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On the Thinnest Covering of Fixed Size Containers with Non-euclidean Metric by Incongruent Circles

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

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Abstract

The paper is devoted to the circle covering problem with unequal circles. The number of circles is given. Also, we know a function, which determines a relation between the radii of two neighboring circles. The circle covering problem is usually studied in the case when the distance between points is Euclidean. We assume that the distance is determined by means of some special metric, which, generally speaking, is not Euclidean. The special numerical algorithm is suggested and implemented. It based on optical-geometric approach, which is developed by the authors in recent years and previously used only for circles of the equal radius. The results of a computational experiment are presented and discussed.

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Acknowledgements

This work was partially supported by the Russian Foundation for Basic Research, research project No. 18-08-00604.

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory of SB RAS, 664033, Irkutsk, Russia

    Alexander Kazakov & Anna Lempert

  2. Irkutsk National Research Technical University (Baikal School of BRICS), 664074, Irkutsk, Russia

    Quang Mung Le

Authors
  1. Alexander Kazakov
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  2. Anna Lempert
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  3. Quang Mung Le
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Corresponding author

Correspondence to Anna Lempert .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Kazakov, A., Lempert, A., Le, Q.M. (2019). On the Thinnest Covering of Fixed Size Containers with Non-euclidean Metric by Incongruent Circles. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_15

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

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