Tropical bisectors and Voronoi diagrams

dc.contributor.authorCriado, Francisco
dc.contributor.authorJoswig, Michael
dc.contributor.authorSantos, Francisco
dc.date.accessioned2022-10-04T09:46:40Z
dc.date.available2022-10-04T09:46:40Z
dc.date.issued2021-09-07
dc.description.abstractIn 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.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2021en
dc.identifier.eissn1615-3383
dc.identifier.issn1615-3375
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/17026
dc.identifier.urihttps://doi.org/10.14279/depositonce-15805
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherpolyhedral normsen
dc.subject.otherpolytropesen
dc.subject.otherrandomized algorithmsen
dc.subject.otherVoronoi diagramsen
dc.titleTropical bisectors and Voronoi diagramsen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s10208-021-09538-4en
dcterms.bibliographicCitation.journaltitleFoundations of Computational Mathematicsen
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.originalpublisherplaceHeidelbergen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Diskrete Mathematik / Geometriede
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Diskrete Mathematik / Geometriede
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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