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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 9, Pages 1697–1708 (Mi zvmmf4941)  
This article is cited in 2 scientific papers (total in 2 papers)

On a characterization of noninteger vertices of the relaxational polyhedron in the multi-index axial assignment problem

V. M. Kravtsov

Economic Research Institute, Ministry for Economics of the Republic of Belarus, ul. Slavinskogo 1, korp. 1, Minsk, 220086 Belarus
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Abstract: Theorems about the characterization and exponential growth of the denominators of fractional components of noninteger vertices of the relaxation polyhedron in the multi-index axial assignment problem are proved. They made it possible to obtain new lower bounds on the number of noninteger vertices of this polyhedron and to refute the conjecture on the estimate of the ratio of the number of integer vertices to the number of all vertices of the multi-index axial transportation polyhedron determined by integer vectors.
Key words: relaxation polyhedron in the multi-index axial assignment problem, $r$-noninteger vertex, $(p-1)$ section of $p$-index matrix.
Received: 16.03.2009
Revised: 01.04.2010
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 9, Pages 1615–1626
DOI: https://doi.org/10.1134/S0965542510090125
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: V. M. Kravtsov, “On a characterization of noninteger vertices of the relaxational polyhedron in the multi-index axial assignment problem”, Zh. Vychisl. Mat. Mat. Fiz., 50:9 (2010), 1697–1708; Comput. Math. Math. Phys., 50:9 (2010), 1615–1626
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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