Approximate Counting of Matchings in Sparse Hypergraphs
  In this paper we give a fully polynomial randomized approximation scheme (FPRAS) for the number of all matchings in hypergraphs belonging to a class of sparse, uniform hypergraphs. Our method is based on a generalization of the canonical path method to the case of uniform hypergraphs. 
Marek Karpinski, Andrzej Rucinski, Edyta Szymanska
cs.DS cs.DM