Chapter

Parameterized and Exact Computation

Volume 7112 of the series Lecture Notes in Computer Science pp 1-12

On Multiway Cut Parameterized above Lower Bounds

  • Marek CyganAffiliated withInstitute of Informatics, University of Warsaw
  • , Marcin PilipczukAffiliated withInstitute of Informatics, University of Warsaw
  • , Michał PilipczukAffiliated withInstitute of Informatics, University of Warsaw
  • , Jakub Onufry WojtaszczykAffiliated withGoogle Inc.

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Abstract

In this paper we consider two above lower bound parameterizations of the Node Multiway Cut problem — above the maximum separating cut and above a natural LP-relaxation — and prove them to be fixed-parameter tractable. Our results imply O *(4 k ) algorithms for Vertex Cover above Maximum Matching and Almost 2-SAT as well as an O *(2 k ) algorithm for Node Multiway Cut with a standard parameterization by the solution size, improving previous bounds for these problems.