An Almost Linear Time Approximation Algorithm for the Permanent of a Random (0-1) Matrix
Author | : Martin Fürer |
Publisher | : |
Total Pages | : 11 |
Release | : 2004 |
Genre | : Approximation theory |
ISBN | : |
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Abstract: "We present a simple randomized algorithm for approximating permanents of random (0-1) matrices. The algorithm with inputs a, [epsilon]> 0 produces an output X[subscript A] with (1-[epsilon])per(A) [or =] X[subscript A] [or =] (1 + [epsilon])per(A) for almost all (0-1) matrices A. For every positive constant [epsilon] 0, the algorithm runs in time O(n2[omega]), i.e., almost linear in the size of the matrix, where [omega] = [omega](n) is any function satisfying [omega](n) - [infinity] as n -> [infinity]. This improves the previous bound of O(n3[infinity]) for such matrices."