A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix
Name
0702039v1.pdf
Description
http://arxiv.org/abs/math/0702039
Size
157.3 KB
Format
Adobe PDF
Checksum (MD5)
5226a7ce9f8270fa2579fa7c737371a7
Author(s)
Gamarnik, David
Rogozhnikov, Dmitriy A.
Date Issued
May 2010
Journal
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
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 ( 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.
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcss.2010.05.002
