@MISC{To_onreducing, author = {Ratio To}, title = {On reducing the cut ratio to the multicut problem}, year = {} }

Share

OpenURL

Abstract

We compare two multicommodity flow problems, the maximum sum of flow, and the maximum concurrent flow. We show that, for a given graph and a given set of k commodities with specified demands, if the minimum capacity of a multicut is approximated by the maximum sum of flow within a factor of ff, for any subset of commodities, then the minimum cut ratio is approximated by the maximum concurrent flow within a factor of O(ff ln k). 1 Introduction Throughout this note, we are given an undirected graph G = (V; E) where each edge e is assigned a nonnegative real number c(e), called capacity of e . A flow from a vertex s called source to a vertex t called sink is a function ff from the set of paths P(s; t) from s to t into the set of nonnegative real numbers. The value of the flow ff is P P2P(s;t) ff(P ). In a multicommodity flow problem, we are given a set Q of k commodities. A commodity i is specified by a pair of source and sink (s i ; t i ). A flow in this case is a function ff that as...