Simplex partitioning via exponential clocks and the multiway-cut problem

Niv Buchbinder, Joseph Naor, Roy Schwartz

Research output: Contribution to journalArticlepeer-review

Abstract

The Multiway-Cut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called terminals. This problem is NP-hard and there is a well-known geometric relaxation in which the graph is embedded into a high dimensional simplex. Rounding a solution to the geometric relaxation is equivalent to partitioning the simplex. We present a novel simplex partitioning algorithm which is based on two ingredients: competing exponential clocks and distortion. Unlike previous methods, it utilizes cuts that are not parallel to the faces of the simplex. Applying this partitioning algorithm to the multiway cut problem, we obtain a simple (4/3)-approximation algorithm, thus, improving upon the current best-known result. This bound is further pushed to obtain an approximation factor of 1.32388. It is known that under the assumption of the unique games conjecture, the best possible approximation for the Multiway-Cut problem can be attained via the geometric relaxation.

Original languageEnglish
Pages (from-to)1463-1482
Number of pages20
JournalSIAM Journal on Computing
Volume47
Issue number4
DOIs
StatePublished - 2018

Keywords

  • Approximation algorithms
  • Cut
  • Multiway
  • Randomized
  • Simplex

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