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On the Structure of Higher Order Voronoi Cells

Author

Listed:
  • Juan Enrique Martínez-Legaz

    (Universitat Autònoma de Barcelona, and BGSMath)

  • Vera Roshchina

    (UNSW Sydney)

  • Maxim Todorov

    (UDLAP
    Institute of Mathematics and Informatics, BAS)

Abstract

The classic Voronoi cells can be generalized to a higher order version by considering the cells of points for which a given k-element subset of the set of sites consists of the k closest sites. We study the structure of the k-order Voronoi cells and illustrate our theoretical findings with a case study of two-dimensional higher order Voronoi cells for four points.

Suggested Citation

  • Juan Enrique Martínez-Legaz & Vera Roshchina & Maxim Todorov, 2019. "On the Structure of Higher Order Voronoi Cells," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 24-49, October.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01555-2
    DOI: 10.1007/s10957-019-01555-2
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    Cited by:

    1. Mercè Claverol & Andrea de las Heras Parrilla & Clemens Huemer & Alejandra Martínez-Moraian, 2024. "The edge labeling of higher order Voronoi diagrams," Journal of Global Optimization, Springer, vol. 90(2), pages 515-549, October.
    2. Stegehuis, Clara & Weedage, Lotte, 2022. "Degree distributions in AB random geometric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).

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