Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Fast hierarchical clustering and other applications of dynamic closest pairs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for projective clustering
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for geometric k-clustering
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A local search approximation algorithm for k-means clustering
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On k-Median clustering in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
How to get close to the median shape
Proceedings of the twenty-second annual symposium on Computational geometry
Universal ε-approximators for integrals
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Data reduction for weighted and outlier-resistant clustering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
An effective coreset compression algorithm for large scale sensor networks
Proceedings of the 11th international conference on Information Processing in Sensor Networks
The single pixel GPS: learning big data signals from tiny coresets
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
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Given a set P of n points on the real line and a (potentially infinite) family of functions, we investigate the problem of finding a small (weighted) subset ${\mathcal{S}} \subseteq P$, such that for any $f \in {\mathcal{F}}$, we have that f(P) is a (1±ε)-approximation to $f({\mathcal{S}})$. Here, f(Q)=∑q∈Qw(q) f(q) denotes the weighted discrete integral of f over the point set Q, where w(q) is the weight assigned to the point q. We study this problem, and provide tight bounds on the size ${\mathcal{S}}$ for several families of functions. As an application, we present some coreset constructions for clustering.