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Hardness Results and an Exact Exponential Algorithm for the Spanning Tree Congestion Problem

  • Yoshio Okamoto
  • Yota Otachi
  • Ryuhei Uehara
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6648)

Abstract

Spanning tree congestion is a relatively new graph parameter, which has been studied intensively. This paper studies the complexity of the problem to determine the spanning tree congestion for non-sparse graph classes, while it was investigated for some sparse graph classes before. We prove that the problem is NP-hard even for chain graphs and split graphs. To cope with the hardness of the problem, we present a fast (exponential-time) exact algorithm that runs in O  ∗ (2 n ) time, where n denotes the number of vertices. Additionally, we provide a constant-factor approximation algorithm for cographs, and a linear-time algorithm for chordal cographs.

Keywords

Discrete Math Weighted Graph Chordal Graph Hardness Result Graph Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yoshio Okamoto
    • 1
  • Yota Otachi
    • 2
  • Ryuhei Uehara
    • 3
  • Takeaki Uno
    • 4
  1. 1.Center for Graduate Education InitiativeJAISTIshikawaJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  3. 3.School of Information ScienceJAISTIshikawaJapan
  4. 4.National Institute of InformaticsChiyoda-kuJapan

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