Computational geometry: an introduction
Computational geometry: an introduction
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Farthest neighbors, maximum spanning trees and related problems in higher dimensions
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
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Competitive Analysis of Aggregate Max in Windowed Streaming
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Tracking distributed aggregates over time-based sliding windows
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
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We study the problem of maintaining a (1+ε)-factor approximation of the diameter of a stream of points under the sliding window model In one dimension, we give a simple algorithm that only needs to store $O(\frac{1}{\epsilon}{\rm log}R)$ points at any time, where the parameter R denotes the “spread” of the point set This bound is optimal and improves Feigenbaum, Kannan, and Zhang's recent solution by two logarithmic factors We then extend our one-dimensional algorithm to higher constant dimensions and, at the same time, correct an error in the previous solution In high nonconstant dimensions, we also observe a constant-factor approximation algorithm that requires sublinear space Related optimization problems, such as the width, are also considered in the two-dimensional case.