A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix

We construct a deterministic approximation algorithm for computing a permanent of a 0, 1 n by n matrix to within a multiplicative factor (1 + ǫ)n, for arbitrary ǫ > 0. When the graph underlying the matrix is a constant degree expander our algorithm runs in polynomial time (PTAS). In the general case the running time of the algorithm is exp(O(n 2 3 log n)). For the class of graphs which are constant degree expanders the first result is an improvement over the best known approximation factor en obtained in [LSW00]. Our results use a recently developed deterministic approximation algorithm for counting partial matchings of a graph [BGK] and Jerrum-Vazirani expander decomposition method of [JV96].