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Diskretn. Anal. Issled. Oper., 2017, Volume 24, Number 2, Pages 87–106 (Mi da871)  

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

Proof of covering minimality by generalizing the notion of independence

I. P. Chukhrov

Institute of Computer Aided Design RAS, 19/18 Vtoraya Brestskaya St., 123056 Moscow, Russia

Abstract: A method is proposed for obtaining lower bounds for the length of the shortest cover and complexity of the minimal cover based on the notion of independent family of sets. For the problem of minimization of Boolean functions, we provide the functions and construct coverings by faces of the set of unit vertices for which the suggested lower bounds can be achieved in the case of five or more variables. The lower bounds, based on independent sets, are unreachable and cannot be used as sufficient conditions for minimality of such functions. Bibliogr. 11.

Keywords: set covering problem, complexity, shortest cover, minimum cover, independent set, lower bound, condition of minimality.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00593а


DOI: https://doi.org/10.17377/daio.2017.24.540

Full text: PDF file (347 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2017, 11:2, 193–203

UDC: 519.157.1
Received: 27.04.2016
Revised: 17.11.2016

Citation: I. P. Chukhrov, “Proof of covering minimality by generalizing the notion of independence”, Diskretn. Anal. Issled. Oper., 24:2 (2017), 87–106; J. Appl. Industr. Math., 11:2 (2017), 193–203

Citation in format AMSBIB
\Bibitem{Chu17}
\by I.~P.~Chukhrov
\paper Proof of covering minimality by generalizing the notion of independence
\jour Diskretn. Anal. Issled. Oper.
\yr 2017
\vol 24
\issue 2
\pages 87--106
\mathnet{http://mi.mathnet.ru/da871}
\crossref{https://doi.org/10.17377/daio.2017.24.540}
\elib{http://elibrary.ru/item.asp?id=29275516}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 2
\pages 193--203
\crossref{https://doi.org/10.1134/S1990478917020053}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019768117}


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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. I. P. Chukhrov, “On the complexity of minimizing quasicyclic Boolean functions”, J. Appl. Industr. Math., 12:3 (2018), 426–441  mathnet  crossref  crossref  elib
  • Дискретный анализ и исследование операций
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