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Diskr. Mat., 2010, Volume 22, Issue 1, Pages 58–73 (Mi dm1084)  

This article is cited in 8 scientific papers (total in 8 papers)

Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem

R. M. Kolpakov, M. A. Posypkin

Abstract: This paper is devoted to questions concerning the complexity of solution of the problem on one-dimensional Boolean knapsack by the branch and bound method. For this complexity we obtain two upper bounds. We separate the special case of the knapsack problem where the complexity is polynomially bounded by the dimension of the problem. We also obtain an upper and lower bounds for the complexity of solution by the branch and bound method of the subset sum problem which is a special case of the knapsack problem.

DOI: https://doi.org/10.4213/dm1084

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English version:
Discrete Mathematics and Applications, 2010, 20:1, 95–112

Bibliographic databases:

UDC: 519.7
Received: 01.04.2009

Citation: R. M. Kolpakov, M. A. Posypkin, “Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem”, Diskr. Mat., 22:1 (2010), 58–73; Discrete Math. Appl., 20:1 (2010), 95–112

Citation in format AMSBIB
\by R.~M.~Kolpakov, M.~A.~Posypkin
\paper Upper and lower bounds for the complexity of the branch and bound method for the knapsack problem
\jour Diskr. Mat.
\yr 2010
\vol 22
\issue 1
\pages 58--73
\jour Discrete Math. Appl.
\yr 2010
\vol 20
\issue 1
\pages 95--112

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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. Kolpakov R., Posypkin M., “The Scalability Analysis of a Parallel Tree Search Algorithm”, Optim. Lett.  crossref  mathscinet  isi
    2. Kolpakov R., Posypkin M., “The Lower Bound on Complexity of Parallel Branch-and-Bound Algorithm For Subset Sum Problem”, Numerical Computations: Theory and Algorithms (Numta-2016), AIP Conference Proceedings, 1776, eds. Sergeyev Y., Kvasov D., DellAccio F., Mukhametzhanov M., Amer Inst Physics, 2016, 050008  crossref  isi  scopus
    3. R. M. Kolpakov, M. A. Posypkin, “On the best choice of a branching variable in the subset sum problem”, Discrete Math. Appl., 28:1 (2018), 29–34  mathnet  crossref  crossref  isi  elib
    4. A. Yu. Popkov, B. S. Darkhovsky, Yu. S. Popkov, “Iterative MC-algorithm to solve the global optimization problems”, Autom. Remote Control, 78:2 (2017), 261–275  mathnet  crossref  isi  elib
    5. R. M. Kolpakov, M. A. Posypkin, Si Tu Tant Sin, “Complexity of solving the Subset Sum problem with the branch-and-bound method with domination and cardinality filtering”, Autom. Remote Control, 78:3 (2017), 463–474  mathnet  crossref  isi  elib
    6. R. M. Kolpakov, M. A. Posypkin, “Effective parallelization strategy for the solution of subset sum problems by the branch-and-bound method”, Discrete Math. Appl., 30:5 (2020), 313–325  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Dolgui A., Gafarov E., “Can a Branch and Bound Algorithm Solve All Instances of Salbp-1 Efficiently?”, IFAC PAPERSONLINE, 52:13 (2019), 2788–2791  crossref  isi
    8. Kolpakov R., Posypkin M., “Optimality and Complexity Analysis of a Branch-and-Bound Method in Solving Some Instances of the Subset Sum Problem”, Open Comput. Sci., 11:1 (2020), 116–126  crossref  isi
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