Discrete & Computational Geometry

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

Range Counting over Multidimensional Data Streams

Article

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.

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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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