# Approximating permanents and hafnians

@article{Barvinok2016ApproximatingPA,
title={Approximating permanents and hafnians},
author={Alexander I. Barvinok},
journal={arXiv: Combinatorics},
year={2016}
}
• A. Barvinok
• Published 27 January 2016
• Mathematics, Computer Science
• arXiv: Combinatorics
We prove that the logarithm of the permanent of an nxn real matrix A and the logarithm of the hafnian of a 2nx2n real symmetric matrix A can be approximated within an additive error 1 > epsilon > 0 by a polynomial p in the entries of A of degree O(ln n - ln epsilon) provided the entries a_ij of A satisfy delta 0, fixed in advance. Moreover, the polynomial p can be computed in n^{O(ln n - ln epsilon)} time. We also improve bounds for approximating ln per A, ln haf A and logarithms of multi…

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• A. Barvinok
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It is concluded that Barvinok's estimator gives a polynomial-time algorithm for the approximate (up to subexponential errors) evaluation of the number of perfect matchings.

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