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International Conference on Analysis of Images, Social Networks and Texts

AIST 2016: Analysis of Images, Social Networks and Texts pp 58–68Cite as

The Problem of the Optimal Packing of the Equal Circles for Special Non-Euclidean Metric

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 661))

Abstract

The optimal packing problem of equal circles (2-D spheres) in a bounded set P in a two-dimensional metric space is considered. The sphere packing problem is to find an arrangement in which the spheres fill as large proportion of the space as possible. In the case where the space is Euclidean this problem is well known, but the case of non-Euclidean metrics is studied much worse. However there are some applied problems, which lead us to use other special non-Euclidean metrics. For instance such statements appear in the logistics when we need to locate a given number of commercial facilities and to maximize the overall service area. Notice, that we consider the optimal packing problem in the case, where P is a multiply-connected domain. The special algorithm based on optical-geometric approach is suggested and implemented. The results of numerical experiment are presented and discussed.

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Acknowledgements

The reported study was particulary funded by RFBR according to the research projects No. 14-07-00222 and No. 16-06-00464.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Alexander L. Kazakov & Anna A. Lempert

  2. Irkutsk National Research Technical University, Irkutsk, Russia

    Huy L. Nguyen

Authors
  1. Alexander L. Kazakov
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  2. Anna A. Lempert
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  3. Huy L. Nguyen
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Corresponding author

Correspondence to Anna A. Lempert .

Editor information

Editors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    Dmitry I. Ignatov

  2. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Mikhail Yu. Khachay

  3. Ural Federal University, Yekaterinbug, Russia

    Valeri G. Labunets

  4. Research Computing Center, Lomonosov Moscow State University, Moscow, Russia

    Natalia Loukachevitch

  5. National Research University Higher School of Economics, St. Petersburg, Russia

    Sergey I. Nikolenko

  6. Technische Universität Darmstadt, Darmstadt, Germany

    Alexander Panchenko

  7. Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Andrey V. Savchenko

  8. Dorodnicyn Computing Centre of Russian Academy of Sciences, Moscow, Russia

    Konstantin Vorontsov

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Kazakov, A.L., Lempert, A.A., Nguyen, H.L. (2017). The Problem of the Optimal Packing of the Equal Circles for Special Non-Euclidean Metric. In: Ignatov, D., et al. Analysis of Images, Social Networks and Texts. AIST 2016. Communications in Computer and Information Science, vol 661. Springer, Cham. https://doi.org/10.1007/978-3-319-52920-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-52920-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52919-6

  • Online ISBN: 978-3-319-52920-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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