A Permanent Algorithm with exp[Ω (n ^{1/3}/2 ln n )] Expected Speedup for 0-1 Matrices

Abstract

This paper outlines a permanent algorithm with mildly exponential expected speedup over Ryser's inclusion and exclusion algorithm for 0-1 matrices. The algorithm is based on a finite-difference formula that is a generalization of Ryser's formula. The matrix is augmented by a column of entries selected to produce zero-valued terms in the formula. The algorithm achieves speedup by avoiding computation of many zero-valued terms.