Covering compact metric spaces greedily
arXiv:1710.06002 · doi:10.1007/s10474-018-0829-4
Abstract
A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvatal's analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the n-dimensional sphere and n-dimensional Euclidean space to give short and transparent proofs of several best known bounds obtained from deterministic constructions in the literature on sphere coverings.
(v2) 10 pages, minor revision, accepted in Acta Math. Hungar