On farthest Voronoi cells

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 corresp...

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Detalles Bibliográficos
Autores: Goberna Torrent, Miguel Angel, Martínez Legaz, Juan Enrique|||0000-0002-6845-6202, Todorov, Maxim
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:224364
Acceso en línea:https://ddd.uab.cat/record/224364
https://dx.doi.org/urn:doi:10.1016/j.laa.2019.09.002
Access Level:acceso abierto
Palabra clave:Farthest Voronoi cells
Linear inequality systems
Boundedly exposed points
Descripción
Sumario: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.