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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 4, Pages 716–728 (Mi zvmmf10886)  

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

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

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.

DOI: https://doi.org/10.1134/S0044466919040033


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:4, 676–687

Bibliographic databases:

UDC: 519.7
Received: 24.10.2017
Revised: 14.11.2018
Accepted:14.11.2018

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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\paper Optimization of the number and arrangement of circles of two radii for forming a $k$-covering of a bounded set
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
\vol 59
\issue 4
\pages 716--728
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\crossref{https://doi.org/10.1134/S0044466919040033}
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\transl
\jour Comput. Math. Math. Phys.
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\vol 59
\issue 4
\pages 676--687
\crossref{https://doi.org/10.1134/S0965542519040031}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. L. Kazakov, A. A. Lempert, K. M. Le, “O zadachakh postroeniya mnogokratnykh pokrytii i upakovok v dvumernom neevklidovom prostranstve”, UBS, 81 (2019), 6–25  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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