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Diskretnyi Analiz i Issledovanie Operatsii, 2017, Volume 24, Issue 2, Pages 87–106
DOI: https://doi.org/10.17377/daio.2017.24.540 (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
Full-text PDF (347 kB) Citations (1) English version article
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DOI: https://doi.org/10.17377/daio.2017.24.540
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
Received: 27.04.2016
Revised: 17.11.2016
English version:
Journal of Applied and Industrial Mathematics, 2017, Volume 11, Issue 2, Pages 193–203
DOI: https://doi.org/10.1134/S1990478917020053
Bibliographic databases:
Document Type: Article
UDC: 519.157.1
Language: Russian
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{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019768117}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Дискретный анализ и исследование операций
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