, Volume 16, Issue 4-5, pp 392-401

A mildly exponential approximation algorithm for the permanent

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Abstract

A new approximation algorithm for the permanent of ann ×n 0,1-matrix is presented. The algorithm is shown to have worst-case time complexity exp(O(n 1/2 log2 n)). Asymptotically, this represents a considerable improvement over the best existing algorithm, which has worst-case time complexity exp(Θ(n)).

Supported by SERC Grant GR/F 90363; work done in part while visiting DIMACS (Center for Discrete Mathematics and Computer Science).
Supported by an NSF PYI grant, with matching equipment grant from the AT&T Foundation; work done in part while visiting DIMACS.
Communicated by M. Luby.