"Algorithms of optimal packing construction for planar compact sets"
Kazakov A.L. and Lebedev P.D.

The best packing problem for a prescribed number of equal disks in a compact planar set with their minimally possible radius is considered. An analytical algorithm for constructing the one disk best packing in a polygon in Euclidean space based on the maximization of the distance function from the boundary is proposed. An iteration algorithm based on the previous one is developed using the splitting into subsets (Dirichlet zones) with the aid of the Voronoi diagram. A numerical algorithm for packing in a nonconvex set in non-Euclidian metrics based on the optical geometric analogy is also proposed. A number of examples are numerically solved with a large number of packing elements and for a special non-Euclidian metrics.

Keywords: disk packing, Dirichlet zone, Voronoi diagram, optical geometric method, numerical algorithm, program complex.

  • Kazakov A.L. – Matrosov Institute for System Dynamics and Control Theory, Branch of Russian Academy of Sciences; ulitsa Lermontova 134, Irkutsk, 664033, Russia; Dr. Sci., Head of Laboratory, e-mail: kazakov@icc.ru
  • Lebedev P.D. – Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Sof ’i Kovalevskoi 16, Ekaterinburg, 620990, Russia; Ph.D., Scientist, e-mail: pleb@yandex.ru