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Finding the anti-block vital edge of a shortest path between two nodes

Author

Listed:
  • Bing Su

    (Xi’an JiaoTong University
    The State Key Lab for Manufacturing Systems Engineering)

  • Qingchuan Xu

    (Xi’an JiaoTong University
    The State Key Lab for Manufacturing Systems Engineering)

  • Peng Xiao

    (Xi’an JiaoTong University
    The State Key Lab for Manufacturing Systems Engineering)

Abstract

Let P G (s,t) denote a shortest path between two nodes s and t in an undirected graph G with nonnegative edge weights. A detour at a node u∈P G (s,t)=(s,…,u,v,…,t) is defined as a shortest path P G−e (u,t) from u to t which does not make use of (u,v). In this paper, we focus on the problem of finding an edge e=(u,v)∈P G (s,t) whose removal produces a detour at node u such that the ratio of the length of P G−e (u,t) to the length of P G (u,t) is maximum. We define such an edge as an anti-block vital edge (AVE for short), and show that this problem can be solved in O(mn) time, where n and m denote the number of nodes and edges in the graph, respectively. Some applications of the AVE for two special traffic networks are shown.

Suggested Citation

  • Bing Su & Qingchuan Xu & Peng Xiao, 2008. "Finding the anti-block vital edge of a shortest path between two nodes," Journal of Combinatorial Optimization, Springer, vol. 16(2), pages 173-181, August.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:2:d:10.1007_s10878-007-9120-2
    DOI: 10.1007/s10878-007-9120-2
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    Cited by:

    1. T. N. Dinh & M. T. Thai & H. T. Nguyen, 2014. "Bound and exact methods for assessing link vulnerability in complex networks," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 3-24, July.

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