RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. IMI UdGU:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. IMI UdGU, 2018, Volume 52, Pages 59–74 (Mi iimi361)  

This article is cited in 1 scientific paper (total in 1 paper)

Algorithms of optimal ball packing into ellipsoids

P. D. Lebedevab, N. G. Lavrovac

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia
b Institute of Natural Sciences and Mathematics, Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
c Institute of Radioelectronics and Information Technologies, Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

Abstract: The article deals with the problem of constructing a package from a set of congruent balls into closed convex sets. As the form of containers for packaging, ellipsoids are chosen. In one case, the number of package elements is considered fixed, and the maximization of the radii of package elements is chosen as the optimization criterion. In another case, the radius of the balls is fixed and the problem of finding the package with the largest number of elements is posed. Iterative algorithms for constructing optimal packages based on the imitation of pushing their centers away from each other and from the container boundary are proposed. Algorithms are developed for constructing packages on the basis of the most dense packaging of three-dimensional space, which is a lattice of various types and their combinations. A simulation of the solution of a number of problems and visualization of results is performed.

Keywords: packing, Chebyshev center, super differential, iterative algorithm, face-centered cubic lattice.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
The work was done with the financial support of the Government of the Russian Federation, decree 211, contract no. 02.A03.21.0006.


DOI: https://doi.org/10.20537/2226-3594-2018-52-05

Full text: PDF file (4627 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 514.174.2
MSC: 05B40, 11H31
Received: 11.10.2018

Citation: P. D. Lebedev, N. G. Lavrov, “Algorithms of optimal ball packing into ellipsoids”, Izv. IMI UdGU, 52 (2018), 59–74

Citation in format AMSBIB
\Bibitem{LebLav18}
\by P.~D.~Lebedev, N.~G.~Lavrov
\paper Algorithms of optimal ball packing into ellipsoids
\jour Izv. IMI UdGU
\yr 2018
\vol 52
\pages 59--74
\mathnet{http://mi.mathnet.ru/iimi361}
\crossref{https://doi.org/10.20537/2226-3594-2018-52-05}
\elib{http://elibrary.ru/item.asp?id=36508456}


Linking options:
  • http://mi.mathnet.ru/eng/iimi361
  • http://mi.mathnet.ru/eng/iimi/v52/p59

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. L. Kazakov, A. A. Lempert, K. M. Le, “O zadachakh postroeniya mnogokratnykh pokrytii iupakovok v dvumernom neevklidovom prostranstve”, UBS, 81 (2019), 6–25  mathnet  crossref
  • Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
    Number of views:
    This page:93
    Full text:57
    References:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020