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

We consider the problem of computing the permanent of a 0,1 n by n matrix. For a class of matrices corresponding to constant degree expanders we construct a deterministic polynomial time approximation algorithm to within a multiplicative factor n(1+ϵ), for arbitrary ϵ>0. This is an improvement over the best known approximation factor en obtained in Linial, Samorodnitsky and Wigderson (2000) [9], , though the latter result was established for arbitrary non-negative matrices. Our results use a recently developed deterministic approximation algorithm for counting partial matchings of a graph (Bayati, Gamarnik, Katz, Nair and Tetali (2007) [2], ) and Jerrum–Vazirani method (Jerrum and Vazirani (1996) [8]) of approximating permanent by near perfect matchings.