On a bidirected relaxation for the Multiway Cut problem

In the MULTIWAY CUT problem, we are given an undirected edge- weighted graph G = (V,E) with "C sub e" denoting the cost (weight) of edge e. We are also given a subset S of V, of size k, called the terminals. The objective is to find a minimum cost set of edges whose removal ensures that the terminals are disconnected. In this paper, we study a bidirected linear programming relaxation of MULTIWAY CUT. We resolve an open problem posed by Vazirani [10], and show that the integrality gap of this relaxation is no better than that for a geometric linear programming relaxation given by Calinescu et al [2], and may be strictly worse on some instances.