted multicommodity flow problem in timeÕ(m 4/3 poly(k, ǫ −1 )) 1 .
doi:10.1145/2213977.2213979 dblp:conf/stoc/KelnerMP12 fatcat:h6y44r645bevjjm53mdbt2uyti