MapReduce Algorithm for Anonymity Problem

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Miri, Hamid | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52400 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Ghodsi, Mohammad
Abstract:
In this research, we focus on r-gather and (r; ϵ)-gather clustering. In the r-gather clustering, the input points are in metric space and must be clustered such that each cluster has at least r points and the objective is to minimize the radius of clustering. (r; ϵ)-gather clustering is a kind of r-gather clustering such that at most nϵ points can be unclustered. MapReduce model is one of the most used parallel models to process huge data and processes the input data in some machine simultaneously in parallel.In this research, we give a lower bound for the approximation factor of r-gather clustering in MapReduce model. This lower bound works in MapReduce model even an optimal algorithm exists in sequential model. Then we give an algorithm for r-gahter clustering with (4 + ϵ) approximation factor which runs in O(log 1ϵ ) rounds. Also, we give an algorithm for (r; ϵ)-gather clustering with (7 + ϵ) approximation factor which rounds in O(log 1 ϵ ) rounds
Keywords:
Anonymity ; Map-Reduce Algorithm ; Clustering ; Computational Geometry ; Mapping Algorithm