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COMPUTING THE PERMANENT OF (SOME) COMPLEX MATRICES
, 2014
"... Abstract. We present a deterministic algorithm, which, for any given 0 < < 1 and an n × n real or complex matrix A = (aij) such that aij − 1  ≤ 0.19 for all i, j computes the permanent of A within relative error in nO(lnn−ln ) time. The method can be extended to computing hafnians and mul ..."
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Abstract. We present a deterministic algorithm, which, for any given 0 < < 1 and an n × n real or complex matrix A = (aij) such that aij − 1  ≤ 0.19 for all i, j computes the permanent of A within relative error in nO(lnn−ln ) time. The method can be extended to computing hafnians and multidimensional permanents. 1. Introduction and
COMPUTING THE PARTITION FUNCTION OF A POLYNOMIAL ON THE BOOLEAN CUBE
, 2015
"... Abstract. For a polynomial f: {−1, 1}n − → C, we define the partition function as the average of eλf(x) over all points x ∈ {−1, 1}n, where λ ∈ C is a parameter. We present an algorithm, which, given such f, λ and > 0 approximates the partition function within a relative error of in NO(lnn−ln ) ..."
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Abstract. For a polynomial f: {−1, 1}n − → C, we define the partition function as the average of eλf(x) over all points x ∈ {−1, 1}n, where λ ∈ C is a parameter. We present an algorithm, which, given such f, λ and > 0 approximates the partition function within a relative error of in NO(lnn−ln ) time provided λ  ≤ (2L√d)−1, where d is the degree, L is (roughly) the Lipschitz constant of f and N is the number of monomials in f. We apply the algorithm to approximate the maximum of a polynomial f: {−1, 1}n − → R. 1. Introduction and