Fast approximation of the permanent for very dense problems

Authors:
Mark Huber;Jenny Law
Affiliations:
Duke University;Duke University
Venue:
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2008

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Abstract

Approximation of the permanent of a matrix with nonnegative entries is a well studied problem. The most successful approach to date for general matrices uses Markov chains to approximately sample from a distribution on weighted permutations, and Jerrum, Sinclair, and Vigoda developed such a method they proved runs in polynomial time in the input. The current bound on the running time of their method is O(n7(log n)4). Here we present a very different approach using sequential acceptance/rejection, and show that for a class of dense problems this method has an O(n4 log n) expected running time.