Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
High-dimensional shape fitting in linear time
Proceedings of the nineteenth annual symposium on Computational geometry
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating extent measures of points
Journal of the ACM (JACM)
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Analysis of incomplete data and an intrinsic-dimension Helly theorem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Efficient algorithm for approximating maximum inscribed sphere in high dimensional polytope
Proceedings of the twenty-second annual symposium on Computational geometry
A fast k-means implementation using coresets
Proceedings of the twenty-second annual symposium on Computational geometry
On approximating the smallest enclosing Bregman Balls
Proceedings of the twenty-second annual symposium on Computational geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Computational Geometry: Theory and Applications
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling algorithms and coresets for ℓp regression
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-fourth annual symposium on Computational geometry
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
Coresets for polytope distance
Proceedings of the twenty-fifth annual symposium on Computational geometry
Efficient approximation algorithms for clustering point-sets
Computational Geometry: Theory and Applications
Maximum margin coresets for active and noise tolerant learning
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
PReMI'07 Proceedings of the 2nd international conference on Pattern recognition and machine intelligence
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
ACM Transactions on Algorithms (TALG)
Optimizing all-nearest-neighbor queries with trigonometric pruning
SSDBM'10 Proceedings of the 22nd international conference on Scientific and statistical database management
A new algorithm for training SVMs using approximate minimal enclosing balls
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Minimal containment under homothetics: a simple cutting plane approach
Computational Optimization and Applications
No dimension independent core-sets for containment under homothetics
Proceedings of the twenty-seventh annual symposium on Computational geometry
INFORMS Journal on Computing
Solving the chromatic cone clustering problem via minimum spanning sphere
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Coresets for discrete integration and clustering
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
On approximating the Riemannian 1-center
Computational Geometry: Theory and Applications
A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems
Computational Optimization and Applications
Range counting coresets for uncertain data
Proceedings of the twenty-ninth annual symposium on Computational geometry
Streaming with minimum space: An algorithm for covering by two congruent balls
Theoretical Computer Science
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
Computational Geometry: Theory and Applications
Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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Given a set of points P ⊂ Rd and value ∊ 0, an ∊-core-set S ⊂ P has the property that the smallest ball containing S is an ∊-approximation of the smallest ball containing P. This paper shows that any point-set has an ∊-core-set of size [2/∊]. We also give a fast algorithm that finds this core-set. These results imply the existence of small core-sets for solving approximate k-center clustering and related problems. The sizes of these core-sets are considerably smaller than the previously known bounds, and imply faster algorithms; one such algorithm needs O(dn/∊ + (l/∊)5) time to compute an ∊-approximate minimum enclosing ball (1-center) of n points in d dimensions. A simple gradient-descent algorithm is also given, for computing the minimum enclosing ball in O(dn/∊2) time. This algorithm also implies slightly faster algorithms for computing approximately the smallest radius k-flat fitting a set of points.