International Journal of Computer Vision
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient and effective querying by image content
Journal of Intelligent Information Systems - Special issue: advances in visual information management systems
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Syntactic clustering of the Web
Selected papers from the sixth international conference on World Wide Web
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Embeddings and non-approximability of geometric problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
High-dimensional computational geometry
High-dimensional computational geometry
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A Nearly Linear-Time Approximation Scheme for the Euclidean $k$-Median Problem
SIAM Journal on Computing
A linear time algorithm for approximate 2-means clustering
Computational Geometry: Theory and Applications
Clustering with internal connectedness
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Some results on approximate 1-median selection in metric spaces
Theoretical Computer Science
An architecture for component-based design of representative-based clustering algorithms
Data & Knowledge Engineering
Data stability in clustering: a closer look
ALT'12 Proceedings of the 23rd international conference on Algorithmic Learning Theory
Deterministic sublinear-time approximations for metric 1-median selection
Information Processing Letters
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We present a general approach for designing approximation algorithms for a fundamental class of geometric clustering problems in arbitrary dimensions. More specifically, our approach leads to simple randomized algorithms for the k-means, k-median and discrete k-means problems that yield (1+ϵ) approximations with probability ≥ 1/2 and running times of O(2(k/ϵ)O(1) dn). These are the first algorithms for these problems whose running times are linear in the size of the input (nd for n points in d dimensions) assuming k and ϵ are fixed. Our method is general enough to be applicable to clustering problems satisfying certain simple properties and is likely to have further applications.