Range Counting over Multidimensional Data Streams

Authors:
Subhash Suri;Csaba D. Toth;Yunhong Zhou
Affiliations:
Department of Computer Science, University of California, Santa Barbara, CA 93106, USA;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA
Venue:
Discrete & Computational Geometry
Year:
2006

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Abstract

We consider the problem of approximate range counting over a stream of d-dimensional points. In the data stream model the algorithm makes a single scan of the data, which is presented in an arbitrary order, and computes a compact summary data structure. The summary, whose size depends on the approximation parameter ε, can be used to count the number of points inside a query range within additive error εn, where n is the size of the stream seen so far. We present several results, deterministic and randomized, for both rectangle and halfspace ranges.