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Finding a contra-risk path between two nodes in undirected graphs

Author

Listed:
  • Mehdi Ghiyasvand

    (Bu-Ali Sina University)

  • Iman Keshtkar

    (Bu-Ali Sina University)

Abstract

Given an undirected graph with a source node s and a sink node t. The anti-risk path problem is defined as the problem of finding a path between node s to node t with the least risk under the assumption that at most one edge of each path may be blocked. Xiao et al. (J Comb Optim 17:235–246, 2009) defined the problem and presented an $$O(mn+n^2 \log n)$$ O ( m n + n 2 log n ) time algorithm to find an anti-risk path, where n and m are the number of nodes and edges, respectively. Recently, Mahadeokar and Saxena (J Comb Optim 27:798–807, 2014) solved the problem in $$O(m+n \log n)$$ O ( m + n log n ) time. In this paper, first, a new version of the anti-risk path (called contra-risk path) is defined, which is more effective than an anti-risk path in many networks. Then, an algorithm to find a contra-risk path is presented, which runs in $$O(m+n \log n)$$ O ( m + n log n ) time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9912-8
    DOI: 10.1007/s10878-015-9912-8
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    References listed on IDEAS

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    1. 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.
    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.
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