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.

• Type: Journal
• Year: 2011
• Where: COCOON
• Authors: Masoud T. Omran, Jörg-Rüdiger Sack, Hamid Zarrabi-Zadeh
• Keywords: Approximation Algorithm, COCOON 2011, Combinatorics, Geographic Information Systems, Theoretical Problem