Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
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 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. © 2010 Elsevier Inc. All rights reserved.
Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ
Matthew A Grayson
Journal of Complexity
A.R. Conn, Nick Gould, et al.
Mathematics of Computation