@article{10902/27731,
year = {2022},
url = {https://hdl.handle.net/10902/27731},
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.},
organization = {F. Criado has been supported by Berlin Mathematical School and Einstein Foundation Berlin (EVF-2015-230). M. Joswig has been supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - The Berlin Mathematics Research Center MATH+ (EXC-2046/1, Project ID 390685689); “Symbolic Tools in Mathematics and their Application” (TRR 195/2, Project-ID 286237555); “Facets of Complexity” (GRK 2434). F. Santos has been supported by the Einstein Foundation Berlin (EVF-2015-230) and by Grants MTM2017-83750-P/AEI/10.13039/ 501100011033 and PID2019-106188GB-I00/AEI/10.13039/501100011033 of the Spanish State Research Agency.},
publisher = {Springer New York LLC},
publisher = {Foundations of Computational Mathematics, 2022, 22, 1923-1960},
title = {Tropical Bisectors and Voronoi Diagrams},
author = {Criado, Francisco and Joswig, Michael and Santos, Francisco},
}