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

Authors:
David Gamarnik;Dmitriy Katz
Affiliations:
Operations Research Center and Sloan School of Management, MIT, Cambridge, MA 02139, United States;T.J. Watson Research Center, IBM, Yorktown Heights, NY 10598, United States
Venue:
Journal of Computer and System Sciences
Year:
2010

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Abstract

We consider the problem of computing the permanent of a 0,1n 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+@e)^n, for arbitrary @e0. 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.