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Solving Circle Packing Problem by Neural Gas

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Mendel 2015 (ICSC-MENDEL 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 378))

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Abstract

This paper considers the problem of finding the densest packing of N (N = 1, 2, …) equal non-overlapping circles in a circle. This and similar packing problems in 2D or 3D space can be considered as a simplified version of various real world problems as container loading, sensor network layout or placing of facilities and therefore it has been thoroughly studied by mathematicians, computer scientists and in operations research. For most problems with smaller N, whether for packing in a circle, square or a triangle, or packing of spheres into three dimensional objects, there have been found provably optimal solutions, and a fierce competition exists to find the most effective algorithm and solutions for higher values of N. In this paper we are not trying to compete with these achievements, but we are trying to experimentally examine a possibility to use a special type of neural network, specifically the neural gas method, to solve such a problem. Experiments show, that the neural gas approach is applicable to this kind of problem and provides reasonable though slightly suboptimal results.

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Acknowledgments

This contribution was supported by Grant Agency VEGA SR under the grant 1/0458/13.

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Authors and Affiliations

  1. Faculty of Natural Sciences, University of SS. Cyril and Methodius in Trnava, 917 01, Trnava, Slovak Republic

    Jiri Pospichal

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  1. Jiri Pospichal
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Correspondence to Jiri Pospichal .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Department of Applied Computer Science, Brno University of Technology, Brno, Czech Republic

    Radek Matoušek

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Pospichal, J. (2015). Solving Circle Packing Problem by Neural Gas. In: Matoušek, R. (eds) Mendel 2015. ICSC-MENDEL 2016. Advances in Intelligent Systems and Computing, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-319-19824-8_23

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  • DOI: https://doi.org/10.1007/978-3-319-19824-8_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19823-1

  • Online ISBN: 978-3-319-19824-8

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