Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Sublinear time algorithms for metric space problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A Nearly Linear-Time Approximation Scheme for the Euclidean kappa-median Problem
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Better streaming algorithms for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
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
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating extent measures of points
Journal of the ACM (JACM)
A Simple Linear Time (1+ ") -Approximation Algorithm for k-Means Clustering in Any Dimensions
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Coresets in dynamic geometric data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Optimal time bounds for approximate clustering
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Linear time algorithms for clustering problems in any dimensions
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A PTAS for k-means clustering based on weak coresets
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Clustering for metric and non-metric distance measures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Summarizing spatial data streams using ClusterHulls
Journal of Experimental Algorithmics (JEA)
Facility Location in Dynamic Geometric Data Streams
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Coresets and approximate clustering for Bregman divergences
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
StarTrack: a framework for enabling track-based applications
Proceedings of the 7th international conference on Mobile systems, applications, and services
Blue-Fi: enhancing Wi-Fi performance using bluetooth signals
Proceedings of the 7th international conference on Mobile systems, applications, and services
Linear-time approximation schemes for clustering problems in any dimensions
Journal of the ACM (JACM)
Small space representations for metric min-sum k-clustering and their applications
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Clustering for metric and nonmetric distance measures
ACM Transactions on Algorithms (TALG)
Clustering with internal connectedness
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Property testing
Property testing
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fast clustering using MapReduce
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Coresets for discrete integration and clustering
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Bregman clustering for separable instances
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Some results on approximate 1-median selection in metric spaces
Theoretical Computer Science
Clustering via geometric median shift over Riemannian manifolds
Information Sciences: an International Journal
Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels
Information Sciences: an International Journal
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We study approximation algorithms for k-median clustering. We obtain small coresets for k-median clustering in metric spaces as well as in Euclidean spaces. Specifically, in Rd, those coresets are of size with only polynomial dependency on d. This leads to a (1 + ε)-approximation algorithm for k-median clustering in Rd, with running time O(ndk +2(k/ε)o(1)d2nσ), for any σ 0. This is an improvement over previous results [5, 20, 21]. We also provide fast constant factor approximation algorithms for k-median clustering in finite metric spaces.We use those coresets to compute (1 + ε)-approximation k-median clustering in the streaming model of computation, using only O(k2de-2log8 n) space, where the points are taken from Rd. This is the first streaming algorithm, for this problem, that has space complexity with only polynomial dependency on the dimension.