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Finding an anti-risk path between two nodes in undirected graphs

Author

Listed:
  • Peng Xiao

    (Xi’an Jiaotong University)

  • Yinfeng Xu

    (State Key Lab for Manufacturing Systems Engineering)

  • Bing Su

    (Xi’an Jiaotong University)

Abstract

Given a weighted graph G=(V,E) with a source s and a destination t, a traveler has to go from s to t. However, some of the edges may be blocked at certain times, and the traveler only observes that upon reaching an adjacent site of the blocked edge. Let ℘={P G (s,t)} be the set of all paths from s to t. The risk of a path is defined as the longest travel under the assumption that any edge of the path may be blocked. The paper will propose the Anti-risk Path Problem of finding a path P G (s,t) in ℘ such that it has minimum risk. We will show that this problem can be solved in O(mn+n 2log n) time suppose that at most one edge may be blocked, where n and m denote the number of vertices and edges in G, respectively.

Suggested Citation

  • Peng Xiao & Yinfeng Xu & Bing Su, 2009. "Finding an anti-risk path between two nodes in undirected graphs," Journal of Combinatorial Optimization, Springer, vol. 17(3), pages 235-246, April.
    • Handle: RePEc:spr:jcomop:v:17:y:2009:i:3:d:10.1007_s10878-007-9110-4
    DOI: 10.1007/s10878-007-9110-4
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    Cited by:

    1. Huili Zhang & Yinfeng Xu & Xingang Wen, 2015. "Optimal shortest path set problem in undirected graphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 511-530, April.
    2. Jay Mahadeokar & Sanjeev Saxena, 2014. "Faster algorithm to find anti-risk path between two nodes of an undirected graph," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 798-807, May.
    3. Mehdi Ghiyasvand & Iman Keshtkar, 2016. "Finding a contra-risk path between two nodes in undirected graphs," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 917-926, October.

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