Finding Paths with Minimum Shared Edges

  • Masoud T. Omran
  • Jörg-Rüdiger Sack
  • Hamid Zarrabi-Zadeh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6842)

Abstract

Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as to minimize the number of edges shared among the paths. This is a generalization of the well-known disjoint paths problem. While disjoint paths can be computed efficiently, we show that finding paths with minimum shared edges is NP-hard. Moreover, we show that it is even hard to approximate the minimum number of shared edges to within a factor of \(2^{\log^{1-\varepsilon }n}\), for any constant ε > 0. On the positive side, we show that there exists a k-approximation algorithm for the problem, using an adaption of a network flow algorithm. We design some heuristics to improve the quality of the output, and provide empirical results.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Masoud T. Omran
    • 1
  • Jörg-Rüdiger Sack
    • 1
  • Hamid Zarrabi-Zadeh
    • 1
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Computer EngineeringSharif University of TechnologyTehranIran

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