Simplex transformations and the multiway cut problem

Niv Buchbinder, Roy Schwartz, Baruch Weizman

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)757-771
Number of pages15
JournalMathematics of Operations Research
Volume46
Issue number2
DOIs
StatePublished - May 2021

Keywords

  • Approximation algorithms
  • Multiway cut
  • Randomized rounding

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