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| Title: | Aspects of Metric Spaces in Computation |
| Authors: | Skala, Matthew Adam |
| Keywords: | metric space
robust hash
NP-complete
intrinsic dimensionality |
| Approved Date: | 6-Jun-2008 |
| Date Submitted: | 2008 |
| 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. |
| Program: | Computer Science |
| Department: | School of Computer Science |
| Degree: | Doctor of Philosophy |
| URI: | http://hdl.handle.net/10012/3788 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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