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The edge labeling of higher order Voronoi diagrams

Author

Listed:
  • Mercè Claverol

    (Universitat Politècnica de Catalunya)

  • Andrea de las Heras Parrilla

    (Universitat Politècnica de Catalunya)

  • Clemens Huemer

    (Universitat Politècnica de Catalunya)

  • Alejandra Martínez-Moraian

    (Universidad de Alcalá)

Abstract

We present an edge labeling of order-k Voronoi diagrams, $$V_k(S)$$ V k ( S ) , of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that $$V_k(S)$$ V k ( S ) has a small orientable cycle and path double cover, and we identify configurations that cannot appear in $$V_k(S)$$ V k ( S ) for small values of k. This paper also contains a systematic study of well-known and new properties of $$V_k(S)$$ V k ( S ) , all whose proofs only rely on elementary geometric arguments in the plane. The maybe most comprehensive study of structural properties of $$V_k(S)$$ V k ( S ) was done by D.T. Lee (On k-nearest neighbor Voronoi diagrams in the plane) in 1982. Our work reviews and extends the list of properties of higher order Voronoi diagrams.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:2:d:10.1007_s10898-024-01386-0
    DOI: 10.1007/s10898-024-01386-0
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    References listed on IDEAS

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    1. Josef Kallrath & Joonghyun Ryu & Chanyoung Song & Mokwon Lee & Deok-Soo Kim, 2021. "Near optimal minimal convex hulls of disks," Journal of Global Optimization, Springer, vol. 80(3), pages 551-594, July.
    2. 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.
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