Optimal covering points and related problems

Justin Tzou, Brian Wetton

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)379-389
Number of pages11
JournalCanadian Applied Mathematics Quarterly
Volume21
Issue number3
Publication statusPublished - 2013
Externally publishedYes

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