Improved approximation algorithm for MULTIWAY CUT

Gruia Calinescu, Howard Karloff, Yuval Rabani

Research output: Contribution to journalConference articlepeer-review

115 Scopus citations

Abstract

Given an undirected graph with edge costs and a subset of k nodes called terminals, a multiway cut is a subset of edges whose removal disconnects each terminal from the rest. MULTIWAY CUT is the problem of finding a multiway cut of minimum cost. Previously, a very simple combinatorial algorithm due to Dahlhaus, Johnson, Papadimitriou, Seymour, and Yannakakis gave a performance guarantee of 2(1 - 1/k). In this paper, we present a new linear programming relaxation for MULTIWAY CUT and a new approximation algorithm based on it. The algorithm breaks the threshold of 2 for approximating MULTIWAY CUT, achieving a performance ratio of at most 1.5 - 1/k. This improves the previous result for every value of k. In particular, for k = 3 we get a ratio of 7/6 < 4/3.

Original languageAmerican English
Pages (from-to)564-574
Number of pages11
JournalJournal of Computer and System Sciences
Volume60
Issue number3
DOIs
StatePublished - Jun 2000
Externally publishedYes
EventThe 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA
Duration: 23 May 199826 May 1998

Bibliographical note

Funding Information:
1Research supported in part by NSF Grant CCR-9319106. 2 Work supported by BSF Grant 96-00402, and by grants from the S. and N. Grand Research Fund, from the Smoler Research Fund, and from the Fund for the Promotion of Research at the Technion.

Fingerprint

Dive into the research topics of 'Improved approximation algorithm for MULTIWAY CUT'. Together they form a unique fingerprint.

Cite this