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 Chvátal’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 constructions in the literature on sphere coverings.
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Dedicated to the 70th birthday of Tibor Bisztriczky, Gábor Fejes Tóth, and Endre Makai
The second author is partially supported by the SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics”, funded by the DFG.
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Rolfes, J.H., Vallentin, F. Covering compact metric spaces greedily. Acta Math. Hungar. 155, 130–140 (2018). https://doi.org/10.1007/s10474-018-0829-4
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DOI: https://doi.org/10.1007/s10474-018-0829-4