Approximating the permanent: A simple approach

Authors:
Lars Eilstrup Rasmussen
Affiliations:
Department of Computer Science, The University of Edinburgh, The King's Building, Mayfield Road, Edinburgh EH9 3J, Scotland
Venue:
Random Structures & Algorithms
Year:
1994

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An almost linear time approximation algorithm for the permanent of a random (0-1) matrix

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Abstract

In this article, we present an efficient and very simple unbiased estimator for the Permanent of square (0–1) matrices. As the main result, we prove that our estimator, even though its worst case behavior is provably very bad, runs in time polynomial in the size of the input matrix for almost all matrices. We also generalize our technique and apply it to another enumeration problem, that of counting Hamilton cycles in directed graphs. The ease with which this was done suggests that the basic technique may have wide applicability. © 1994 John Wiley & Sons, Inc.