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Greedy Edge-Disjoint Paths in Complete Graphs

  • Paz Carmi
  • Thomas Erlebach
  • Yoshio Okamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2880)

Abstract

The maximum edge-disjoint paths problem (MEDP) is one of the most classical NP-hard problems. We study the approximation ratio of a simple and practical approximation algorithm, the shortest-path-first greedy algorithm (SGA), for MEDP in complete graphs. Previously, it was known that this ratio is at most 54. Adapting results by Kolman and Scheideler [Proceedings of SODA, 2002, pp. 184–193], we show that SGA achieves approximation ratio 8F+1 for MEDP in undirected graphs with flow number F and, therefore, has approximation ratio at most 9 in complete graphs. Furthermore, we construct a family of instances that shows that SGA cannot be better than a 3-approximation algorithm. Our upper and lower bounds hold also for the bounded-length greedy algorithm, a simple on-line algorithm for MEDP.

Keywords

Approximation algorithm Greedy algorithm Shortening lemma 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Paz Carmi
    • 1
  • Thomas Erlebach
    • 2
  • Yoshio Okamoto
    • 3
  1. 1.Department of Computer ScienceBen-Gurion University of the NegevIsrael
  2. 2.Computer Engineering and Networks Laboratory, Department of Information Technology and Electrical EngineeringETH ZürichSwitzerland
  3. 3.Institute of Theoretical Computer Science, Department of Computer ScienceETH ZürichSwitzerland

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