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Diskr. Mat., 2017, Volume 29, Issue 1, Pages 51–58 (Mi dm1405)  

This article is cited in 1 scientific paper (total in 1 paper)

On the best choice of a branching variable in the subset sum problem

R. M. Kolpakovab, M. A. Posypkinb

a Lomonosov Moscow State University
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Abstract: The paper is concerned with estimating the computational complexity of the branch-and-bound method for the subset sum problem. We study the relationship between the way of decomposition of subproblems and the number of the method steps. The standard variant of the branch-and-bound method for the subset sum problem with binary branching is considered: any subproblem is decomposed into two more simple subproblems by assigning values $0$ and $1$ to a selected branching variable. It is shown that for any set of parameters of the problem the procedure of branching variables selection in the descending order of their weights is optimal.

Keywords: the branch-and-bound method, computational complexity, the subset sum problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-07-03102_а
Ministry of Education and Science of the Russian Federation НШ-8860.2016.1
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 15-07-03102 A) and the Programme of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. NSh-8860.2016.1).


DOI: https://doi.org/10.4213/dm1405

Full text: PDF file (391 kB)
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English version:
Discrete Mathematics and Applications, 2018, 28:1, 29–34

Bibliographic databases:

UDC: 519.854.2
Received: 31.10.2016

Citation: R. M. Kolpakov, M. A. Posypkin, “On the best choice of a branching variable in the subset sum problem”, Diskr. Mat., 29:1 (2017), 51–58; Discrete Math. Appl., 28:1 (2018), 29–34

Citation in format AMSBIB
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\by R.~M.~Kolpakov, M.~A.~Posypkin
\paper On the best choice of a~branching variable in the subset sum problem
\jour Diskr. Mat.
\yr 2017
\vol 29
\issue 1
\pages 51--58
\mathnet{http://mi.mathnet.ru/dm1405}
\crossref{https://doi.org/10.4213/dm1405}
\elib{http://elibrary.ru/item.asp?id=28405135}
\transl
\jour Discrete Math. Appl.
\yr 2018
\vol 28
\issue 1
\pages 29--34
\crossref{https://doi.org/10.1515/dma-2018-0004}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054968824}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. M. Kolpakov, M. A. Posypkin, “Ob effektivnoi strategii rasparallelivaniya pri reshenii zadach o summe podmnozhestv metodom vetvei i granits”, Diskret. matem., 31:4 (2019), 20–37  mathnet  crossref
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