  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.
