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Iterative Methods for Constructing Approximations to Optimal Coverings of Nonconvex Polygons

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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 proposes algorithms for the iterative construction of optimal coverings of nonconvex flat figures using sets of circles. These algorithms are based on the procedures of dividing the figure into zones of influence of points that serve as the centers of the initial coverings and finding the Chebyshev centers of these zones. To generate the initial array of points, we use stochastic procedures based on the synthesis of optimal hexagonal grids and random vectors.

The work was supported by the Decree no. 211 of the Government of the Russian Federation, contract no. 02.A03.21.0006.

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Author information

Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

    Pavel Lebedev & Vladimir Ushakov

  2. Ural Federal University named after the first President of Russia B.N. Yeltsin, Yekaterinburg, Russia

    Pavel Lebedev & Vladimir Ushakov

Authors
  1. Pavel Lebedev
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  2. Vladimir Ushakov
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Corresponding authors

Correspondence to Pavel Lebedev or Vladimir Ushakov .

Editor information

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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Lebedev, P., Ushakov, V. (2019). Iterative Methods for Constructing Approximations to Optimal Coverings of Nonconvex Polygons. 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_19

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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