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Model. Anal. Inform. Sist., 2010, Volume 17, Number 2, Pages 72–98 (Mi mais5)  

This article is cited in 9 scientific papers (total in 9 papers)

The problem of integer-valued balancing of a three-dimensional matrix and algorithms of its solution

V. S. Rublev, A. V. Smirnov

P. G. Demidov Yaroslavl State University

Abstract: The article is devoted to the problem of integer-valued balancing of a three-dimensional matrix. The reduction of this problem to the problem of finding a maximum flow in the multiple network of integer-valued balancing and the algorithm for this problem are suggested. Also, the comparative characteristic of two algorithms of integer-valued balancing is made according to the results of the computing experiments. NP-completeness of the problem of integer-valued balancing of a three-dimensional matrix is proved in the article. The problem of minimization of the errors of rounding off in the problem of integer-valued balancing is explored.

Keywords: integer-valued balancing, three-dimensional matrices, multiple networks, multiple flows, generalized labeling algorithm, first Gomory algorithm, $NP$-completeness, minimization of the errors of rounding off.

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Document Type: Article
UDC: 519.854.2
Received: 22.04.2010

Citation: V. S. Rublev, A. V. Smirnov, “The problem of integer-valued balancing of a three-dimensional matrix and algorithms of its solution”, Model. Anal. Inform. Sist., 17:2 (2010), 72–98

Citation in format AMSBIB
\Bibitem{RubSmi10}
\by V.~S.~Rublev, A.~V.~Smirnov
\paper The problem of integer-valued balancing of a three-dimensional matrix and algorithms of its solution
\jour Model. Anal. Inform. Sist.
\yr 2010
\vol 17
\issue 2
\pages 72--98
\mathnet{http://mi.mathnet.ru/mais5}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fedotova N.P., “Uniekstremalnye giperploskosti konechnomernykh diskretnykh prostranstv”, Yaroslavskii pedagogicheskii vestnik, 3:1 (2011), 7  elib
    2. Rublev V.S., Smirnov A.V., “Potoki v kratnykh setyakh”, Yaroslavskii pedagogicheskii vestnik, 3:2 (2011), 60–60  elib
    3. A. V. Smirnov, “Nekotorye klassy razreshimosti zadachi tselochislennogo sbalansirovaniya trekhmernoi matritsy s ogranicheniyami vtorogo roda”, Model. i analiz inform. sistem, 20:2 (2013), 54–69  mathnet
    4. A. V. Smirnov, “Evristicheskie algoritmy dlya zadachi tselochislennogo sbalansirovaniya trekhmernoi matritsy s ogranicheniyami vtorogo roda”, Model. i analiz inform. sistem, 21:4 (2014), 132–147  mathnet
    5. A. V. Smirnov, “Zadacha o naibolshem kratnom potoke v delimoi seti i ee chastnye sluchai”, Model. i analiz inform. sistem, 22:4 (2015), 533–545  mathnet  crossref  mathscinet  elib
    6. A. V. Smirnov, “Setevaya model dlya zadachi tselochislennogo sbalansirovaniya chetyrekhmernoi matritsy”, Model. i analiz inform. sistem, 23:4 (2016), 466–478  mathnet  crossref  mathscinet  elib
    7. A. V. Smirnov, “Zadacha o kratchaishem puti v kratnom grafe”, Model. i analiz inform. sistem, 24:6 (2017), 788–801  mathnet  crossref  elib
    8. Smirnov A.V., “Network Model For the Problem of Integer Balancing of a Four-Dimensional Matrix”, Autom. Control Comp. Sci., 51:7 (2017), 558–566  crossref  isi  scopus
    9. A. V. Smirnov, “Ostovnoe derevo v delimom kratnom grafe”, Model. i analiz inform. sistem, 25:4 (2018), 388–401  mathnet  crossref  elib
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