Computing a Tree Having a Small Vertex Cover

Conference paper

DOI: 10.1007/978-3-319-48749-6_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10043)
Cite this paper as:
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

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.

Copyright information

© 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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