Proceedings of the forty-first annual ACM symposium on Theory of computing
A sublinear-time approximation scheme for bin packing
Theoretical Computer Science
Local graph exploration and fast property testing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Property testing
Property testing
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
Min-sum clustering of protein sequences with limited distance information
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
From high definition image to low space optimization
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Active clustering of biological sequences
The Journal of Machine Learning Research
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We present a novel analysis of a random sampling approach for fourclustering problems in metric spaces: k-median,k-means, min-sum k-clustering, and balancedk-median. For all these problems, we consider the followingsimple sampling scheme: select a small sample set of input pointsuniformly at random and then run some approximation algorithm onthis sample set to compute an approximation of the best possibleclustering of this set. Our main technical contribution is asignificantly strengthened analysis of the approximation guaranteeby this scheme for the clustering problems.The main motivationbehind our analyses was to design sublinear-time algorithms forclustering problems. Our second contribution is the development ofnew approximation algorithms for the aforementioned clusteringproblems. Using our random sampling approach, we obtain for theseproblems the first time approximation algorithms that have runningtime independent of the input size, and depending on k andthe diameter of the metric space only. © 2006 WileyPeriodicals, Inc. Random Struct. Alg., 2006A preliminary extendedabstract of this work appeared in Proceedings of the 31st AnnualInternational Colloquium on Automata, Languages and Programming(ICALP), pp. 396-407, 2004.