A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix
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 i...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2017
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| Online Access: | http://hdl.handle.net/1721.1/108274 https://orcid.org/0000-0001-8898-8778 |
| Summary: | 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. |
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