Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
Maintaining approximate extent measures of moving points
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete 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
On coresets for k-means and k-median clustering
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
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
ESA'10 Proceedings of the 18th annual European conference on Algorithms: 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
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
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
Computational Geometry: Theory and Applications
| Hi-index | 0.01 |
We present a new streaming algorithm for maintaining an 茂戮驴-kernel of a point set in 茂戮驴dusing O((1/茂戮驴(d茂戮驴 1)/2) log(1/茂戮驴)) space. The space used by our algorithm is optimal up to a small logarithmic factor. This substantially improves (for any fixed dimension $d \geqslant 3$) the best previous algorithm for this problem that uses O(1/茂戮驴d茂戮驴 (3/2)) space, presented by Agarwal and Yu at SoCG'07. Our algorithm immediately improves the space complexity of the best previous streaming algorithms for a number of fundamental geometric optimization problems in fixed dimensions, including width, minimum enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc.