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Finding paths with minimum shared edges

Omran, M. T ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-22685-4_49
  3. Abstract:
  4. 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-εn, 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
  5. Keywords:
  6. Disjoint paths ; Disjoint paths problem ; Empirical results ; Finding paths ; Graph G ; K-approximation algorithm ; K-paths ; Network flow algorithms ; NP-hard ; Security problems ; Geographic information systems ; Graph theory ; Approximation algorithms
  7. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 14 August 2011 through 16 August 2011 ; Volume 6842 LNCS , August , 2011 , Pages 567-578 ; 03029743 (ISSN) ; 9783642226847 (ISBN)
  8. URL: http://link.springer.com/chapter/10.1007%2F978-3-642-22685-4_49