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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