Tropical Bisectors and Voronoi Diagrams

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 Euclide...

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Detalles Bibliográficos
Autores: Criado, Francisco, Joswig, Michael, Santos, Francisco|||0000-0003-2120-9068
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/27731
Acceso en línea:https://hdl.handle.net/10902/27731
Access Level:acceso abierto
Palabra clave:Polyhedral norms
Polytropes
Randomized algorithms
Voronoi diagrams
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spelling Tropical Bisectors and Voronoi DiagramsCriado, FranciscoJoswig, MichaelSantos, Francisco|||0000-0003-2120-9068Polyhedral normsPolytropesRandomized algorithmsVoronoi diagramsIn 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.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.Springer New York LLCUniversidad de Cantabria20222022-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttps://hdl.handle.net/10902/27731Foundations of Computational Mathematics, 2022, 22, 1923-1960reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/277312026-06-02T12:39:31Z
dc.title.none.fl_str_mv Tropical Bisectors and Voronoi Diagrams
title Tropical Bisectors and Voronoi Diagrams
spellingShingle Tropical Bisectors and Voronoi Diagrams
Criado, Francisco
Polyhedral norms
Polytropes
Randomized algorithms
Voronoi diagrams
title_short Tropical Bisectors and Voronoi Diagrams
title_full Tropical Bisectors and Voronoi Diagrams
title_fullStr Tropical Bisectors and Voronoi Diagrams
title_full_unstemmed Tropical Bisectors and Voronoi Diagrams
title_sort Tropical Bisectors and Voronoi Diagrams
dc.creator.none.fl_str_mv Criado, Francisco
Joswig, Michael
Santos, Francisco|||0000-0003-2120-9068
author Criado, Francisco
author_facet Criado, Francisco
Joswig, Michael
Santos, Francisco|||0000-0003-2120-9068
author_role author
author2 Joswig, Michael
Santos, Francisco|||0000-0003-2120-9068
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Polyhedral norms
Polytropes
Randomized algorithms
Voronoi diagrams
topic Polyhedral norms
Polytropes
Randomized algorithms
Voronoi diagrams
description 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.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10902/27731
url https://hdl.handle.net/10902/27731
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer New York LLC
publisher.none.fl_str_mv Springer New York LLC
dc.source.none.fl_str_mv Foundations of Computational Mathematics, 2022, 22, 1923-1960
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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