Estimating the permanent by importance sampling from a finite population

Abstract

The Calculation of the permanent of a matrix is an extremely difficult task. Indeed it belongs to the class of hard counting problems denoted #P complete and hence any algorithm to compute the permanent must run in exponential time in the order of the matrix. Attention, therefore, has concentrated on Monte Carlo algorithms to estimate permanents with considerable emphasis on deriving randomised polynomial time algorithms. Interest in this area hs largely stemmed from problems in combibatorial enumeration, for instance the permanent of a square(0,1) matrix gives the number of perfect matchings in a bipartite graph.