Faster Replacement Paths Algorithm for Undirected, Positive Integer Weighted Graphs with Small Diameter

  • Jay Mahadeokar
  • Sanjeev Saxena
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)


We consider the replacement path problem for undirected graphs in case of edge failures. Given a 2-edge connected graph G(V,E), where n = |V| and m = |E|, for each edge e on the shortest s − t path of G, we are to report the shortest s − t path in G ∖ e. If d is the diameter of the graph, the proposed algorithm takes O(m + d 2) time.

For graphs where \(d = O(\sqrt{m})\), typically dense graphs, or graphs with small diameter we have a linear time solution.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jay Mahadeokar
    • 1
  • Sanjeev Saxena
    • 1
  1. 1.Dept. of Computer Science and EngineeringIndian Institute of TechnologyKanpurIndia

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