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- W2104070086 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 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−1)-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." @default.
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- W2104070086 date "2012-02-24" @default.
- W2104070086 modified "2023-10-06" @default.
- W2104070086 title "Finding paths with minimum shared edges" @default.
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- W2104070086 doi "https://doi.org/10.1007/s10878-012-9462-2" @default.
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