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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 9, Pages 1697–1708
(Mi zvmmf4941)
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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.
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
Linking options:
https://www.mathnet.ru/eng/zvmmf4941 https://www.mathnet.ru/eng/zvmmf/v50/i9/p1697
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Abstract page: | 209 | Full-text PDF : | 67 | References: | 62 | First page: | 7 |
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