Finding Paths with Minimum Shared Edges

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Finding Paths with Minimum Shared Edges
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.
Masoud T. Omran, Jörg-Rüdiger Sack, Hami
Added 18 Dec 2011
Updated 18 Dec 2011
Type Journal
Year 2011
Authors Masoud T. Omran, Jörg-Rüdiger Sack, Hamid Zarrabi-Zadeh
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