Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{UshLeb15}
\by V.~N.~Ushakov, P.~D.~Lebedev
\paper Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 2
\pages 276--288
\mathnet{http://mi.mathnet.ru/timm1188}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3408896}
\elib{https://elibrary.ru/item.asp?id=23607938}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 293
\issue , suppl. 1
\pages 225--237
\crossref{https://doi.org/10.1134/S0081543816050205}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000380005200020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84978472236}
Linking options:
  • https://www.mathnet.ru/eng/timm1188
  • https://www.mathnet.ru/eng/timm/v21/i2/p276
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:466
    Full-text PDF :131
    References:58
    First page:10
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024