Research article Special Issues

Optimal covering points and curves

  • Received: 26 June 2019 Accepted: 10 July 2019 Published: 03 January 2020
  • MSC : 11H31, 49M15

  • We consider the optimal covering of the unit square by N circles. By optimal, we mean the covering that can be done with N circles of minimum radius. Equivalently, we study the problem of the optimal placement of N points such that the maximum over all locations in the square of the distance of the location to the set of points is minimized. We propose a new algorithm that can identify optimal coverings to high precision. Numerical predictions of optimal coverings for N = 1 to 16 agree with the best known results in the literature. We use the optimal designs in approximations to two novel, related problems involving the optimal placement of curves.

    Citation: Justin Tzou, Brian Wetton. Optimal covering points and curves[J]. AIMS Mathematics, 2019, 4(6): 1796-1804. doi: 10.3934/math.2019.6.1796

    Related Papers:

  • We consider the optimal covering of the unit square by N circles. By optimal, we mean the covering that can be done with N circles of minimum radius. Equivalently, we study the problem of the optimal placement of N points such that the maximum over all locations in the square of the distance of the location to the set of points is minimized. We propose a new algorithm that can identify optimal coverings to high precision. Numerical predictions of optimal coverings for N = 1 to 16 agree with the best known results in the literature. We use the optimal designs in approximations to two novel, related problems involving the optimal placement of curves.



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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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