A simple polynomial time algorithm to approximate the permanent within a simply exponential factor
نویسنده
چکیده
We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of n positive semidefinite n×n matrices within a factor 2. Consequently, the algorithm allows us to approximate in randomized polynomial time the permanent of a given n×n non-negative matrix within a factor 2. When applied to approximating the permanent, the algorithm turns out to be a simple modification of the well-known Godsil-Gutman estimator.
منابع مشابه
Polynomial Time Algorithms to Approximate Permanents and Mixed Discriminants Within a Simply Exponential Factor
We present real, complex, and quaternionic versions of a simple ran-domized polynomial time algorithm to approximate the permanent of a non-negative matrix and, more generally, the mixed discriminant of positive semideenite matrices. The algorithm provides an unbiased estimator, which, with high probability, approximates the true value within a factor of O(c n), where n is the size of the matri...
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