Improved approximation algorithm for MULTIWAY CUT

Gruia Calinescu, Howard Karloff, Yuval Rabani

Research output: Contribution to journalConference articlepeer-review

115 Scopus citations


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
Issue number3
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.


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