On farthest Voronoi cells
Goberna, Miguel Ángel (Universitat d'Alacant)
Martínez Legaz, Juan Enrique (Universitat Autònoma de Barcelona)
Todorov, Maxim (Universidad de las Américas Puebla)

Data:	2019
Resum:	Given an arbitrary set T in the Euclidean space Rn, whose elements are called sites, and a particular site s, the farthest Voronoi cell of s, denoted by FT(s), consists of all points which are farther from s than from any other site. In this paper we study farthest Voronoi cells and diagrams corresponding to arbitrary (possibly infinite) sets. More in particular, we characterize, for a given arbitrary set T, those s∈T such that FT(s) is nonempty and study the geometrical properties of FT(s) in that case. We also characterize those sets T whose farthest Voronoi diagrams are tesselations of the Euclidean space, and those sets that can be written as FT(s) for some T⊂Rn and some s∈T.
Ajuts:	Ministerio de Ciencia e Innovación FEDER/PGC2018-097960-B-C22 Ministerio de Ciencia e Innovación FEDER/PGC2018-097960-B-C21
Nota:	Altres ajuts: SEV-2015-0563
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Farthest Voronoi cells ; Linear inequality systems ; Boundedly exposed points
Publicat a:	Linear Algebra and its Applications, Vol. 583 (December 2019) , p. 306-322, ISSN 0024-3795

Adreça alternativa: https://www.sciencedirect.com/science/article/abs/pii/S0024379519303787
DOI: 10.1016/j.laa.2019.09.002

Postprint 18 p, 302.4 KB

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