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Avtomat. i Telemekh., 2012, Issue 2, Pages 178–190 (Mi at3620)  

This article is cited in 4 scientific papers (total in 4 papers)

Integer Programming Problems

Analysis of integer programming algorithms with $L$-partition and unimodular transformations

A. A. Kolokolov, T. G. Orlovskaya, M. F. Rybalka

Omsk Affiliated Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, Russia

Abstract: We study algorithms for solving integer linear programming problems, in particular, set packing and knapsack problems. We pay special attention to algorithms of lexicographic enumeration of $L$-classes and their combinations with other approaches. We study the problems of using unimodular transformations in order to improve the structure of the problems and speed up the algorithms. We construct estimates on the number of iterations for the algorithms that take into account the specific structure of the problems in question. We also show experimental results.

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English version:
Automation and Remote Control, 2012, 73:2, 369–380

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Presented by the member of Editorial Board: . . 

Received: 06.06.2011

Citation: A. A. Kolokolov, T. G. Orlovskaya, M. F. Rybalka, “Analysis of integer programming algorithms with $L$-partition and unimodular transformations”, Avtomat. i Telemekh., 2012, no. 2, 178–190; Autom. Remote Control, 73:2 (2012), 369–380

Citation in format AMSBIB
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\by A.~A.~Kolokolov, T.~G.~Orlovskaya, M.~F.~Rybalka
\paper Analysis of integer programming algorithms with $L$-partition and unimodular transformations
\jour Avtomat. i Telemekh.
\yr 2012
\issue 2
\pages 178--190
\mathnet{http://mi.mathnet.ru/at3620}
\transl
\jour Autom. Remote Control
\yr 2012
\vol 73
\issue 2
\pages 369--380
\crossref{https://doi.org/10.1134/S0005117912020142}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862154459}


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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. A. V. Seliverstov, “On monomials in quadratic forms”, J. Appl. Industr. Math., 7:3 (2013), 431–434  mathnet  crossref  mathscinet
    2. 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
    3. 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
    4. 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
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