On a bidirected relaxation for the MULTIWAY CUT problem

Authors:
Chandra Chekuri;Anupam Gupta;Amit Kumar
Affiliations:
Lucent Bell Labs, 600 Mountain Avenue, Murray Hill, NJ 07974, USA;Department of Computer Science, Carnegie Mellon University;Department of Computer Science, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

In the MULTIWAY CUT problem, we are given an undirected edge-weighted graph G=(V,E) with c"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 [Approximation Algorithms, first ed., Springer, Berlin, Heidelberg, 2001], and show that the integrality gap of this relaxation is not better than that for a geometric linear programming relaxation given by Ca@?linescu et al. [J. Comput. System Sci. 60(3) (2000) 564-574], and may be strictly worse on some instances.