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Tropical Bisectors and Voronoi Diagrams

Abstract: In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors of finitely many points with respect to arbitrary polyhedral norms. For this more general scenario we show that bisectors of three points are homeomorphic to a non-empty open subset of Euclidean space, provided that certain degenerate cases are excluded. Specializing our results to tropical bisectors then yields structural results and algorithms for tropical Voronoi diagrams.

 Autoría: Criado F., Joswig M., Santos F.,

 Fuente: Foundations of Computational Mathematics, 2022, 22, 1923-1960

Editorial: Springer New York LLC

 Año de publicación: 2022

Nº de páginas: 38

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s10208-021-09538-4

ISSN: 1615-3375,1615-3383

 Proyecto español: PID2019-106188GB-I00

Url de la publicación: https://doi.org/10.1007/s10208-021-09538-4