This article is cited in 5 papers

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.

UDC: 519.8

Received: 29.12.2012
Revised: 19.04.2013

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