Journal of Combinatorial Optimization

, Volume 32, Issue 3, pp 917–926 | Cite as

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

  • Mehdi Ghiyasvand
  • Iman Keshtkar


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 \(O(mn+n^2 \log n)\) 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 \(O(m+n \log n)\) 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 \(O(m+n \log n)\) time.


Network flows The anti-risk path The shortest path problem 



We would like to express our very great appreciation to reviewers for their valuable comments and suggestions, which have helped to improve the quality and presentation of this paper.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceBu-Ali Sina UniversityHamedanIran

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