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Distributed unit clustering

Mirjalali, K ; 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. Given a set of points in the plane, the unit clustering problem asks for finding a minimum-size set of unit disks that cover the whole input set. We study the unit clustering problem in a distributed setting, where input data is partitioned among several machines. We present a (3 + ϵ)-approximation algorithm for the problem in the Euclidean plane, and a (4 + ϵ)-approximation algorithm for the problem under general Lp metric (p1). We also study the capacitated version of the problem, where each cluster has a limited capacity for covering the points. We present a distributed algorithm for the capacitated version of the problem that achieves an approximation factor of 4+" in the L2 plane, and a factor of 5 + " in general Lp metric. We also provide some complementary lower bounds. © CCCG 2019. All rights reserved
  5. Keywords:
  6. Computational geometry ; Approximation factor ; Clustering problems ; Euclidean planes ; Input datas ; Input set ; Limited capacity ; Lower bounds ; Unit disk ; Approximation algorithms
  7. Source: 31st Canadian Conference on Computational Geometry, CCCG 2019, 8 August 2019 through 10 August 2019 ; 2019 , Pages 236-241