Multiple covering of a closed set on a plane with non-Euclidean metrics
Анна Ананьевна Лемперт, Quang Mung Le · IFAC-PapersOnLine · 2018
The article is devoted to multiple circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Such statements arise in the construction of global navigation systems like GPS and Glonass. A similar problem appears in infrastructure logistics if there is a main servicing system and it is necessary to create a duplicate system to support service in the case of failure of one or more nodes. To solve this problem, we propose a computational algorithm based on a combination of the optical-geometric approach due to Fermat and Huygens principles and Voronoi diagram. A key feature of the algorithm is the ability to deal with non-Euclidean metrics. Numerical results and a comparison with known approaches are presented and discussed.