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

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


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.


Short Path Edge Length Short Path Problem Expected Time Negative Cycle 
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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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