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Simplex Transformations and the Multiway Cut Problem

Author

Listed:
  • Niv Buchbinder

    (Statistics and Operations Research Department, Tel Aviv University, Tel Aviv 6997801, Israel)

  • Roy Schwartz

    (Computer Science Department, Technion, Haifa 3200003, Israel)

  • Baruch Weizman

    (The Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 6997801, Israel)

Abstract

We consider multiway cut, a basic graph partitioning problem in which the goal is to find the minimum weight collection of edges disconnecting a given set of special vertices called terminals. Multiway cut admits a well-known simplex embedding relaxation, where rounding this embedding is equivalent to partitioning the simplex. Current best-known solutions to the problem are comprised of a mix of several different ingredients, resulting in intricate algorithms. Moreover, the best of these algorithms is too complex to fully analyze analytically, and a computer was partly used in verifying its approximation factor. We propose a new approach to simplex partitioning and the multiway cut problem based on general transformations of the simplex that allow dependencies between the different variables. Our approach admits much simpler algorithms and, in addition, yields an approximation guarantee for the multiway cut problem that (roughly) matches the current best computer-verified approximation factor.

Suggested Citation

  • Niv Buchbinder & Roy Schwartz & Baruch Weizman, 2021. "Simplex Transformations and the Multiway Cut Problem," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 757-771, May.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:2:p:757-771
    DOI: 10.1287/moor.2020.1073
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    References listed on IDEAS

    as
    1. David R. Karger & Philip Klein & Cliff Stein & Mikkel Thorup & Neal E. Young, 2004. "Rounding Algorithms for a Geometric Embedding of Minimum Multiway Cut," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 436-461, August.
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