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Complexity Results for the Spanning Tree Congestion Problem

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Graph Theoretic Concepts in Computer Science (WG 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6410))

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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.

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Author information

Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Yota Otachi

  2. Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Hans L. Bodlaender

  3. Department of Informatics, University of Bergen, P.O. Box 7803, 5020, Bergen, Norway

    Erik Jan van Leeuwen

Authors
  1. Yota Otachi
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  2. Hans L. Bodlaender
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  3. Erik Jan van Leeuwen
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimioupolis, GR-15784, Athens, Greece

    Dimitrios M. Thilikos

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Otachi, Y., Bodlaender, H.L., van Leeuwen, E.J. (2010). Complexity Results for the Spanning Tree Congestion Problem. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-16926-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16925-0

  • Online ISBN: 978-3-642-16926-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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