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On the Maximum Weight Minimal Separator

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Theory and Applications of Models of Computation (TAMC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

This study is partially supported by NWO Gravity grant “Networks” (024.002.003), JSPS KAKENHI Grant Numbers JP26540005, 26241031, and Asahi Glass Foundation.

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Acknowledgments

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

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Authors and Affiliations

  1. Department of Economic Engineering, Kyushu University, 6-19-1, Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

    Tesshu Hanaka & Hirotaka Ono

  2. Department of Computer Science, Utrecht University, PO Box 80.089, 3508 TB, Utrecht, The Netherlands

    Hans L. Bodlaender & Tom C. van der Zanden

  3. Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands

    Hans L. Bodlaender

Authors
  1. Tesshu Hanaka
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  2. Hans L. Bodlaender
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  3. Tom C. van der Zanden
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  4. Hirotaka Ono
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Corresponding author

Correspondence to Tesshu Hanaka .

Editor information

Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

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Hanaka, T., Bodlaender, H.L., van der Zanden, T.C., Ono, H. (2017). On the Maximum Weight Minimal Separator. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_22

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  • DOI: https://doi.org/10.1007/978-3-319-55911-7_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55910-0

  • Online ISBN: 978-3-319-55911-7

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