Uniform multicommodity flow through the complete graph with random edge-capacities

  • Authors:

  • David J. Aldous;Colin Mcdiarmid;Alex Scott

  • Affiliations:

  • Department of Statistics, University of California, Berkeley, CA 94720-3860, USA;Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK;Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, UK

  • Venue:
  • Operations Research Letters
  • Year:
  • 2009

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Abstract

Give random capacities C to the edges of the complete n-vertex graph. Consider the maximum flow @F"n that can be simultaneously routed between each source-destination pair. We prove that @F"n-@f in probability where the limit constant @f depends on the distribution of C in a simple way, and that asymptotically one need use only 1- and 2-step routes. The proof uses a reduction to a random graph problem.