Approximate max-integral-flow/min-multicut theorems

We establish several approximate max-integral-flow / minmulticut theorems. While in general this ratio can be very large, we prove strong approximation ratios in the case where the min-multicut is a constant fraction of the total capacity of the graph. This setting is motivated by several combinatorial and algorithmic applications. Prior to this work, a general max-integral-flow / min-multicut bound was known only for the special case where the graph is a tree. We prove that, for arbitrary graphs, the max-integral-flow / min-multicut ratio is O( -1 log k), where k is the number of commodites; for graphs excluding a fixed subgraph as a minor (for instance, planar graphs), O(1/ ); and, for dense graphs, O(1/ ). Our proofs are constructive in the sense that we give efficient algorithms which compute either an integral flow achieving the claimed approximation ratios, or a witness that the precondition is violated. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Probl...

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Kenji Obata
• Keywords: Algorithms, Approximation Ratios, O( -1 Log, STOC 2004, Strong Approximation Ratios