A simple polynomial time algorithm to approximate the permanent within a simply exponential factor
<|reference_start|>A simple polynomial time algorithm to approximate the permanent within a simply exponential factor: We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of $n$ positive semidefinite $n \times n$ matrices within a factor $2^{O(n)}$. Consequently, the algorithm allows us to approximate in randomized polynomial time the permanent of a given $n \times n$ non-negative matrix within a factor $2^{O(n)}$. When applied to approximating the permanent, the algorithm turns out to be a simple modification of the well-known Godsil-Gutman estimator.<|reference_end|>
@article{barvinok1997a,
    title={A simple polynomial time algorithm to approximate the permanent within a
  simply exponential factor},
    author={Alexander Barvinok},
    journal={arXiv preprint arXiv:math/9704218},
    year={1997},
    number={MSRI 1997-031, formerly math.LA/9704218},
    archivePrefix={arXiv},
    eprint={math/9704218},
    primaryClass={math.RA cs.DS}
}