On the linear classification of even and odd permutation matrices and the complexity of computing the permanent

The problem of linear classification of the parity of permutation matrices is studied. This problem is related to the analysis of complexity of a class of algorithms designed for computing the permanent of a matrix that generalizes the Kasteleyn algorithm. Exponential lower bounds on the magnitude o...

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Vydáno v:Computational mathematics and mathematical physics Ročník 57; číslo 2; s. 362 - 371
Hlavní autoři: Babenko, A. V., Vyalyi, M. N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.02.2017
Springer Nature B.V
Témata:
Algebra
Algorithms
Classification
Codes
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Linear programming
Lower bounds
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Matrix
Matrix methods
Permutations
Physics
Polynomials
Studies
United States > US
theta function
independence number
permutation matrix
parity
permanent
linear classification
ISSN:0965-5425, 1555-6662
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Shrnutí:The problem of linear classification of the parity of permutation matrices is studied. This problem is related to the analysis of complexity of a class of algorithms designed for computing the permanent of a matrix that generalizes the Kasteleyn algorithm. Exponential lower bounds on the magnitude of the coefficients of the functional that classifies the even and odd permutation matrices in the case of the field of real numbers and similar linear lower bounds on the rank of the classifying map for the case of the field of characteristic 2 are obtained.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542517020038