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

Authors:
Martin Fürer;Shiva Prasad Kasiviswanathan
Affiliations:
Computer Science and Engineering, Pennsylvania State University, University Park, PA;Computer Science and Engineering, Pennsylvania State University, University Park, PA
Venue:
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Year:
2004

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Abstract

We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ε0 produces an output XA with (1−ε)per(A)≤XA≤(1+ε) per (A) for almost all (0-1) matrices A. For any positive constant ε 0 , and almost all (0-1) matrices the algorithm runs in time O(n2ω), i.e., almost linear in the size of the matrix, where ω = ω(n) is any function satisfying ω(n) → ∞ as n → ∞. This improves the previous bound of O(n3ω) for such matrices. The estimator can also be used to estimate the size of a backtrack tree.