Covering compact metric spaces greedily
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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 phrasesgeometric covering problem set cover greedy algorithm
Mathematics Subject Classification52C17 90C27
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- 3.K. Böröczky, Jr. and G. Wintsche, Covering the sphere by equal spherical balls, in: Discrete and Computational Geometry, Algorithms Combin., vol. 25, Springer (Berlin, 2003), pp. 235–251Google Scholar
- 6.I. Dinur and D. Steurer, Analytical approach to parallel repetition, in: Proceedings of the 2014 ACM Symposium on Theory of Computing, IEEE Computer Soc. (Los Alamitos, CA, 2014), pp. 624–633Google Scholar
- 9.G. B. Folland, Real analysis. Modern Techniques and Their Application, 2nd ed., John Wiley & Sons (1999)Google Scholar
- 10.S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing, Birkhäuser/Springer (2013)Google Scholar
- 15.R. Prosanov, Chromatic numbers of spheres, arXiv:1711.03193 [math.CO], 20 pp
- 16.C. A. Rogers, Packing and Covering, Cambridge University Press (1964)Google Scholar