A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix
Author(s)
Gamarnik, David; Rogozhnikov, Dmitriy A.
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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 ( 1 + ∈)[superscript η] for arbitrary∈ > 0. This is an improvement over the best known approximation factor e[superscript η] 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.
Date issued
2010-05Department
Sloan School of ManagementJournal
Journal of Computer and System Sciences
Publisher
Elsevier
Citation
Gamarnik, David and Katz, Dmitriy. “A Deterministic Approximation Algorithm for Computing the Permanent of a 0, 1 Matrix.” Journal of Computer and System Sciences 76, no. 8 (December 2010): 879–883. © 2010 Elsevier Inc
Version: Original manuscript
ISSN
0022-0000
1090-2724