Improved approximation algorithm for MULTIWAY CUT

Gruia Calinescu; Howard Karloff; Yuval Rabani

doi:10.1006/jcss.1999.1687

Improved approximation algorithm for MULTIWAY CUT

Gruia Calinescu
, Howard Karloff
, Yuval Rabani

Research output: Contribution to journal › Conference article › peer-review

123 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 language	English
Pages (from-to)	564-574
Number of pages	11
Journal	Journal of Computer and System Sciences
Volume	60
Issue number	3
DOIs	https://doi.org/10.1006/jcss.1999.1687
State	Published - Jun 2000
Externally published	Yes
Event	The 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA Duration: 23 May 1998 → 26 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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10.1006/jcss.1999.1687

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title = "Improved approximation algorithm for MULTIWAY CUT",

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.",

author = "Gruia Calinescu and Howard Karloff and Yuval Rabani",

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.; The 30th Annual ACM Symposium on Theory of Computing ; Conference date: 23-05-1998 Through 26-05-1998",

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AU - Karloff, Howard

AU - Rabani, Yuval

N1 - 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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N2 - 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.

AB - 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.

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Y2 - 23 May 1998 through 26 May 1998

ER -

Improved approximation algorithm for MULTIWAY CUT

Abstract

Bibliographical note

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