Abstract
We present a deterministic algorithm, which, for any given \(0< \epsilon < 1\) and an \(n \times n\) real or complex matrix \(A=\left( a_{ij}\right) \) such that \(\left| a_{ij}-1 \right| \le 0.19\) for all \(i, j\) computes the permanent of \(A\) within relative error \(\epsilon \) in \(n^{O\left( \ln n -\ln \epsilon \right) }\) time. The method can be extended to computing hafnians and multidimensional permanents.
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The author is grateful to the anonymous referees for their careful reading of the paper, useful suggestions and interesting questions.
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Communicated by Stephen Cook.
This research was partially supported by NSF Grants DMS 0856640 and DMS 1361541.
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Barvinok, A. Computing the Permanent of (Some) Complex Matrices. Found Comput Math 16, 329–342 (2016). https://doi.org/10.1007/s10208-014-9243-7
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DOI: https://doi.org/10.1007/s10208-014-9243-7