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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 242–248 (Mi zvmmf4823)  

This article is cited in 5 scientific papers (total in 5 papers)

Estimates for the average number of iterations for some algorithms for solving the set packing problem

L. A. Zaozerskaya, A. A. Kolokolov

Omsk Division of the Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia

Abstract: The set packing problem and the corresponding integer linear programming model are considered. Using the regular partitioning method and available estimates of the average number of feasible solutions of this problem, upper bounds on the average number of iterations for the first Gomory method, the branch-and-bound method (the Land and Doig scheme), and the $L$-class enumeration algorithm are obtained. The possibilities of using the proposed approach for other integer programs are discussed.

Key words: discrete optimization, integer programming, set packing problem ,Gomory cut, $L$-partitioning, enumeration of $L$-classes.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:2, 231–237

Bibliographic databases:

UDC: 519.658
Received: 26.02.2009
Revised: 27.07.2009

Citation: L. A. Zaozerskaya, A. A. Kolokolov, “Estimates for the average number of iterations for some algorithms for solving the set packing problem”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 242–248; Comput. Math. Math. Phys., 50:2 (2010), 231–237

Citation in format AMSBIB
\by L.~A.~Zaozerskaya, A.~A.~Kolokolov
\paper Estimates for the average number of iterations for some algorithms for solving the set packing problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 2
\pages 242--248
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 2
\pages 231--237

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    This publication is cited in the following articles:
    1. L. A. Zaozerskaya, A. A. Kolokolov, N. G. Gofman, “Otsenki srednego chisla iteratsii dlya algoritmov resheniya nekotorykh zadach buleva programmirovaniya”, Diskretn. analiz i issled. oper., 18:3 (2011), 49–64  mathnet  mathscinet  zmath
    2. A. A. Kolokolov, T. G. Orlovskaya, M. F. Rybalka, “Analysis of integer programming algorithms with $L$-partition and unimodular transformations”, Autom. Remote Control, 73:2 (2012), 369–380  mathnet  crossref  isi
    3. A. A. Kolokolov, T. G. Orlovskaya, “Issledovanie nekotorykh zadach tselochislennogo programmirovaniya na osnove unimodulyarnykh preobrazovanii i regulyarnykh razbienii”, Tr. IMM UrO RAN, 19, no. 2, 2013, 193–202  mathnet  mathscinet  elib
    4. A. A. Kolokolov, L. A. Zaozerskaya, “Finding and analysis of estimation of the number of iterations in integer programming algorithms using the regular partitioning method”, Russian Math. (Iz. VUZ), 58:1 (2014), 35–46  mathnet  crossref
    5. Kolokolov A.A., Zaozerskaya L.A., “Analysis of Some Cutting Plane Algorithms of Integer Programming”, 2016 Dynamics of Systems, Mechanisms and Machines (Dynamics), Dynamics of Systems Mechanisms and Machines, ed. Kosykh A., IEEE, 2016  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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