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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 4, Pages 757–769 (Mi zvmmf4867)  
This article is cited in 25 scientific papers (total in 25 papers)

Optimization of a multiple covering of a bounded set with circles

Sh. I. Galiev, M. A. Karpova

Kazan State Technical University, ul. K. Marksa 10, Kazan, 420111 Russia
Full-text PDF (279 kB) Citations (25)
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Abstract: Numerical algorithms for the optimization of multiple covering of a bounded set $G$ in the plane $P$ with equal circles are proposed. The variants in which $G$ is a connected bounded set in $P$ or a finite set in $P$ are considered. The circles may be centered at arbitrary points of $G$ or at points belonging to a given set. Minimization of the radius of the given number of circles and minimization of the number of circles of a given radius are considered. Models and solution algorithms are described, and estimates of the solutions provided by most variants are given. Numerical results are presented.
Key words: numerical methods for covering optimization, multiple covering with circles, minimal covering of a set with circles.
Received: 22.12.2008
Revised: 19.10.2009
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 4, Pages 721–732
DOI: https://doi.org/10.1134/S0965542510040135
Bibliographic databases:
Document Type: Article
UDC: 519.6:519.147
Language: Russian
Citation: Sh. I. Galiev, M. A. Karpova, “Optimization of a multiple covering of a bounded set with circles”, Zh. Vychisl. Mat. Mat. Fiz., 50:4 (2010), 757–769; Comput. Math. Math. Phys., 50:4 (2010), 721–732
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:81
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