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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 5, Pages 825–836 (Mi zvmmf9863)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.7868/S0044466913050086

Full text: PDF file (209 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:5, 655–665

Bibliographic databases:

UDC: 519.7
Received: 10.09.2011
Revised: 03.12.2012

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 articles:
    1. S. N. Medvedev, O. A. Medvedeva, “Adaptivnyi algoritm resheniya aksialnoi trekhindeksnoi zadachi o naznacheniyakh”, Avtomat. i telemekh., 2019, no. 4, 156–172  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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