Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
More planar two-center algorithms
Computational Geometry: Theory and Applications
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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)
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
Smaller Coresets for k-Median and k-Means Clustering
Discrete & Computational Geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Streaming Algorithms for k-Center Clustering with Outliers and with Anonymity
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Tight results for clustering and summarizing data streams
Proceedings of the 12th International Conference on Database Theory
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
| Hi-index | 5.23 |
In this paper we design a simple streaming algorithm for maintaining two smallest balls (of equal radius) in d-dimension to cover a set of points in an on-line fashion. Different from most of the traditional streaming models, at any step we use the minimum amount of space by only storing the locations and the (common) radius of the balls. Previously, such a geometric algorithm is only investigated for covering with one ball (one-center) by Zarrabi-Zadeh and Chan (2006) [16]. We give an analysis of our algorithm, which is significantly different from the one-center algorithm due to the obvious possibility of grouping points wrongly under this streaming model. We show that our algorithm has an approximation ratio 2 for d=1 and at most 5.611 for any fixed d1. We also present lower bounds of 1.5 and 1.604 for the problem in the d=1 and d1 cases respectively.