A 2-Approximation Algorithm for the Directed Multiway Cut Problem

Abstract

A directed multiway cut separates a set of terminals T={s1, . . . , sk} in a directed capacitated graph G=(V,E). Finding a minimum directed multiway cut is an NP-hard problem. We give a polynomial-time algorithm that achieves an approximation factor of 2 for this problem. This improves the result of Garg, Vazirani, and Yannakakis [Proceedings of the 21st International Colloquium on Automata, Languages, and Programming, Jerusalem, Israel, 1994, pp. 487--498], who gave an algorithm that achieves an approximation factor of 2 log k. Our approximation algorithm uses a novel technique for relaxing a multiway flow function in order to find a directed multiway cut. It also implies that the integrality gap of the linear program for the directed multiway cut problem is at most 2.