Geodesic
Optimization of a multiple covering of a bounded set with circles
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 757-769

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

Numerical algorithms for the optimization of multiple covering of a bounded set $G$ in the plane $P$ with equal circles are proposed. The variants in which $G$ is a connected bounded set in $P$ or a finite set in $P$ are considered. The circles may be centered at arbitrary points of $G$ or at points belonging to a given set. Minimization of the radius of the given number of circles and minimization of the number of circles of a given radius are considered. Models and solution algorithms are described, and estimates of the solutions provided by most variants are given. Numerical results are presented. 
@article{ZVMMF_2010_50_4_a12,
     author = {Sh. I. Galiev and M. A. Karpova},
     title = {Optimization of a multiple covering of a bounded set with circles},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {757--769},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a12/}
}
TY  - JOUR
AU  - Sh. I. Galiev
AU  - M. A. Karpova
TI  - Optimization of a multiple covering of a bounded set with circles
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 757
EP  - 769
VL  - 50
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a12/
LA  - ru
ID  - ZVMMF_2010_50_4_a12
ER  - 
%0 Journal Article
%A Sh. I. Galiev
%A M. A. Karpova
%T Optimization of a multiple covering of a bounded set with circles
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 757-769
%V 50
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a12/
%G ru
%F ZVMMF_2010_50_4_a12
Sh. I. Galiev; M. A. Karpova. Optimization of a multiple covering of a bounded set with circles. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 757-769. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a12/