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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 4, Pages 88–99 (Mi vuu404)  

This article is cited in 6 scientific papers (total in 6 papers)

MATHEMATICS

Algorithms of the best approximations of the flat sets by the union of circles

P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: The article is devoted to the problem of constructing an optimal approximating circle-cover for the bounded flat set by the finite number of circles with equal radius. The problem is solved if the best $n$-net in meaning of Hausdorff metric is constructed for the considered set. Sufficient conditions of optimality of the $n$-nets are given. The best net-construction algorithm based on dividing of the set $M$ into subsets and finding their Chebyshev centers is realized. This algorithm is proved to be efficient with the examples of sets with different geometry.

Keywords: Chebyshev center, the best net, circle cover.

Full text: PDF file (260 kB)
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UDC: 514.174.3
MSC: 05B40
Received: 30.10.2013

Citation: P. D. Lebedev, A. A. Uspenskii, V. N. Ushakov, “Algorithms of the best approximations of the flat sets by the union of circles”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4, 88–99

Citation in format AMSBIB
\Bibitem{LebUspUsh13}
\by P.~D.~Lebedev, A.~A.~Uspenskii, V.~N.~Ushakov
\paper Algorithms of the best approximations of the flat sets by the union of circles
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 4
\pages 88--99
\mathnet{http://mi.mathnet.ru/vuu404}


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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. V. N. Ushakov, A. S. Lakhtin, P. D. Lebedev, “Optimization of the Hausdorff distance between sets in Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 222–238  mathnet  crossref  mathscinet  isi  elib
    2. V. N. Ushakov, P. D. Lebedev, “Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 225–237  mathnet  crossref  mathscinet  isi  elib
    3. V. N. Ushakov, P. D. Lebedev, “Algoritmy optimalnogo pokrytiya mnozhestv na ploskosti $\mathbb{R}^2$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:2 (2016), 258–270  mathnet  crossref  mathscinet  elib
    4. A. L. Kazakov, P. D. Lebedev, “Algorithms for constructing optimal $n$-networks in metric spaces”, Autom. Remote Control, 78:7 (2017), 1290–1301  mathnet  crossref  mathscinet  isi  elib
    5. P. D. Lebedev, “Iteratsionnye metody postroeniya approksimatsii optimalnykh pokrytii nevypuklykh ploskikh mnozhestv”, Chelyab. fiz.-matem. zhurn., 4:1 (2019), 5–17  mathnet  crossref  elib
    6. A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849  mathnet  crossref  crossref  mathscinet  adsnasa  isi
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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