Separation and approximation of polyhedral objects
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
SIAM Journal on Computing
Deterministic sampling and range counting in geometric data streams
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)
Adaptive sampling for geometric problems over data streams
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Range Counting over Multidimensional Data Streams
Discrete & Computational Geometry
Streaming algorithms for geometric problems
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Streaming algorithms for line simplification
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Simplified Planar Coresets for Data Streams
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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 and dynamic algorithms for minimum enclosing balls in high dimensions
Computational Geometry: Theory and Applications
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Given a point set P⊆R2, a subset Q⊆ P is an ε-kernel of P if for every slab W containing Q, the (1+ε)-expansion of W also contains P. We present a data-stream algorithm for maintaining an ε-kernel of a stream of points in R2 that uses O(1/√ ε) space and takes O(log (1/ε)) amortized time to process each point. This is the first space-optimal data-stream algorithm for this problem.