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arXiv · 1906.10950

Tropical bisectors and Voronoi diagrams

Francisco Criado·Michael Joswig·Francisco Santos
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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.

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Francisco Criado, Michael Joswig, Francisco Santos. 2021-09-14. Tropical bisectors and Voronoi diagrams. https://doi.org/10.1007/s10208-021-09538-4

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