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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 2, Pages 276–288 (Mi timm1188)  
This article is cited in 6 scientific papers (total in 6 papers)

Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space

V. N. Ushakovab, P. D. Lebedevb

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (3908 kB) Citations (6)
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Abstract: The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented.
Keywords: Hausdorff deviation, best $n$-net, ball cover, Chebyshev center.
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 293, Issue 1, Pages 225–237
DOI: https://doi.org/10.1134/S0081543816050205
Bibliographic databases:
Document Type: Article
UDC: 514.174.3
Language: Russian
Citation: V. N. Ushakov, P. D. Lebedev, “Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 2, 2015, 276–288; Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 225–237
Citation in format AMSBIB
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\vol 21
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\pages 276--288
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\jour Proc. Steklov Inst. Math. (Suppl.)
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  • https://www.mathnet.ru/eng/timm/v21/i2/p276
    • This publication is cited in the following 6 articles:
    1. Nikolay A. Krasovskii, Alexander M. Tarasyev, Static & Dynamic Game Theory: Foundations & Applications, Frontiers of Dynamic Games, 2020, 99  crossref
    2. P. D. Lebedev, “Iteratsionnye metody postroeniya approksimatsii optimalnykh pokrytii nevypuklykh ploskikh mnozhestv”, Chelyab. fiz.-matem. zhurn., 4:1 (2019), 5–17  mathnet  crossref  elib
    3. 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  zmath  adsnasa  isi  elib
    4. 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
    5. Pavel Lebedev, Vladimir Ushakov, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 244  crossref
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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