A linear time deterministic algorithm to find a small subset that approximates the centroid

Authors:
Pratik Worah;Sandeep Sen
Affiliations:
Department of Computer Science, University of Illinois, Urbana Champaign, IL 61801, USA;Department of C.S.E., I.I.T. Delhi, New Delhi 110016, India
Venue:
Information Processing Letters
Year:
2008

Citing 4
Cited 0

Applications of weighted Voronoi diagrams and randomization to variance-based k-clustering: (extended abstract)

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
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Abstract

Given a set of points S in any dimension, we describe a deterministic algorithm for finding a T@?S,|T|=O(1/@e) such that the centroid of T approximates the centroid of S within a factor 1+@e for any fixed @e0. We achieve this in linear time by an efficient derandomization of the algorithm in [M. Inaba, N. Katoh, H. Imai, Applications of weighted Voronoi diagrams and randomization to variance-based k-clustering (extended abstract), in: Proceedings of the Tenth Annual Symposium on Computational Geometry, 1994, pp. 332-339].