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)


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.


Span Tree Planar Graph Linear Time Tree Decomposition Chordal Graph 
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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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