Geodesic
On some problems of covering the plane with circles
Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 1, pp. 84-102

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DA_2014_21_1_a6,
     author = {I. I. Takhonov},
     title = {On some problems of covering the plane with circles},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {84--102},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2014_21_1_a6/}
}
TY  - JOUR
AU  - I. I. Takhonov
TI  - On some problems of covering the plane with circles
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2014
SP  - 84
EP  - 102
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2014_21_1_a6/
LA  - ru
ID  - DA_2014_21_1_a6
ER  - 
%0 Journal Article
%A I. I. Takhonov
%T On some problems of covering the plane with circles
%J Diskretnyj analiz i issledovanie operacij
%D 2014
%P 84-102
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2014_21_1_a6/
%G ru
%F DA_2014_21_1_a6
I. I. Takhonov. On some problems of covering the plane with circles. Diskretnyj analiz i issledovanie operacij, Tome 21 (2014) no. 1, pp. 84-102. http://geodesic.mathdoc.fr/item/DA_2014_21_1_a6/