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

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Theory and Applications of Models of Computation (TAMC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,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  ∗ (2n) 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.

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Author information

Authors and Affiliations

  1. Center for Graduate Education Initiative, JAIST, Asahidai 1-1, Nomi, Ishikawa, 923-1292, Japan

    Yoshio Okamoto

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

    Yota Otachi

  3. School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa, 923-1292, Japan

    Ryuhei Uehara

  4. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Takeaki Uno

Authors
  1. Yoshio Okamoto
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  2. Yota Otachi
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  3. Ryuhei Uehara
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  4. Takeaki Uno
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Miami, 1365 Memorial Drive, 33146, Coral Gables, FL, USA

    Mitsunori Ogihara

  2. Department of Information and Communication Engineering, University of Electro-Comm, Chofugaoga 1-5-1, Chofu, 182-8585, Tokyo, Japan

    Jun Tarui

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© 2011 Springer-Verlag Berlin Heidelberg

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Okamoto, Y., Otachi, Y., Uehara, R., Uno, T. (2011). Hardness Results and an Exact Exponential Algorithm for the Spanning Tree Congestion Problem. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_44

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  • DOI: https://doi.org/10.1007/978-3-642-20877-5_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20876-8

  • Online ISBN: 978-3-642-20877-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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