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Avtomat. i Telemekh., 2010, Issue 10, Pages 156–166 (Mi at902)  

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

Parallel and Distributed Systems

On a lower bound on the computational complexity of a parallel implementation of the branch-and-bound method

R. M. Kolpakova, M. A. Posypkinb, I. Kh. Sigalc

a Moscow State University, Moscow, Russia
b Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia
c Computer Centre, Russian Academy of Sciences, Moscow, Russia

Abstract: We study parallel complexity of the branch-and-bound method for optimization problems. We consider a standard implementation scheme for the branch-and-bound method on a parallel system, in which first only one processor is working, and then the resulting subtasks are given out to other processors. For this scheme, we give a lower bound on the parallel complexity independent of the problem. We study the complexity of this scheme for the Boolean knapsack problem. For a classical algorithmically hard example, we obtain parallel complexity bounds and show that these bounds coincide in order with each other and with the common lower bound on parallel complexity. Thus, we show that the common lower bound is achieved, in the order, for some optimization problems.

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English version:
Automation and Remote Control, 2010, 71:10, 2152–2161

Bibliographic databases:

Presented by the member of Editorial Board: А. А. Лазарев

Received: 12.01.2010

Citation: R. M. Kolpakov, M. A. Posypkin, I. Kh. Sigal, “On a lower bound on the computational complexity of a parallel implementation of the branch-and-bound method”, Avtomat. i Telemekh., 2010, no. 10, 156–166; Autom. Remote Control, 71:10 (2010), 2152–2161

Citation in format AMSBIB
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\by R.~M.~Kolpakov, M.~A.~Posypkin, I.~Kh.~Sigal
\paper On a~lower bound on the computational complexity of a~parallel implementation of the branch-and-bound method
\jour Avtomat. i Telemekh.
\yr 2010
\issue 10
\pages 156--166
\mathnet{http://mi.mathnet.ru/at902}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2779041}
\zmath{https://zbmath.org/?q=an:1243.90249}
\transl
\jour Autom. Remote Control
\yr 2010
\vol 71
\issue 10
\pages 2152--2161
\crossref{https://doi.org/10.1134/S0005117910100140}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77958460514}


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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. Kolpakov R.M., Posypkin M.A., “Estimating the Computational Complexity of One Variant of Parallel Realization of the Branch-and-Bound Method for the Knapsack Problem”, Journal of Computer and Systems Sciences International, 50:5 (2011), 756–765  crossref  mathscinet  zmath  isi  elib  scopus
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