An equivalence class decomposition of finite metric spaces via Gromov products

dc.contributor.authorBilge, Ayşe Hümeyra
dc.contributor.authorÇelik, Derya
dc.contributor.authorKoçak, Şahin
dc.date.accessioned2020-12-22T20:15:24Z
dc.date.available2020-12-22T20:15:24Z
dc.date.issued2017
dc.departmentFakülteler, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.description.abstractLet (X, d) be a finite metric space with elements P-i, i = 1,..., n and with the distance functions d(ij) The Gromov Product of the "triangle" (P-i, P-j, P-k) with vertices P-t, P-j and P-k at the vertex Pi is defined by Delta(ijk) = 1/2(d(ij) + d(ik) - d(jk)). We show that the collection of Gromov products determines the metric. We call a metric space Delta-generic, if the set of all Gromov products at a fixed vertex P-i has a unique smallest element (for i = 1,., n). We consider the function assigning to each vertex P-i the edge {P-i, P-k} of the triangle (P-i, P-j, P-k) realizing the minimal Gromov product at P-i and we call this function the Gromov product structure of the metric space (X, d). We say two Delta-generic metric spaces (X, d) and (X, d') to be Gromov product equivalent, if the corresponding Gromov product structures are the same up to a permutation of X. For n = 3, 4 there is one (Delta-generic) Gromov equivalence class and for n = 5 there are three (Delta-generic) Gromov equivalence classes. For n = 6 we show by computer that there are 26 distinct (Delta-generic) Gromov equivalence classes. (C) 2017 Elsevier B.V. All rights reserved.en_US
dc.identifier.citation2
dc.identifier.doi10.1016/j.disc.2017.03.023en_US
dc.identifier.endpage1932en_US
dc.identifier.issn0012-365Xen_US
dc.identifier.issn1872-681Xen_US
dc.identifier.issn0012-365X
dc.identifier.issn1872-681X
dc.identifier.issue8en_US
dc.identifier.scopus2-s2.0-85018902568en_US
dc.identifier.scopusqualityQ1
dc.identifier.startpage1928en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12469/3625
dc.identifier.urihttps://doi.org/10.1016/j.disc.2017.03.023
dc.identifier.volume340en_US
dc.identifier.wosWOS:000402211100016en_US
dc.identifier.wosqualityQ3
dc.institutionauthorBilge, Ayşe Hümeyraen_US
dc.language.isoenen_US
dc.publisherElsevier Science Bven_US
dc.relation.journalDiscrete Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectFinite metric spacesen_US
dc.subjectGromov producten_US
dc.subjectWeighted graphsen_US
dc.titleAn equivalence class decomposition of finite metric spaces via Gromov productsen_US
dc.typeArticleen_US
dspace.entity.typePublication
relation.isAuthorOfPublication1b50a6b2-7290-44da-b8d5-f048fea8b315
relation.isAuthorOfPublication.latestForDiscovery1b50a6b2-7290-44da-b8d5-f048fea8b315

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