Two-Commodity Flow

Abstract

An algorithm is given to fmd maxtmum two-commodity flow m an undirected graph The algorithm is an improvement on Hu's two-commodity flow algorithm using the methods of Dmlc's single-commodity flow algorithm Karzanov's Improvement of Dmlc's algorithm can be applied to yield an O(IV)3 algorithm. It is shown that finding maximum two-commodity flow m a dwected graph is much more dffficuh, in fact it Is as difficult as hnear programming FmaUy, the problem of finding feasible flow m an undirected graph with lower and upper bounds on the edges is shown to be NP-complete even for a single commodity. © 1978, ACM. All rights reserved.