sphere packing

Upper bounds for packings of spheres of several radii

  • David de Laat
  • Fernando Mário de Oliveira Filho
  • Frank Vallentin
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , , ,

    We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds for packings of spherical caps and of convex bodies through the use of semidefinite programming. We … Read more

    Disk Packing in a Square: A New Global Optimization Approach

  • Bernardetta Addis
  • Marco Locatelli
  • Fabio Schoen
    • Categories Global Optimization, Stochastic Approaches Tags , , , , ,

    We present a new computational approach to the problem of placing $n$ identical non overlapping disks in the unit square in such a way that their radius is maximized. The problem has been studied in a large number of papers, both from a theoretical and from a computational point of view. In this paper we … Read more