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Diskretn. Anal. Issled. Oper., 2019, Volume 26, Number 1, Pages 33–54 (Mi da916)  

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

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

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.

DOI: https://doi.org/10.33048/daio.2019.26.609

Full text: PDF file (433 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:1, 43–53

UDC: 519.6:519.147
Received: 07.02.2018
Revised: 22.10.2018
Accepted:28.11.2018

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
\Bibitem{GalKho19}
\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}
\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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    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. Sh. I. Galiev, A. V. Khor'kov, “Linear and nonlinear optimization models of multiple covering of a bounded plane domain with circles”, Kompyuternye issledovaniya i modelirovanie, 11:6 (2019), 1101–1110  mathnet  crossref
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