Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
On linear-time deterministic algorithms for optimization problems in fixed dimension
Journal of Algorithms
Communication complexity
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
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
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Approximating extent measures of points
Journal of the ACM (JACM)
Data Streams: Models and Algorithms (Advances in Database Systems)
Data Streams: Models and Algorithms (Advances in Database Systems)
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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
Hardness of Nearest Neighbor under L-infinity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Numerical linear algebra in the streaming model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Coresets for polytope distance
Proceedings of the twenty-fifth annual symposium on Computational geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Space-constrained interval selection
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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
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We develop (single-pass) streaming algorithms for maintaining extent measures of a stream S of n points in Rd. We focus on designing streaming algorithms whose working space is polynomial in d (poly(d)) and sublinear in n. For the problems of computing diameter, width and minimum enclosing ball of S, we obtain lower bounds on the worst-case approximation ratio of any streaming algorithm that uses poly(d) space. On the positive side, we introduce the notion of blurred ball cover and use it for answering approximate farthest-point queries and maintaining approximate minimum enclosing ball and diameter of S. We describe a streaming algorithm for maintaining a blurred ball cover whose working space is linear in d and independent of n.