Modelirovanie i Analiz Informatsionnykh Sistem
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Model. Anal. Inform. Sist.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Modelirovanie i Analiz Informatsionnykh Sistem, 2013, Volume 20, Number 2, Pages 54–69 (Mi mais297)  

This article is cited in 2 scientific papers (total in 2 papers)

Some Solvability Classes for the Problem of Integer Balancing of a Three-Dimensional Matrix with Constraints of Second Type

A. V. Smirnov

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
Full-text PDF (990 kB) Citations (2)
References:
Abstract: The problem of integer balancing of a three-dimensional matrix with constraints of second type is studied. The elements of the inner part (all three indices are greater than zero) of the three-dimensional matrix are summed in each direction and each section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements of the inner part with the largest previous or the smallest following integer. At the same time variations of the sums of elements from that in the initial matrix should be less than 2 and the element with three zero indices should be produced with standard rules of rounding-off. Some solvability classes for this problem are defined. Also, a model of reducing this problem to a problem of finding the maximum flow in a multiple network and an algorithm for the corresponding flow problem are suggested. A polynomial algorithm for the particular case of $n=2$ is described.
Keywords: integer balancing, three-dimensional matrices, constraints of second type, solvability classes, multiple networks, multiple flows, generalized labeling algorithm.
Received: 07.10.2012
Document Type: Article
UDC: 519.854.2
Language: Russian
Citation: A. V. Smirnov, “Some Solvability Classes for the Problem of Integer Balancing of a Three-Dimensional Matrix with Constraints of Second Type”, Model. Anal. Inform. Sist., 20:2 (2013), 54–69
Citation in format AMSBIB
\Bibitem{Smi13}
\by A.~V.~Smirnov
\paper Some Solvability Classes for the Problem of Integer Balancing of a Three-Dimensional Matrix with Constraints of Second Type
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 2
\pages 54--69
\mathnet{http://mi.mathnet.ru/mais297}
Linking options:
  • https://www.mathnet.ru/eng/mais297
  • https://www.mathnet.ru/eng/mais/v20/i2/p54
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Моделирование и анализ информационных систем
    Statistics & downloads:
    Abstract page:324
    Full-text PDF :87
    References:71
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024