Computing the Gromov hyperbolicity constant of a discrete metric space

Handle URI:
http://hdl.handle.net/10754/244575
Title:
Computing the Gromov hyperbolicity constant of a discrete metric space
Authors:
Ismail, Anas
Abstract:
Although it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields. It has applications in Biology, Networking, Graph Theory, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant of a discrete metric space is the brute force algorithm with running time O (n4) using the four- point condition. In this thesis, we first introduce an approximation algorithm which calculates a O (log n)-approximation of the hyperbolicity constant , based on a layering approach, in time O (n2), where n is the number of points in the metric space. We also calculate the fixed base point hyperbolicity constant r for a fixed point r using a (max; min)􀀀matrix multiplication algorithm by Duan in time O (n2:688) [2]. We use this result to present a 2-approximation algorithm for calculating the hyperbolicity constant in time O (n2:688). We also provide an exact algorithm to compute the hyperbolicity constant in time O (n3:688) for a discrete metric space. We then present some partial results we obtained for designing some approximation algorithms to compute the hyperbolicity constant.
Advisors:
Vigneron, Antoine E. ( 0000-0003-3586-3431 )
Committee Member:
Chikalov, Igor; Gao, Xin ( 0000-0002-7108-3574 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Computer Science
Issue Date:
Jul-2012
Type:
Thesis
Appears in Collections:
Theses; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorVigneron, Antoine E.en
dc.contributor.authorIsmail, Anasen
dc.date.accessioned2012-09-18T09:12:12Z-
dc.date.available2012-09-18T09:12:12Z-
dc.date.issued2012-07en
dc.identifier.urihttp://hdl.handle.net/10754/244575en
dc.description.abstractAlthough it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields. It has applications in Biology, Networking, Graph Theory, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant of a discrete metric space is the brute force algorithm with running time O (n4) using the four- point condition. In this thesis, we first introduce an approximation algorithm which calculates a O (log n)-approximation of the hyperbolicity constant , based on a layering approach, in time O (n2), where n is the number of points in the metric space. We also calculate the fixed base point hyperbolicity constant r for a fixed point r using a (max; min)􀀀matrix multiplication algorithm by Duan in time O (n2:688) [2]. We use this result to present a 2-approximation algorithm for calculating the hyperbolicity constant in time O (n2:688). We also provide an exact algorithm to compute the hyperbolicity constant in time O (n3:688) for a discrete metric space. We then present some partial results we obtained for designing some approximation algorithms to compute the hyperbolicity constant.en
dc.language.isoenen
dc.subjectGromoven
dc.subjectHyperbolic groupsen
dc.subjectDiscrete metricen
dc.titleComputing the Gromov hyperbolicity constant of a discrete metric spaceen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberChikalov, Igoren
dc.contributor.committeememberGao, Xinen
thesis.degree.disciplineComputer Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id113029en
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