A simple polynomial time algorithm to approximate the permanent within a simply exponential factor

Details A simple polynomial time algorithm to approximate the permanent within a simply exponential factor A simple polynomial time algorithm to approximate the permanent within a simply exponential factor

1997-04-09

arxiv.org/abs/math/9704218v1

Mathematics

Rings and Algebras

Scientific paper

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.

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