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...
| Autores: | , , |
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| 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 |
| 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. |
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