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Num. Meth. Prog., 2015, Volume 16, Issue 2, Pages 307–317 (Mi vmp542)  

This article is cited in 7 scientific papers (total in 7 papers)

Algorithms of optimal packing construction for planar compact sets

A. L. Kazakova, P. D. Lebedevb

a Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: 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.

Full text: PDF file (684 kB)
UDC: 514.174.2:519.6
Received: 27.03.2015

Citation: A. L. Kazakov, P. D. Lebedev, “Algorithms of optimal packing construction for planar compact sets”, Num. Meth. Prog., 16:2 (2015), 307–317

Citation in format AMSBIB
\by A.~L.~Kazakov, P.~D.~Lebedev
\paper Algorithms of optimal packing construction for planar compact sets
\jour Num. Meth. Prog.
\yr 2015
\vol 16
\issue 2
\pages 307--317

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    This publication is cited in the following articles:
    1. P. D. Lebedev, A. A. Uspenskii, “Postroenie funktsii optimalnogo rezultata i rasseivayuschikh linii v zadachakh bystrodeistviya s nevypuklym tselevym mnozhestvom”, Tr. IMM UrO RAN, 22, no. 2, 2016, 188–198  mathnet  crossref  mathscinet  elib
    2. V. N. Ushakov, P. D. Lebedev, N. G. Lavrov, “Algoritmy postroeniya optimalnykh upakovok v ellipsy”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:3 (2017), 67–79  mathnet  crossref  elib
    3. P. D. Lebedev, A. L. Kazakov, “Iteratsionnye metody postroeniya upakovok iz krugov razlichnogo diametra na ploskosti”, Tr. IMM UrO RAN, 24, no. 2, 2018, 141–151  mathnet  crossref  elib
    4. A. S. Shirokanev, D. V. Kirsh, N. Yu. Ilyasova, A. V. Kupriyanov, “Issledovanie algoritmov rasstanovki koagulyatov na izobrazhenie glaznogo dna”, Kompyuternaya optika, 42:4 (2018), 712–721  mathnet  crossref
    5. P. D. Lebedev, A. L. Kazakov, A. A. Lempert, “Chislennye metody postroeniya upakovok iz razlichnykh sharov v vypuklye kompakty”, Tr. IMM UrO RAN, 26, no. 2, 2020, 173–187  mathnet  crossref  elib
    6. A. L. Kazakov, A. A. Lempert, Ch. T. Ta, “O zadachakh upakovok neravnykh sharov v trekhmernom prostranstve”, UBS, 87 (2020), 47–66  mathnet  crossref
    7. P. D. Lebedev, A. L. Kazakov, “Iteratsionnye algoritmy postroeniya nailuchshikh pokrytii vypuklykh mnogogrannikov naborami razlichnykh sharov”, Tr. IMM UrO RAN, 27, no. 1, 2021, 116–129  mathnet  crossref  elib
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