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Tropical bisectors and Voronoi diagrams

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arxiv 1906.10950 v4 pith:AMPFXWNU submitted 2019-06-26 math.CO math.MG

Francisco Criado , Michael Joswig , Francisco Santos This is my paper · ORCID
classification math.COmath.MG
keywords bisectorstropicaldiagramsvoronoipointsresultsalgorithmsarbitrary
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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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Cited by 1 Pith paper

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  1. Tropical Ehrhart Theory and Tropical Volume

    math.MG 2019-08 accept novelty 7.0 of 10

    A new tropical volume, called the tropical barycentric volume, is defined from a tropical Ehrhart polynomial and is shown to satisfy the standard volume axioms and to be upper bounded by the dequantized tropical volume.

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