The edge labeling of higher order Voronoi diagrams

Mercè Claverol (), Andrea de las Heras Parrilla (), Clemens Huemer () and Alejandra Martínez-Moraian ()
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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

Journal of Global Optimization, 2024, vol. 90, issue 2, No 9, 515-549

Abstract: 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.

Keywords: Voronoi diagram; Higher order Voronoi diagram; Double cover; Edge labeling; Alternating hexagon (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01386-0

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