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A mapreduce algorithm for metric anonymity problems

Aghamolaei, S ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. Publisher: Canadian Conference on Computational Geometry , 2019
  3. Abstract:
  4. We focus on two metric clusterings namely r-gather and (r, ?)-gather. The objective of r-gather is to minimize the radius of clustering, such that each cluster has at least r points. (r, ?)-gather is a version of r-gather with the extra condition that at most n? points can be left unclustered (outliers). MapReduce is a model used for processing big data. In each round, it distributes data to multiple servers, then simultaneously processes each server's data. We prove a lower bound 2 on the approximation factor of metric r-gather in the MapReduce model, even if an optimal algorithm for r-gather exists. Then, we give a (4+ δ)-approximation algorithm for r-gather in MapReduce which runs in O( 1/δ) rounds. Also, for (r, ?)-gather, we give a (7 + δ)-approximation algorithm which runs in O( 1/δ) MapReduce rounds, for any constant δ > 0. © CCCG 2019. All rights reserved
  5. Keywords:
  6. Computational geometry ; Data handling ; Approximation factor ; Clusterings ; Lower bounds ; Map-reduce ; MapReduce models ; Multiple servers ; Optimal algorithm ; Approximation algorithms
  7. Source: 31st Canadian Conference on Computational Geometry, CCCG 2019, 8 August 2019 through 10 August 2019 ; 2019 , Pages 117-123
  8. URL: http://sharif.edu/~ghodsi/papers/sepideh-cccg2019.pdf