Aspects of Metric Spaces in Computation

dc.contributor.authorSkala, Matthew Adam
dc.date.accessioned2008-06-06T14:43:31Z
dc.date.available2008-06-06T14:43:31Z
dc.date.issued2008-06-06T14:43:31Z
dc.date.submitted2008
dc.description.abstractMetric spaces, which generalise the properties of commonly-encountered physical and abstract spaces into a mathematical framework, frequently occur in computer science applications. Three major kinds of questions about metric spaces are considered here: the intrinsic dimensionality of a distribution, the maximum number of distance permutations, and the difficulty of reverse similarity search. Intrinsic dimensionality measures the tendency for points to be equidistant, which is diagnostic of high-dimensional spaces. Distance permutations describe the order in which a set of fixed sites appears while moving away from a chosen point; the number of distinct permutations determines the amount of storage space required by some kinds of indexing data structure. Reverse similarity search problems are constraint satisfaction problems derived from distance-based index structures. Their difficulty reveals details of the structure of the space. Theoretical and experimental results are given for these three questions in a wide range of metric spaces, with commentary on the consequences for computer science applications and additional related results where appropriate.en
dc.identifier.urihttp://hdl.handle.net/10012/3788
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectmetric spaceen
dc.subjectrobust hashen
dc.subjectNP-completeen
dc.subjectintrinsic dimensionalityen
dc.subject.programComputer Scienceen
dc.titleAspects of Metric Spaces in Computationen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentSchool of Computer Scienceen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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