Efficient Covering of Thin Convex Domains Using Congruent Discs

Shai Gul and Reuven Cohen
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Shai Gul: Department of Applied Mathematics, Holon Institute of Technology, Holon 5810201, Israel
Reuven Cohen: Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel

Mathematics, 2021, vol. 9, issue 23, 1-10

Abstract: We present efficient strategies for covering classes of thin domains in the plane using unit discs. We start with efficient covering of narrow domains using a single row of covering discs. We then move to efficient covering of general rectangles by discs centered at the lattice points of an irregular hexagonal lattice. This optimization uses a lattice that leads to a covering using a small number of discs. We compare the bounds on the covering using the presented strategies to the bounds obtained from the standard honeycomb covering, which is asymptotically optimal for fat domains, and show the improvement for thin domains.

Keywords: covering; thin domains; optimal placement (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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