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Computing a Tree Having a Small Vertex Cover

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Combinatorial Optimization and Applications (COCOA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10043))

Abstract

In this paper, we consider a new Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an \(O(\log n)\)-approximation algorithm in general graphs with n vertices. This approximation factor is tight because it is known to be NP-hard to achieve an \(o(\log n)\)-approximation for the problem with general graphs. In this paper, we present constant-factor approximation algorithms for the problem with unit disk graphs and with graphs excluding a fixed minor.

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Author information

Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Takuro Fukunaga

  2. JST, ERATO, Kawarabayashi Large Graph Project, Tokyo, Japan

    Takuro Fukunaga

  3. Department of Mathematical and Systems Engineering, Shizuoka University, Shizuoka, Japan

    Takanori Maehara

Authors
  1. Takuro Fukunaga
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  2. Takanori Maehara
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Corresponding author

Correspondence to Takuro Fukunaga .

Editor information

Editors and Affiliations

  1. University of Hong Kong, Hong Kong, China

    T-H. Hubert Chan

  2. City University of Hong Kong, Hong Kong, China

    Minming Li

  3. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

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Fukunaga, T., Maehara, T. (2016). Computing a Tree Having a Small Vertex Cover. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-48749-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48748-9

  • Online ISBN: 978-3-319-48749-6

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