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Average-case complexity of shortest-paths problems in the vertex-potential model

  • Colin Cooper
  • Alan Frieze
  • Kurt Mehlhorn
  • Volker Priebe
Approximation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1269)

Abstract

We study the average-case complexity of shortest paths problems in the vertex-potential model. The vertex-potential model is a family of probability distributions on complete directed graphs with arbitrary real edge lengths but without negative cycles. We show that on a graph with n vertices and with respect to this model, the single-source shortest-paths problem can be solved in O(n2) expected time, and the all-pairs shortest-paths problem can be solved in O(n2 log n) expected time.

Keywords

Short Path Edge Length Short Path Problem Expected Time Negative Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Colin Cooper
    • 1
  • Alan Frieze
    • 2
  • Kurt Mehlhorn
    • 3
  • Volker Priebe
    • 3
  1. 1.School of Mathematical SciencesUniversity of North LondonLondonUK
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  3. 3.Max-Planck-Institut für Informatik, Im StadtwaldSaarbrfürckenGermany

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