On reserve and double covering problems for the sets with non-Euclidean metrics

Anna Lempert, Alexander Kazakov, Quang Le
2018 Yugoslav Journal of Operations Research  
The article is devoted to Circle covering problem for a bounded set in a twodimensional 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
more » ... 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.
doi:10.2298/yjor171112010l fatcat:rfbonojz55c2hjj7nliw77cdie