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Modified Bethe Permanent of a Nonnegative Matrix
Authors
Shashank Vatedka
Pascal Vontobel
Publication date
1 January 2020
Publisher
'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Cite
Abstract
Currently the best deterministic polynomial-time algorithm for approximating the permanent of a non-negative matrix is based on minimizing the Bethe free energy function of a certain normal factor graph (NFG). In order to improve the approximation guarantee, we propose a modified NFG with fewer cycles, but still manageable function-node complexity; we call the approximation obtained by minimizing the function of the modified normal factor graph the modified Bethe permanent. For nonnegative matrices of size 3× 3, we give a tight characterization of the modified Bethe permanent. For non-negative matrices of size n× n with n≥ 3, we present a partial characterization, along with promising numerical results. The analysis of the modified NFG is also interesting because of its tight connection to an NFG that is used for approximating a permanent-like quantity in quantum information processing. © 2020 IEEE
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Research Archive of Indian Institute of Technology Hyderabad
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oai:raiith.iith.ac.in:11255
Last time updated on 22/11/2022
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