Computing the Gromov hyperbolicity of a discrete metric space

Handle URI:
http://hdl.handle.net/10754/348468
Title:
Computing the Gromov hyperbolicity of a discrete metric space
Authors:
Fournier, Hervé; Ismail, Anas ( 0000-0002-3891-6271 ) ; Vigneron, Antoine E. ( 0000-0003-3586-3431 )
Abstract:
We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n2.69) time. It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time. We also give a (2log2⁡n)-approximation algorithm that runs in O(n2) time, based on a tree-metric embedding by Gromov. We also show that hyperbolicity at a fixed base-point cannot be computed in O(n2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication than currently known.
KAUST Department:
Visual Computing Center (VCC)
Citation:
Computing the Gromov hyperbolicity of a discrete metric space 2015, 115 (6-8):576 Information Processing Letters
Publisher:
Elsevier BV
Journal:
Information Processing Letters
Issue Date:
12-Feb-2015
DOI:
10.1016/j.ipl.2015.02.002
ARXIV:
arXiv:1210.3323
Type:
Article
ISSN:
00200190
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0020019015000198; http://arxiv.org/abs/1210.3323
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorFournier, Hervéen
dc.contributor.authorIsmail, Anasen
dc.contributor.authorVigneron, Antoine E.en
dc.date.accessioned2015-04-02T13:39:03Zen
dc.date.available2015-04-02T13:39:03Zen
dc.date.issued2015-02-12en
dc.identifier.citationComputing the Gromov hyperbolicity of a discrete metric space 2015, 115 (6-8):576 Information Processing Lettersen
dc.identifier.issn00200190en
dc.identifier.doi10.1016/j.ipl.2015.02.002en
dc.identifier.urihttp://hdl.handle.net/10754/348468en
dc.description.abstractWe give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n2.69) time. It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time. We also give a (2log2⁡n)-approximation algorithm that runs in O(n2) time, based on a tree-metric embedding by Gromov. We also show that hyperbolicity at a fixed base-point cannot be computed in O(n2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication than currently known.en
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0020019015000198en
dc.relation.urlhttp://arxiv.org/abs/1210.3323en
dc.rightsArchived with thanks to Information Processing Lettersen
dc.titleComputing the Gromov hyperbolicity of a discrete metric spaceen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalInformation Processing Lettersen
dc.eprint.versionPost-printen
dc.contributor.institutionUniv Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu, UMR 7586 CNRS, 75205 Paris, Franceen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxividarXiv:1210.3323en
kaust.authorVigneron, Antoine E.en
kaust.authorIsmail, Anasen
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