An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem

  • Authors:
  • Jianer Chen;Yang Liu;Songjian Lu

  • Affiliations:
  • Texas A&M University, Department of Computer Science, 77843, College Station, TX, USA;Texas A&M University, Department of Computer Science, 77843, College Station, TX, USA;Texas A&M University, Department of Computer Science, 77843, College Station, TX, USA

  • Venue:
  • Algorithmica
  • Year:
  • 2009

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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(k4k 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).