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dc.contributor.authorZarrabi-Zadeh, Hamid 14:02:27 (GMT) 14:02:27 (GMT)
dc.description.abstractThe online and data stream models of computation have recently attracted considerable research attention due to many real-world applications in various areas such as data mining, machine learning, distributed computing, and robotics. In both these models, input items arrive one at a time, and the algorithms must decide based on the partial data received so far, without any secure information about the data that will arrive in the future. In this thesis, we investigate efficient algorithms for a number of fundamental geometric optimization problems in the online and data stream models. The problems studied in this thesis can be divided into two major categories: geometric clustering and computing various extent measures of a set of points. In the online setting, we show that the basic unit clustering problem admits non-trivial algorithms even in the simplest one-dimensional case: we show that the naive upper bounds on the competitive ratio of algorithms for this problem can be beaten using randomization. In the data stream model, we propose a new streaming algorithm for maintaining "core-sets" of a set of points in fixed dimensions, and also, introduce a new simple framework for transforming a class of offline algorithms to their equivalents in the data stream model. These results together lead to improved streaming approximation algorithms for a wide variety of geometric optimization problems in fixed dimensions, including diameter, width, k-center, smallest enclosing ball, minimum-volume bounding box, minimum enclosing cylinder, minimum-width enclosing spherical shell/annulus, etc. In high-dimensional data streams, where the dimension is not a constant, we propose a simple streaming algorithm for the minimum enclosing ball (the 1-center) problem with an improved approximation factor.en
dc.publisherUniversity of Waterlooen
dc.subjectComputational Geometryen
dc.subjectOptimization Problemsen
dc.subjectApproximation Algorithmsen
dc.subjectOnline Algorithmsen
dc.subjectData Streamsen
dc.titleGeometric Approximation Algorithms in the Online and Data Stream Modelsen
dc.typeDoctoral Thesisen
dc.comment.hiddenI am willing to complete my degree requirements by Friday, Oct 24, in order to be eligible for half-term tuition refund. So, I would like to ask you please reply to this submission by this Thursday in order to allow me to do the binding (and the remained paperwork) by Friday. Thanks a lot.en
dc.subject.programComputer Scienceen of Computer Scienceen
uws-etd.degreeDoctor of Philosophyen

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