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The capacitated max k-cut problem

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An Erratum to this article was published on 18 September 2010

Abstract

We consider a capacitated max k-cut problem in which a set of vertices is partitioned into k subsets. Each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that maximizes the sum of edge weights across all pairs of vertices that lie in different subsets. We describe a local-search algorithm that obtains a solution with value no smaller than 1 − 1/k of the optimal solution value. This improves a previous bound of 1/2 for the max k-cut problem with fixed, though possibly different, sizes of subsets.

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Authors and Affiliations

  1. University of Lethbridge, Lethbridge, Canada

    Daya Ram Gaur

  2. Simon Fraser University, Burnaby, Canada

    Ramesh Krishnamurti

  3. Columbia University, Uris Hall, 3022 Broadway, New York, NY, 10027, USA

    Rajeev Kohli

Authors
  1. Daya Ram Gaur
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  2. Ramesh Krishnamurti
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  3. Rajeev Kohli
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Corresponding author

Correspondence to Rajeev Kohli.

Additional information

We thank an anonymous referee for extensive and constructive comments. The first and second authors are grateful for the support provided by the Natural Sciences and Engineering Research Council of Canada.

An erratum to this article is available at http://dx.doi.org/10.1007/s10107-010-0404-4.

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Gaur, D.R., Krishnamurti, R. & Kohli, R. The capacitated max k-cut problem. Math. Program. 115, 65–72 (2008). https://doi.org/10.1007/s10107-007-0139-z

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