Off-line dynamic maintenance of the width of a planar point set
Computational Geometry: Theory and Applications
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
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
Design of Dynamic Data Structures
Design of Dynamic Data Structures
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Equivalence between Priority Queues and Sorting
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Semi-Online Maintenance of Geometric Optima and Measures
SIAM Journal on Computing
Approximation algorithms for projective clustering
Journal of Algorithms
SIAM Journal on Computing
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Discrete & Computational Geometry
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)
Coresets in dynamic geometric data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sampling in dynamic data streams and applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Smaller Coresets for k-Median and k-Means Clustering
Discrete & Computational Geometry
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Voronoi diagrams in n · 2o(√lg lg n) time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Well-separated pair decomposition in linear time?
Information Processing Letters
FSTTCS '05 Proceedings of the 25th 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
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Streaming with minimum space: An algorithm for covering by two congruent balls
Theoretical Computer Science
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We give a dynamic data structure that can maintain an μ-coreset of n points, with respect to the extent measure, in O(log n) time for any constant μ 0 and any constant dimension. The previous method by Agarwal, Har-Peled, and Varadarajan requires polylogarithmic update time. For points with integer coordinates bounded by U, we alternatively get O(log log U) time. Numerous applications follow, for example, on dynamically approximating the width, smallest enclosing cylinder, minimum bounding box, or minimum-width annulus. We can also use the same approach to maintain approximate k-centers in O(min log n, log log U) randomized amortized time for any constant k and any constant dimension. For the smallest enclosing cylinder problem, we also show that a constant-factor approximation can be maintained in O(1) randomized amortized time on the word RAM.