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

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Book cover Randomization and Approximation Techniques in Computer Science (RANDOM 1997)

Part of the book series: Lecture Notes in Computer Science ((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(n 2) expected time, and the all-pairs shortest-paths problem can be solved in O(n 2 log n) expected time.

Research supported by NSF grant CCR-9225008.

Research partially supported by ESPRIT LTR Project No. 20244 (ALCOM-IT).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of North London, N7 8DB, London, UK

    Colin Cooper

  2. Department of Mathematical Sciences, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Alan Frieze

  3. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrfürcken, Germany

    Kurt Mehlhorn & Volker Priebe

Authors
  1. Colin Cooper
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  2. Alan Frieze
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  3. Kurt Mehlhorn
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  4. Volker Priebe
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José Rolim

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© 1997 Springer-Verlag Berlin Heidelberg

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Cooper, C., Frieze, A., Mehlhorn, K., Priebe, V. (1997). Average-case complexity of shortest-paths problems in the vertex-potential model. In: Rolim, J. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1997. Lecture Notes in Computer Science, vol 1269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63248-4_2

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  • DOI: https://doi.org/10.1007/3-540-63248-4_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63248-1

  • Online ISBN: 978-3-540-69247-8

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