Computing permanents of complex diagonally dominant matrices and tensors
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We prove that for any λ > 1, fixed in advance, the permanent of an n × n complex matrix, where the absolute value of each diagonal entry is at least λ times bigger than the sum of the absolute values of all other entries in the same row, can be approximated within any relative error 0 < ϵ < 1 in quasi-polynomial n^O( n - ϵ) time. We extend this result to multidimensional permanents of tensors and discuss its application to weighted counting of perfect matchings in hypergraphs.
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