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A general greedy approach to construct coverings of compact metric spaces bymetric balls is given and analyzed. The analysis is a continuous version ofChvatal's analysis of the greedy algorithm for the weighted set cover problem.The approach is demonstrated in an exemplary manner to construct efficientcoverings of the n-dimensional sphere and n-dimensional Euclidean space to giveshort and transparent proofs of several best known bounds obtained fromdeterministic constructions in the literature on sphere coverings.

Covering compact metric spaces greedily