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Optimal circle covering problems and their applications

Author

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  • Balázs Bánhelyi

    ()

  • Endre Palatinus

    ()

  • Balázs Lévai

    ()

Abstract

We study a special type of circle covering problem, the complete cover of polygons by not necessarily congruent circles with prescribed centres. We introduce a branch-and-bound algorithm which is able to check whether an actual set of circles covers a given polygon. Furthermore, we present a method capable of finding the optimal cover with arbitrary precision. These techniques are based on interval arithmetic, therefore our results are numerically reliable. To demonstrate the performance of the developed optimization method, we determine the optimal cover of the unit square and an irregular polygon. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Balázs Bánhelyi & Endre Palatinus & Balázs Lévai, 2015. "Optimal circle covering problems and their applications," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 815-832, December.
  • Handle: RePEc:spr:cejnor:v:23:y:2015:i:4:p:815-832
    DOI: 10.1007/s10100-014-0362-7
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    References listed on IDEAS

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    1. T. Kubach & A. Bortfeldt & H. Gehring, 2009. "Parallel greedy algorithms for packing unequal circles into a strip or a rectangle," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(4), pages 461-477, December.
    2. Riccardo Cambini & Claudio Sodini, 2008. "A computational comparison of some branch and bound methods for indefinite quadratic programs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 139-152, June.
    3. L. Casado & I. García & B. Tóth & E. Hendrix, 2011. "On determining the cover of a simplex by spheres centered at its vertices," Journal of Global Optimization, Springer, vol. 50(4), pages 645-655, August.
    4. Elvira Antal & Tibor Csendes & János Virágh, 2013. "Nonlinear transformations for the simplification of unconstrained nonlinear optimization problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 665-684, December.
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    Cited by:

    1. Botond Bertók & Tibor Csendes & Tibor Illés, 2015. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 811-813, December.

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