Streaming Algorithms for Shape Fitting in High Dimensions

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Eslami Bidgoli, Mohammad Javad | 2022

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 54932 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Zarrabizadeh, Hamid
Abstract:
In this research, we investigate shape fitting problems in high dimensional streams and we provide lower bounds for the problems of minimum enclosing spherical shell and minimum enclosing cylindrical shell in streaming model. We will prove that no streaming algorithm can approximate these problems with constant factor with storage sub-exponential in dimension. More precisely, we will prove that every streaming algorithm that can solve these problems with storage sub-exponential in dimension, does not have an approximation factor better than√28 d1/3, where d is dimension of the input points. This is the first lower bound that has been proved for these two problems in high dimensional streams
Keywords:
Data Stream ; Minimum Enclosing Spherical Shell ; Minimum Enclosing Cylindrical Shell ; High Dimensions ; Shape Fitting

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