Aspects of Metric Spaces in Computation
| dc.contributor.author | Skala, Matthew Adam | |
| dc.date.accessioned | 2008-06-06T14:43:31Z | |
| dc.date.available | 2008-06-06T14:43:31Z | |
| dc.date.issued | 2008-06-06T14:43:31Z | |
| dc.date.submitted | 2008 | |
| dc.description.abstract | Metric 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.uri | http://hdl.handle.net/10012/3788 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | metric space | en |
| dc.subject | robust hash | en |
| dc.subject | NP-complete | en |
| dc.subject | intrinsic dimensionality | en |
| dc.subject.program | Computer Science | en |
| dc.title | Aspects of Metric Spaces in Computation | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | School of Computer Science | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |