Abstract
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 ( 1 + ϵ ) n , for arbitrary ϵ > 0 . This is an improvement over the best known approximation factor e n 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.
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