Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sib. J. Pure and Appl. Math.:
Year:
Volume:
Issue:
Page:
Find




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

Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2014, Volume 14, Issue 1, Pages 112–128 (Mi vngu330)  
Multilevel Regular Coverings of the Plane by Discs

I. I. Takhonov

Novosibirsk State University
Full-text PDF (433 kB)
References:
PDF
HTML
Abstract: In this paper, the problem of the least dense regular covering the plane with disks of different radii is discussed. The author generalizes different types of regular coverings and introduces a new one, the “multilevel” covering. The bounds for these coverings densities are obtained and a three-level covering with density $\approx 1.083$ is proposed.
Keywords: covering the plane by discs, wireless sensor networks.
Received: 24.12.2012
English version:
Journal of Mathematical Sciences, 2015, Volume 211, Issue 6, Pages 886–901
DOI: https://doi.org/10.1007/s10958-015-2642-8
Document Type: Article
UDC: 519.8
Language: Russian
Citation: I. I. Takhonov, “Multilevel Regular Coverings of the Plane by Discs”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:1 (2014), 112–128; J. Math. Sci., 211:6 (2015), 886–901
Citation in format AMSBIB
\Bibitem{Tak14}
\by I.~I.~Takhonov
\paper Multilevel Regular Coverings of the Plane by Discs
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 1
\pages 112--128
\mathnet{http://mi.mathnet.ru/vngu330}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 211
\issue 6
\pages 886--901
\crossref{https://doi.org/10.1007/s10958-015-2642-8}
Linking options:
  • https://www.mathnet.ru/eng/vngu330
  • https://www.mathnet.ru/eng/vngu/v14/i1/p112
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025