Sphere Coverage in n Dimensions

Tatiana Tabirca, Fangda Zou and Sabin Tabirca ()
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Tatiana Tabirca: School of Computer Science and Information Technology, University College Cork, T12 XF62 Cork, Ireland
Fangda Zou: School of Computer Science and Information Technology, University College Cork, T12 XF62 Cork, Ireland
Sabin Tabirca: School of Computer Science and Information Technology, University College Cork, T12 XF62 Cork, Ireland

Mathematics, 2024, vol. 12, issue 23, 1-10

Abstract: This paper presents some theoretical results on the sphere coverage problem in the n -dimensional space. These results refer to the minimal number of spheres, denoted by N k ( a ) , to cover a cuboid. The first properties outline some theoretical results for the numbers N k ( a ) , including sub-additivity and monotony on each variable. We use then these results to establish some lower and upper bounds for N k ( a ) , as well as for the minimal density of spheres to achieve k -coverage. Finally, a computation is proposed to approximate the N k ( a ) numbers, and some tables are produced to show them for 2D and 3D cuboids.

Keywords: space coverage; minimal number of spheres (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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