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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 1, Pages 84–102 (Mi da762)  

This article is cited in 1 scientific paper (total in 1 paper)

On some problems of covering the plane with circles

I. I. Takhonov

Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: We study regular circle plane coverings in which the plane is split into regular polygons (tiles) and all the tiles are covered identically. The density of a regular covering can be calculated by dividing total area of circles covering a tile by the tile's area. We focus on regular coverings containing circles of four, five and six different radii. We prove optimality of several known coverings in their classes, find tight lower bounds for densities depending on radii of circles in a covering, and propose new coverings which are optimal in their classes under some additional constraints on radii. Ill. 14, bibliogr. 15.

Keywords: plane covering, density, regular covering, wireless sensor network.

Full text: PDF file (402 kB)
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Bibliographic databases:
UDC: 519.8
Received: 29.12.2012
Revised: 19.04.2013

Citation: I. I. Takhonov, “On some problems of covering the plane with circles”, Diskretn. Anal. Issled. Oper., 21:1 (2014), 84–102

Citation in format AMSBIB
\Bibitem{Tak14}
\by I.~I.~Takhonov
\paper On some problems of covering the plane with circles
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 1
\pages 84--102
\mathnet{http://mi.mathnet.ru/da762}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3288383}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sh. I. Galiev, A. V. Khorkov, “Mnogokratnye pokrytiya krugami ravnostoronnego treugolnika, kvadrata i kruga”, Diskretn. analiz i issled. oper., 22:6 (2015), 5–28  mathnet  crossref  mathscinet  elib
  • Дискретный анализ и исследование операций
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