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Complexity Results for the Spanning Tree Congestion Problem

  • Yota Otachi
  • Hans L. Bodlaender
  • Erik Jan van Leeuwen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

We study the problem of determining the spanning tree congestion of a graph. We present some sharp contrasts in the complexity of this problem. First, we show that for every fixed k and d the problem to determine whether a given graph has spanning tree congestion at most k can be solved in linear time for graphs of degree at most d. In contrast, if we allow only one vertex of unbounded degree, the problem immediately becomes NP-complete for any fixed k ≥ 10. For very small values of k however, the problem becomes polynomially solvable. We also show that it is NP-hard to approximate the spanning tree congestion within a factor better than 11/10. On planar graphs, we prove the problem is NP-hard in general, but solvable in linear time for fixed k.

Keywords

Span Tree Planar Graph Linear Time Tree Decomposition Chordal Graph 
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 2010

Authors and Affiliations

  • Yota Otachi
    • 1
  • Hans L. Bodlaender
    • 2
  • Erik Jan van Leeuwen
    • 3
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Institute of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  3. 3.Department of InformaticsUniversity of BergenBergenNorway

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