Geodesic
Description of the types of maximum noninteger vertices of the polyhedron in the three-index axial assignment problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1908-1912 
V. M. Kravtsov. Description of the types of maximum noninteger vertices of the polyhedron in the three-index axial assignment problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1908-1912. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a16/
@article{ZVMMF_2006_46_10_a16,
     author = {V. M. Kravtsov},
     title = {Description of the types of maximum noninteger vertices of the polyhedron in the three-index axial assignment problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1908--1912},
     year = {2006},
     volume = {46},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a16/}
}
TY  - JOUR
AU  - V. M. Kravtsov
TI  - Description of the types of maximum noninteger vertices of the polyhedron in the three-index axial assignment problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1908
EP  - 1912
VL  - 46
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a16/
LA  - ru
ID  - ZVMMF_2006_46_10_a16
ER  - 
%0 Journal Article
%A V. M. Kravtsov
%T Description of the types of maximum noninteger vertices of the polyhedron in the three-index axial assignment problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1908-1912
%V 46
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a16/
%G ru
%F ZVMMF_2006_46_10_a16

Voir la notice de l'article provenant de la source Math-Net.Ru

For an arbitrary $r\in\{3n-4,3n-3,3n-2\}$, a description of all the types of $r$-noninteger vertices (i.e., the vertices with $r$ fractional components) of the polyhedron of the three-index axial assignment problem of order $n$ with $n\ge4$ is proposed.

[1] Pierskalla W. P., “The multidimensional assignment problem”, Operat. Res., 16 (1968), 422–431 | DOI | Zbl

[2] Poore A. B., “Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking”, Comput. Optimizat. and Appl., 3 (1994), 27–54 | DOI | MR

[3] Arbib C., Pacciarelli D., Smriglio S., “A three-dimensional matching model for perishable production scheduling”, Discrete Appl. Math., 92 (1999), 1–15 | DOI | MR | Zbl

[4] Kravtsov M. K., Kravtsov V. M., Lukshin E. B., “O tipakh $(3n-2)$-netselochislennykh vershin mnogogrannika trekhindeksnoi aksialnoi zadachi vybora”, Izv. vuzov. Matem., 2002, no. 12, 84–90 | MR

[5] Kravtsov V. M., “O novykh tipakh maksimalno netselochislennykh vershin mnogogrannika trekhindeksnoi aksialnoi zadachi o naznacheniyakh”, Vestn. BGU. Ser. 1, 2003, no. 3, 80–85 | MR | Zbl

[6] Kravtsov V. M., “O maksimalno netselochislennykh vershinakh mnogogrannika trekhindeksnoi aksialnoi zadachi o naznacheniyakh”, Avtomatika i telemekhan., 2004, no. 3, 62–70 | MR | Zbl

[7] Kravtsov V. M., “O novykh svoistvakh maksimalno netselochislennykh vershin mnogogrannika trekhindeksnoi aksialnoi zadachi o naznacheniyakh”, Izv. vuzov. Matematika, 2004, no. 12, 37–45 | MR

[8] Kravtsov V. M., “Ob odnom tipe maksimalno netselochislennykh vershin mnogogrannika trekhindeksnoi aksialnoi zadachi o naznacheniyakh”, Vestn. BGU. Ser. 1, 2005, no. 3, 83–90 | MR | Zbl

[9] Kravtsov M. K., Kravtsov V. M., Lukshin E. V., “O netselochislennykh vershinakh mnogogrannika trekhindeksnoi aksialnoi zadachi o naznacheniyakh”, Diskretnaya matem., 13:2 (2001), 120–143 | MR | Zbl

[10] Kholl M., Kombinatorika, Nauka, M., 1970

[11] Emelichev V. A., Kovalev M. M., Kravtsov M. K., Mnogogranniki, grafy, optimizatsiya, Nauka, M., 1981 | MR

[12] Kravtsov M. K., Kravtsov V. M., Lukshin E. V., “O chisle netselochislennykh vershin mnogogrannika trekhindeksnoi aksialnoi zadachi o naznacheniyakh”, Vestsi HAH Belarusi. Ser. fiz.-matem. navuk, 2000, no. 4, 59–65 | MR