A Parallel Algorithm for Sampling Matchings from an Almost Uniform Distribution

  • J. Diaz
  • J. Petit
  • P. Psycharis
  • M. Serna
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1533)


In this paper we present a randomized parallel algorithm to sample matchings from an almost uniform distribution on the set of matchings of all sizes in a graph. First we prove that the direct NC simulation of the sequential Markov chain technique for this problem is P-complete. Afterwards we present a randomized parallel algorithm for the problem. The technique used is based on the definition of a genetic system that converges to the uniform distribution. The system evolves according to a non-linear equation. Little is known about the convergence of these systems. We can define a non-linear system which converges to a stationary distribution under quite natural conditions. We prove convergence for the system corresponding to the almost uniform sampling of matchings in a graph (up to know the only known convergence for non-linear systems for matchings was matchings on a tree 5). We give empirical evidence that the system converges faster, in polylogarithmic parallel time.


Markov Chain Initial Distribution Parallel Algorithm Genetic System Markov Chain Monte Carlo Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • J. Diaz
    • 1
  • J. Petit
    • 1
  • P. Psycharis
    • 2
  • M. Serna
    • 1
  1. 1.Departament de Llenguatges i SistemesUniversitat Politècnica CatalunyaBarcelonaSpain
  2. 2.Computer Technology Institute (C.T.I.)PatrasGreece

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