Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
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


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 4, Pages 757–769 (Mi zvmmf4867)  
This article is cited in 25 scientific papers (total in 25 papers)

Optimization of a multiple covering of a bounded set with circles

Sh. I. Galiev, M. A. Karpova

Kazan State Technical University, ul. K. Marksa 10, Kazan, 420111 Russia
Full-text PDF (279 kB) Citations (25)
References:
PDF
HTML
Abstract: Numerical algorithms for the optimization of multiple covering of a bounded set $G$ in the plane $P$ with equal circles are proposed. The variants in which $G$ is a connected bounded set in $P$ or a finite set in $P$ are considered. The circles may be centered at arbitrary points of $G$ or at points belonging to a given set. Minimization of the radius of the given number of circles and minimization of the number of circles of a given radius are considered. Models and solution algorithms are described, and estimates of the solutions provided by most variants are given. Numerical results are presented.
Key words: numerical methods for covering optimization, multiple covering with circles, minimal covering of a set with circles.
Received: 22.12.2008
Revised: 19.10.2009
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 4, Pages 721–732
DOI: https://doi.org/10.1134/S0965542510040135
Bibliographic databases:
Document Type: Article
UDC: 519.6:519.147
Language: Russian
Citation: Sh. I. Galiev, M. A. Karpova, “Optimization of a multiple covering of a bounded set with circles”, Zh. Vychisl. Mat. Mat. Fiz., 50:4 (2010), 757–769; Comput. Math. Math. Phys., 50:4 (2010), 721–732
Citation in format AMSBIB
\Bibitem{GalKar10}
\by Sh.~I.~Galiev, M.~A.~Karpova
\paper Optimization of a multiple covering of a bounded set with circles
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 4
\pages 757--769
\mathnet{http://mi.mathnet.ru/zvmmf4867}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2761710}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2010CMMPh..50..721G}
\transl
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 4
\pages 721--732
\crossref{https://doi.org/10.1134/S0965542510040135}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000277337600013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952153528}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf4867
  • https://www.mathnet.ru/eng/zvmmf/v50/i4/p757
    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:1189
    Full-text PDF :423
    References:81
    First page:33
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024