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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 5, Pages 825–836
DOI: https://doi.org/10.7868/S0044466913050086 (Mi zvmmf9863) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem

V. M. Kravtsov, M. K. Kravtsov

Scientific and research economic institute of Ministry of economy of the Republic of Belarus
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DOI: https://doi.org/10.7868/S0044466913050086
Abstract: For the relaxation polyhedron $M(4,n)$ in the four-index axial assignment problem of order $n$, $n\geqslant 3$, a characterization of all possible types (except for a single case) of maximum noninteger vertices, i.e., vertices with $4n-3$ fractional components is proposed. A formula enumerating all the maximum noninteger vertices of the same type in $M(4,n)$ is derived.
Key words: relaxation polyhedron in the four-index axial assignment problem, $r$-noninteger vertex, maximum noninteger vertex, identification of vertex types, three-dimensional section of four-index matrix.
Received: 10.09.2011
Revised: 03.12.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 5, Pages 655–665
DOI: https://doi.org/10.1134/S0965542513050072
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: V. M. Kravtsov, M. K. Kravtsov, “Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 825–836; Comput. Math. Math. Phys., 53:5 (2013), 655–665
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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