Finding paths with minimum shared edges

  • Authors:

  • Masoud T. Omran;Jörg-Rüdiger Sack;Hamid Zarrabi-Zadeh

  • Affiliations:

  • School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Ottawa, Ontario, Canada and Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

  • Venue:
  • COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
  • Year:
  • 2011

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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 2log1-ε 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.