Algorithms for dynamic geometric problems over data streams
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
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
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We show how to compute the width of a dynamic set of low-dimensional points in the streaming model. In particular, we assume the stream contains both insertions of points and deletions of points to a set S, and the goal is to compute the width of the set S, namely the minimal distance between two parallel lines sandwiching the pointset S. Our algorithm 1 + ε approximates the width of the set S using space polylogarithmic in the size of S and the aspect ratio of S. This is the first such algorithm that supports both insertions and deletions of points to the set S: previous algorithms for approximating the width of a pointset only supported additions [AHPV04, Cha06], or a sliding window [CS06]. This solves an open question from the "2009 Kanpur list" of Open Problems in Data Streams, Property Testing, and Related Topics [IMNO11].