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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/s10878-012-9462-2
  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 within a factor of 2log1-εn, 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
  5. Keywords:
  6. Approximation algorithm ; Disjoint paths problem ; Finding paths ; Inapproximability ; Minimum shared edges problem ; Network flow algorithms ; Positive sides ; Security problems ; Approximation algorithms ; Geographic information systems ; Heuristic algorithms ; Graph theory
  7. Source: Journal of Combinatorial Optimization ; Volume 26, Issue 4 , 2013 , Pages 709-722 ; 13826905 (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs10878-012-9462-2