A deterministic approximation algorithm for computing the permanent of a matrix

Abstract: We consider the problem of computing the permanent of a 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 , for arbitrary . This is an improvement over the best known approximation factor obtained in Linial, Samorodnitsky and Wigderson (2000) , 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) ) and Jerrum–Vazirani method (Jerrum and Vazirani (1996) ) of approximating permanent by near perfect matchings. [ABSTRACT FROM AUTHOR]