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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 1, Pages 112–128 (Mi vngu330)  

Multilevel Regular Coverings of the Plane by Discs

I. I. Takhonov

Novosibirsk State University

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.

Full text: PDF file (433 kB)
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English version:
Journal of Mathematical Sciences, 2015, 211:6, 886–901

Document Type: Article
UDC: 519.8
Received: 24.12.2012

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}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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