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International Workshop on Randomization and Approximation Techniques in Computer Science

International Workshop on Approximation Algorithms for Combinatorial Optimization

RANDOM 2010, APPROX 2010: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques pp 274–286Cite as

An O(logn)-Approximation Algorithm for the Disjoint Paths Problem in Eulerian Planar Graphs and 4-Edge-Connected Planar Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6302))

Abstract

In this paper, we study an approximation algorithm for the maximum edge-disjoint paths problem. In the maximum edge-disjoint paths problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be connected by edge-disjoint paths. We give an O(logn)-approximation algorithm for the maximum edge-disjoint paths problem when an input graph is either 4-edge-connected planar or Eulerian planar. This improves an O(log2 n)-approximation algorithm given by Kleinberg [10] for Eulerian planar graphs. Our result also generalizes the result by Chekuri, Khanna and Shepherd [2,3] who gave an O(logn)-approximation algorithm for the edge-disjoint paths problem with congestion 2 when an input graph is planar.

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Author information

Authors and Affiliations

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

    Ken-ichi Kawarabayashi & Yusuke Kobayashi

  2. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, 113-8656, Japan

    Ken-ichi Kawarabayashi & Yusuke Kobayashi

Authors
  1. Ken-ichi Kawarabayashi
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  2. Yusuke Kobayashi
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Editor information

Editors and Affiliations

  1. Universitat Politecnica de Catalunya, Departament de Llenguatges i Sistemes Informatics, Campus Nord - Ed Omega, Desp. 235, Jordi Girona, 1-3, 08034, Barcelona, Spain

    Maria Serna

  2. Department of Computer Science, University of Haifa, Mount Carmel, 31905, Haifa, Israel

    Ronen Shaltiel

  3. Department of Computer Science, University of Kiel, Olshausenstrasse 40, 24098, Kiel, Germany

    Klaus Jansen

  4. University of Geneva, Centre Universitaire d’Informatique, Battelle Bat. A, 7 rte de Drize, 1227, Carouge, Switzerland

    José Rolim

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Kawarabayashi, Ki., Kobayashi, Y. (2010). An O(logn)-Approximation Algorithm for the Disjoint Paths Problem in Eulerian Planar Graphs and 4-Edge-Connected Planar Graphs. In: Serna, M., Shaltiel, R., Jansen, K., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2010 2010. Lecture Notes in Computer Science, vol 6302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15369-3_21

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  • DOI: https://doi.org/10.1007/978-3-642-15369-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15368-6

  • Online ISBN: 978-3-642-15369-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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