Technical Report CS0103

Title: Two Commodity Flow
Authors: Alon Itai
Abstract: An algorithm is given to find maximum two commodity flow in an undirected graph. The algorithm is an improvement of T.C. Hu's two commodity flow algorithm using the methods of Dinic's single commodjty flow algorithm. Karzanov's improvement of Dinic's algorithm can be applied to yield an O(|v|^3) algorithm. It is shown that finding maximum two commodity flow in a directed graph is much mere difficult and in fact is as hard as linear programming. Finally, the problem of finding feasible flow in an undirected graph with lower and upper bounds on the edges is shown to be NP-complete for a single commodity.
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