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)


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.


Discrete Math Weighted Graph Chordal Graph Hardness Result Graph Class 
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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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