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Algorithmica

, Volume 55, Issue 1, pp 1–13 | Cite as

An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem

  • Jianer Chen
  • Yang Liu
  • Songjian Lu
Article

Abstract

The parameterized node multiway cut problem is for a given graph to find a separator of size bounded by k whose removal separates a collection of terminal sets in the graph. In this paper, we develop an O(k4 k n 3) time algorithm for this problem, significantly improving the previous algorithm of time \(O(4^{k^{3}}n^{5})\) for the problem. Our result gives the first polynomial time algorithm for the minimum node multiway cut problem when the separator size is bounded by O(log n).

Keywords

Multiway cut problem Parameterized algorithm Fixed-parameter tractability Minimum cut Network flow 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceTexas A&M UniversityCollege StationUSA

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