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Zh. Vychisl. Mat. Mat. Fiz., 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:9, 1615–1626

Bibliographic databases:

UDC: 519.7
Received: 16.03.2009
Revised: 01.04.2010

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. K. Kravtsov, V. M. Kravtsov, “Types of maximally noninteger vertices of the relaxation polyhedron of the four-index axial assignment problem”, Russian Math. (Iz. VUZ), 56:3 (2012), 6–13  mathnet  crossref  mathscinet
    2. 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”, Comput. Math. Math. Phys., 53:5 (2013), 655–665  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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