Sphere Coverage in n Dimensions

Sphere Coverage in n Dimensions

Blog Article

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 Nk(a), to Shaker cover a cuboid.The first properties outline some theoretical results for the numbers Nk(a), including sub-additivity and monotony on each variable.We use then these results to establish some lower and upper bounds for Nk(a), as well as for the minimal density of spheres to achieve k-coverage.Finally, a Handbags computation is proposed to approximate the Nk(a) numbers, and some tables are produced to show them for 2D and 3D cuboids.