Geodesic
The problem of integer-valued balancing of a three-dimensional matrix and network model
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 3, pp. 70-76.

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The article is devoted to the problem of integer-valued balancing of a three-dimensional matrix. A problem of reducing this problem to the problem of finding a maximum flow in network is explored.
Keywords: integer-valued balancing, three-dimensional matrices, flows in networks. 
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A. V. Smirnov. The problem of integer-valued balancing of a three-dimensional matrix and network model. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 3, pp. 70-76. http://geodesic.mathdoc.fr/item/MAIS_2009_16_3_a6/

[1] N. M. Korshunova, V. S. Rublev, “Zadacha tselochislennogo sbalansirovaniya matritsy”, Sovremennye problemy matematiki i informatiki, 3, YarGU im. P. G. Demidova, Yaroslavl, 2000, 145–150

[2] L. G. Afraimovich, M. Kh. Prilutskii, “Mnogoindeksnye zadachi raspredeleniya resursov v ierarkhicheskikh sistemakh”, Avtomatika i telemekhanika, 157:6 (2006), 194–205 | MR

[3] L. G. Afraimovich, M. Kh. Prilutskii, “Mnogoproduktovye potoki v drevovidnykh setyakh”, Izvestiya RAN. Teoriya i sistemy upravleniya, 157:2 (2008), 57–63 | MR

[4] A. A. Korbut, Yu. Yu. Finkelshtein, Diskretnoe programmirovanie, Nauka, M., 1969 | MR | Zbl

[5] L. G. Raskin, I. O. Kirichenko, Mnogoindeksnye zadachi lineinogo programmirovaniya, Radio i svyaz, M., 1982 | MR | Zbl

[6] A. D. Gofman, D. B. Kraskal, “Tselochislennye granichnye tochki vypuklykh mnogogrannikov”, Lineinye neravenstva i smezhnye voprosy, IL, M., 1959, 325–347

[7] V. S. Rublev, A. V. Smirnov, “Tselochislennoe sbalansirovanie 3-mernoi matritsy plana”, Trudy VII mezhdunarodnoi konferentsii «Diskretnye modeli v teorii upravlyayuschikh sistem», Pokrovskoe 4–6 marta 2006 g., MGU, M., 2006, 302–308

[8] V. S. Rublev, A. V. Smirnov, “Posloinyi algoritm tselochislennogo sbalansirovaniya trekhmernoi matritsy”, Materialy IX Mezhdunarodnogo seminara «Diskretnaya matematika i ee prilozheniya», posvyaschennogo 75-letiyu so dnya rozhdeniya akademika O. B. Lupanova (Moskva, MGU, 18–23 iyunya 2007 g.), MGU, M., 2007, 351–353