Geodesic
On Reserve and Double Covering Problems for the Sets With Non-Euclidean Metrics
Yugoslav journal of operations research, Tome 29 (2019) no. 1, p. 69 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The article is devoted to Circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Here we focus on a more complex problem of constructing reserve and multiply coverings. Besides that, we consider the case where covering set is a multiply-connected domain. The numerical algorithms based on fundamental physical principles, established by Fermat and Huygens, are suggested and implemented. This allows us to solve the problems for the cases of non-convex sets and non-Euclidean metrics. Preliminary results of numerical experiments are presented and discussed. Calculations show the applicability of the proposed approach.
Classification : 65K10, 90B06
Keywords: Covering Problem, Fermat Principle, Huygens Principle, Wave Front, Non-Euclidean Metric, Reserve Covering, Double Covering, Computational Experiment 
@article{YJOR_2019_29_1_a4,
     author = {Anna Lempert and Alexander Kazakov and Quang Mung Le},
     title = {On {Reserve} and {Double} {Covering} {Problems} for the {Sets} {With} {Non-Euclidean} {Metrics}},
     journal = {Yugoslav journal of operations research},
     pages = {69 },
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2019_29_1_a4/}
}
TY  - JOUR
AU  - Anna Lempert
AU  - Alexander Kazakov
AU  - Quang Mung Le
TI  - On Reserve and Double Covering Problems for the Sets With Non-Euclidean Metrics
JO  - Yugoslav journal of operations research
PY  - 2019
SP  - 69 
VL  - 29
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/YJOR_2019_29_1_a4/
LA  - en
ID  - YJOR_2019_29_1_a4
ER  - 
%0 Journal Article
%A Anna Lempert
%A Alexander Kazakov
%A Quang Mung Le
%T On Reserve and Double Covering Problems for the Sets With Non-Euclidean Metrics
%J Yugoslav journal of operations research
%D 2019
%P 69 
%V 29
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/YJOR_2019_29_1_a4/
%G en
%F YJOR_2019_29_1_a4
Anna Lempert; Alexander Kazakov; Quang Mung Le. On Reserve and Double Covering Problems for the Sets With Non-Euclidean Metrics. Yugoslav journal of operations research, Tome 29 (2019) no. 1, p. 69 . http://geodesic.mathdoc.fr/item/YJOR_2019_29_1_a4/