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arXiv · 2109.13002

The edge labeling of higher order Voronoi diagrams

Mercè Claverol·Andrea de las Heras Parrilla·Clemens Huemer·Alejandra Martínez-Moraian
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Abstract

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

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Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer, Alejandra Martínez-Moraian. 2021-09-27. The edge labeling of higher order Voronoi diagrams. https://arxiv.org/abs/2109.13002

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