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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)

Abstract

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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