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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2019, Volume 4, Issue 1, Pages 5–17
DOI: https://doi.org/10.24411/2500-0101-2019-14101 (Mi chfmj122) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Iterative methods for approximations constructing of optimal covering for nonconvex plane sets

P. D. Lebedevab

a Ural Federal University named after the first President of Russia B. N. Yeltsin, Yekaterinburg, Russia
b Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia
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DOI: https://doi.org/10.24411/2500-0101-2019-14101
Abstract: Algorithms are offered for the iterative constructing of the optimal coverages for nonconvex plane figures by sets of discs. Their basis are procedures for dividing a figure into areas of the influence of points that serve as the centers of elements of the initial packaging, and finding the Chebyshev centers of these zones. To generate the initial array of points, stochastic procedures are applied that use the synthesis of optimal hexagonal grids and random vectors.
Keywords: optimal coverage, Chebyshev center, Voronoy diagram, Dirichlet zone, nonconvex polygon.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00221
18-31-00018
Government of the Russian Federation 02.A03.21.0006
The work is partially supported by grants 18-01-00221 and 18-31-00018_mol_a of Russian Foundation of Basic Research and by Act 211 of Government of the Russian Federation, contract 02.A03.21.0011.
Received: 23.01.2019
Revised: 27.02.2019
Bibliographic databases:
Document Type: Article
UDC: 514.174.3
Language: Russian
Citation: P. D. Lebedev, “Iterative methods for approximations constructing of optimal covering for nonconvex plane sets”, Chelyab. Fiz.-Mat. Zh., 4:1 (2019), 5–17
Citation in format AMSBIB
\Bibitem{Leb19}
\by P.~D.~Lebedev
\paper Iterative methods for approximations constructing of optimal covering for nonconvex plane sets
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2019
\vol 4
\issue 1
\pages 5--17
\mathnet{http://mi.mathnet.ru/chfmj122}
\crossref{https://doi.org/10.24411/2500-0101-2019-14101}
\elib{https://elibrary.ru/item.asp?id=37152099}
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    • This publication is cited in the following 4 articles:
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    		Chelyabinskiy Fiziko-Matematicheskiy Zhurnal
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