On the Problem of Covering a Convex Set by Equal balls in a Three-dimensional Space with a non-Euclidean Metric

The paper considers the problem of covering a closed convex set with equal balls. To solve it, we proposed a new numerical algorithm based on the optical-geometric approach. The feature of the algorithm is to replace the distance between objects with the time of movement between them. This allows us to apply an approach based on the physical principles of light wave propagation. The proposed mathematical apparatus and software are useful for modeling since they allow us to consider some additional assumptions and restrictions. In particular, for the sensor location problem, we can describe the situation when the sensor operating area does not have the shape of a ball due to some reason. This can help improve the accuracy of the modeling and avoid the occurrence of blind spots. For the logistics facilities, the proposed approach allows you to assess their transport accessibility and attractiveness of the location more accurately. The results of the computational experiments are presented and discussed.