Algorithms for constructing optimal n-networks in metric spaces

We study optimal approximations of sets in various metric spaces with sets of balls of equal radius. We consider an Euclidean plane, a sphere, and a plane with a special non‐uniform metric. The main component in our constructions of coverings are optimal Chebyshev n‐networks and their generalizations. We propose algorithms for constructing optimal coverings based on partitioning a given set into subsets and finding their Chebyshev centers in the Euclidean metric and their counterparts in non‐Euclidean ones. Our results have both theoretical and practical value and can be used to solve problems arising in security, communication, and infrastructural logistics.