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On the Maximum Weight Minimal Separator

  • Tesshu Hanaka
  • Hans L. Bodlaender
  • Tom C. van der Zanden
  • Hirotaka Ono
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)

Abstract

Given an undirected and connected graph \(G=(V, E)\) and two vertices \(s, t\in V\), a vertex subset S that separates s and t is called an s-t separator, and an s-t separator is called minimal if no proper subset of S separates s and t. In this paper, we consider finding a minimal s-t separator with maximum weight on a vertex-weighted graph. We first prove that this problem is NP-hard. Then, we propose an \(\mathbf{tw}^{O(\mathbf{tw})}n\)-time deterministic algorithm based on tree decompositions. Moreover, we also propose an \(O^*(9^\mathbf{tw}\cdot W^2)\)-time randomized algorithm to determine whether there exists a minimal s-t separator where W is its weight and \(\mathbf{tw}\) is the treewidth of G.

Keywords

Parameterized algorithm Minimal separator Treewidth 

Notes

Acknowledgments

We are grateful to Dr. Jesper Nederlof for helpful discussions.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tesshu Hanaka
    • 1
  • Hans L. Bodlaender
    • 2
    • 3
  • Tom C. van der Zanden
    • 2
  • Hirotaka Ono
    • 1
  1. 1.Department of Economic EngineeringKyushu UniversityFukuokaJapan
  2. 2.Department of Computer ScienceUtrecht UniversityUtrechtThe Netherlands
  3. 3.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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