Computing a Tree Having a Small Vertex Cover

  • Takuro Fukunaga
  • Takanori Maehara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10043)


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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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.National Institute of InformaticsTokyoJapan
  2. 2.JST, ERATO, Kawarabayashi Large Graph ProjectTokyoJapan
  3. 3.Department of Mathematical and Systems EngineeringShizuoka UniversityShizuokaJapan

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