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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 4, Pages 716–728
DOI: https://doi.org/10.1134/S0044466919040033 (Mi zvmmf10886) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Optimization of the number and arrangement of circles of two radii for forming a $k$-covering of a bounded set

Sh. I. Galiev, A. V. Khor'kov

Tupolev Kazan National Research Technical University, Kazan, 420111 Russia
Citations (2)
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DOI: https://doi.org/10.1134/S0044466919040033
Abstract: A numerical method for investigating $k$-coverings of a convex bounded closed set with nonempty interior with circles of two given radii is proposed. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the $k$-covering of the given domain are found. Cases with constraints on the distances between the covering circle centers and problems with a variable (given) covering multiplicity are also considered. Numerical results demonstrating the effectiveness of the proposed methods are presented.
Key words: $k$-covering with circles of two radii, multiple coverings, estimation of density of a $k$-covering with circles of two radii.
Received: 24.10.2017
Revised: 14.11.2018
Accepted: 14.11.2018
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 4, Pages 676–687
DOI: https://doi.org/10.1134/S0965542519040031
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: Sh. I. Galiev, A. V. Khor'kov, “Optimization of the number and arrangement of circles of two radii for forming a $k$-covering of a bounded set”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 716–728; Comput. Math. Math. Phys., 59:4 (2019), 676–687
Citation in format AMSBIB
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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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