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Avtomatika i Telemekhanika, 2012, Issue 3, Pages 79–90 (Mi at3779)  

This article is cited in 10 scientific papers (total in 10 papers)

Applications of Mathematical Programming

Approximating sets on a plane with optimal sets of circles

P. D. Lebedev, A. V. Ushakov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
References:
Abstract: We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 06.06.2011
English version:
Automation and Remote Control, 2012, Volume 73, Issue 3, Pages 485–493
DOI: https://doi.org/10.1134/S0005117912030071
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. D. Lebedev, A. V. Ushakov, “Approximating sets on a plane with optimal sets of circles”, Avtomat. i Telemekh., 2012, no. 3, 79–90; Autom. Remote Control, 73:3 (2012), 485–493
Citation in format AMSBIB
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\by P.~D.~Lebedev, A.~V.~Ushakov
\paper Approximating sets on a~plane with optimal sets of circles
\jour Avtomat. i Telemekh.
\yr 2012
\issue 3
\pages 79--90
\mathnet{http://mi.mathnet.ru/at3779}
\transl
\jour Autom. Remote Control
\yr 2012
\vol 73
\issue 3
\pages 485--493
\crossref{https://doi.org/10.1134/S0005117912030071}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000301791500007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862135254}
Linking options:
  • https://www.mathnet.ru/eng/at3779
  • https://www.mathnet.ru/eng/at/y2012/i3/p79
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
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    Abstract page:628
    Full-text PDF :246
    References:113
    First page:18
     
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