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arXiv · 1601.07518

Approximating permanents and hafnians

Alexander Barvinok
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Abstract

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 < a_ij < 1 for an arbitrarily small 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-dimensional permanents for complex matrices and tensors A.

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Alexander Barvinok. 2017-01-13. Approximating permanents and hafnians. https://arxiv.org/abs/1601.07518

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