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...

Full description

Saved in:
Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 57; no. 2; pp. 362 - 371
Main Authors: Babenko, A. V., Vyalyi, M. N.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.02.2017
Springer Nature B.V
Subjects:
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-1
ObjectType-Feature-2
content type line 23
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542517020038