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Diskretnyi Analiz i Issledovanie Operatsii, 2019, Volume 26, Issue 1, Pages 33–54
DOI: https://doi.org/10.33048/daio.2019.26.609 (Mi da916) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the number and arrangement of sensors for the multiple covering of bounded plane domains

Sh. I. Galiev, A. V. Khorkov

Tupolev Kazan National Research Technical University, 10 Karl Marks Street, 420011 Kazan, Russia
Full-text PDF (433 kB) Citations (2)
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DOI: https://doi.org/10.33048/daio.2019.26.609
Abstract: We propose a method for determining the number of sensors, their arrangement, and approximate lower bounds for the number of sensors for the multiple covering of an arbitrary closed bounded convex area in a plane. The problem of multiple covering is considered with restrictions on the minimal possible distances between the sensors and without such restrictions. To solve these problems, some 0–1 linear programming (LP) problems are constructed. We use a heuristic solution algorithm for 0–1 LP problems of higher dimensions. The results of numerical implementation are given and for some particular cases it is obtained that the number of sensors found can not be decreased. Tab. 1, illustr. 3, bibliogr. 42.
Keywords: wireless sensor network, multiple covering, $k$-fold covering, $k$-covering with circles of given radius, number of sensors for monitoring of given area, arrangement of sensors.
Received: 07.02.2018
Revised: 22.10.2018
Accepted: 28.11.2018
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 1, Pages 43–53
DOI: https://doi.org/10.1134/S199047891901006X
Bibliographic databases:
Document Type: Article
UDC: 519.6:519.147
Language: Russian
Citation: Sh. I. Galiev, A. V. Khorkov, “On the number and arrangement of sensors for the multiple covering of bounded plane domains”, Diskretn. Anal. Issled. Oper., 26:1 (2019), 33–54; J. Appl. Industr. Math., 13:1 (2019), 43–53
Citation in format AMSBIB
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\by Sh.~I.~Galiev, A.~V.~Khorkov
\paper On the number and arrangement of sensors for~the~multiple covering of bounded plane~domains
\jour Diskretn. Anal. Issled. Oper.
\yr 2019
\vol 26
\issue 1
\pages 33--54
\mathnet{http://mi.mathnet.ru/da916}
\crossref{https://doi.org/10.33048/daio.2019.26.609}
\elib{https://elibrary.ru/item.asp?id=41315126}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 1
\pages 43--53
\crossref{https://doi.org/10.1134/S199047891901006X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064952887}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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