Geodesic
Algorithms of optimal packing construction for planar compact sets
Numerical methods and programming, Tome 16 (2015) no. 2, pp. 307-317.

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

The best packing problem for a prescribed number of equal disks in a compact planar set with their minimally possible radius is considered. An analytical algorithm for constructing the one disk best packing in a polygon in Euclidean space based on the maximization of the distance function from the boundary is proposed. An iteration algorithm based on the previous one is developed using the splitting into subsets (Dirichlet zones) with the aid of the Voronoi diagram. A numerical algorithm for packing in a nonconvex set in non-Euclidian metrics based on the optical geometric analogy is also proposed. A number of examples are numerically solved with a large number of packing elements and for a special non-Euclidian metrics.
Keywords: disk packing, Dirichlet zone, Voronoi diagram, optical geometric method, numerical algorithm, program complex. 
@article{VMP_2015_16_2_a12,
     author = {A. L. Kazakov and P. D. Lebedev},
     title = {Algorithms of optimal packing construction for planar compact sets},
     journal = {Numerical methods and programming},
     pages = {307--317},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_2_a12/}
}
TY  - JOUR
AU  - A. L. Kazakov
AU  - P. D. Lebedev
TI  - Algorithms of optimal packing construction for planar compact sets
JO  - Numerical methods and programming
PY  - 2015
SP  - 307
EP  - 317
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2015_16_2_a12/
LA  - ru
ID  - VMP_2015_16_2_a12
ER  - 
%0 Journal Article
%A A. L. Kazakov
%A P. D. Lebedev
%T Algorithms of optimal packing construction for planar compact sets
%J Numerical methods and programming
%D 2015
%P 307-317
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2015_16_2_a12/
%G ru
%F VMP_2015_16_2_a12
A. L. Kazakov; P. D. Lebedev. Algorithms of optimal packing construction for planar compact sets. Numerical methods and programming, Tome 16 (2015) no. 2, pp. 307-317. http://geodesic.mathdoc.fr/item/VMP_2015_16_2_a12/