Algorithms of optimal packing construction for planar compact sets


  • A.L. Kazakov Matrosov Institute for System Dynamics and Control Theory of SB RAS (IDSTU SB RAS)
  • P.D. Lebedev N.N. Krasovskii Institute of Mathematics and Mechanics of UB RAS (IMM UB RAS)



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


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.

Author Biographies

A.L. Kazakov

P.D. Lebedev


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How to Cite

Казаков А.Л., Лебедев П.Д. Algorithms of Optimal Packing Construction for Planar Compact Sets // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 307-317. doi 10.26089/NumMet.v16r230



Section 1. Numerical methods and applications