We present a parallel algorithm to sample matchings from an almost
uniform distribution on the set of matchings of all sizes in a
graph. 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). We give empirical evidence that the system converges fast.
We present a parallel algorithm to sample matchings from an almost
uniform distribution on the set of matchings of all sizes in a
graph. 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). We give empirical evidence that the system converges fast.
