Discrete & Computational Geometry

, Volume 36, Issue 4, pp 633–655 | Cite as

Range Counting over Multidimensional Data Streams

  • Subhash SuriEmail author
  • Csaba D. TothEmail author
  • Yunhong ZhouEmail author


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.


Data Stream Query Range Range Space Representative System Range Counting 
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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Computer Science, University of CaliforniaSanta Barbara, CA 93106USA
  2. 2.Department of Mathematics, Massachusetts Institute of TechnologyCambridge, MA 02139USA
  3. 3.Hewlett-Packard Laboratories, 1501 Page Mill RoadPalo Alto, CA 94304USA

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