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. © Springer-Verlag Berlin Heidelberg 1998.
CITATION STYLE
Diaz, J., Petit, J., Psycharis, P., & Serna, M. (1998). A parallel algorithm for sampling matchings from an almost uniform distribution. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1533 LNCS, pp. 457–467). Springer Verlag. https://doi.org/10.1007/3-540-49381-6_48
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