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Acta Mathematica Hungarica

, Volume 155, Issue 1, pp 130–140 | Cite as

Covering compact metric spaces greedily

  • J. H. Rolfes
  • F. VallentinEmail author
Article

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.

Key words and phrases

geometric covering problem set cover greedy algorithm 

Mathematics Subject Classification

52C17 90C27 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität zu KölnKölnGermany

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