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

被引：1

作者：

Kravtsov, V. M. ^{[1
]}

机构：

[1] Minist Econ Republ Belarus, Econ Res Inst, Minsk 220086, Belarus, BELARUS

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2010年 / 50卷 / 09期

关键词：

relaxation polyhedron in the multi-index axial assignment problem; r-noninteger vertex; (p-1) section of p-index matrix;

D O I：

10.1134/S0965542510090125

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1615 / 1626

页数：12

共 49 条

[1] On the characterization of noninteger vertices of the relaxation polyhedron in the multi-index axial assignment problem
V. M. Kravtsov
[J]. Computational Mathematics and Mathematical Physics, 2010, 50 : 1615 - 1626
[2] Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem
M. K. Kravtsov
V. M. Kravtsov
[J]. Computational Mathematics and Mathematical Physics, 2013, 53 : 655 - 665
[3] Characterization of the types of maximum noninteger vertices in the relaxation polyhedron of the four-index axial assignment problem
Kravtsov, M. K.
Kravtsov, V. M.
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2013, 53 (05) : 655 - 665
[4] Types of maximum noninteger vertices of the relaxation polyhedron of the four-index axial assignment problem
M. K. Kravtsov
V. M. Kravtsov
[J]. Russian Mathematics, 2012, 56 (3) : 6 - 13
[5] Types of Maximum Noninteger Vertices of the Relaxation Polyhedron of the Four-Index Axial Assignment Problem
Kravtsov, M. K.
Kravtsov, V. M.
[J]. RUSSIAN MATHEMATICS, 2012, 56 (03) : 6 - 13
[6] On the Maximum Noninteger Polyhedron Vertices of the Three-index Axial Assignment Problem
V. M. Kravtsov
[J]. Automation and Remote Control, 2004, 65 : 413 - 421
[7] On the maximum noninteger polyhedron vertices of the three-index axial assignment problem
Kravtsov, VM
[J]. AUTOMATION AND REMOTE CONTROL, 2004, 65 (03) : 413 - 421
[8] Description of the types of maximum noninteger vertices of the polyhedron in the three-index axial assignment problem
Kravtsov V.M.
[J]. Computational Mathematics and Mathematical Physics, 2006, 46 (10) : 1821 - 1825
[9] On the noninteger polyhedron vertices of the three-index axial transportation problem
Kravtsov, MK
Lukshin, EV
[J]. AUTOMATION AND REMOTE CONTROL, 2004, 65 (03) : 422 - 430
[10] On the Noninteger Polyhedron Vertices of the Three-index Axial Transportation Problem
M. K. Kravtsov
E. V. Lukshin
[J]. Automation and Remote Control, 2004, 65 : 422 - 430

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