Covering compact metric spaces greedily
Metric Geometry
2019-11-07 v2 Computational Geometry
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.
Cite
@article{arxiv.1710.06002,
title = {Covering compact metric spaces greedily},
author = {Jan Hendrik Rolfes and Frank Vallentin},
journal= {arXiv preprint arXiv:1710.06002},
year = {2019}
}
Comments
(v2) 10 pages, minor revision, accepted in Acta Math. Hungar