Approximation Algorithms for Geometric Optimization on Sliding Windows

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Salehnamadi, Navid | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49877 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Zarrabi Zadeh, Hamid
Abstract:
In this thesis, we focus on a subset of geometric optimization problems (including k-center) in the Sliding Window model. The sliding window model is driven from the Data Stream model in which input points arrive one by one and the space is limited. The main diffrenece of these two models is that in the sliding window model we are interested in the N latest points not all of the arrived points. In this thesis, we study Minimum Enclosing Ball, 2-center, and Euclidean k-center in the Sliding Window model. We provide a (1 + ")-approximation algorithm for MEB in d-dimensions. To our knowledge there is no algorithm for MEB in d-dimensions where d >2. We also provide a (1 + ")-approximation algorithm for 2-center in 2-dimensions, which improves the previous (4+")-approximation algorithm. At last we study the k-center problem and provide a (2+")-approximation algorithm for it. Our algoithm improves the previous (6+")-pproximation algorithm which was designed for the metric space. The space complexity is poly(R; d; 1 ϵd ). The R denotes the “spread” of the point set or the ratio of maximum result to minimum distance of any two points in the window
Keywords:
Approximate Algorithm ; Geometry Optimization ; Sliding Window ; Massive Data