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Adaptive Spatial Partitioning for Multidimensional Data Streams

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Abstract

We propose a space-efficient scheme for summarizing multidimensional data streams. Our sketch can be used to solve spatial versions of several classical data stream queries efficiently. For instance, we can track ε-hot spots, which are congruent boxes containing at least an ε fraction of the stream, and maintain hierarchical heavy hitters in d dimensions. Our sketch can also be viewed as a multidimensional generalization of the ε-approximate quantile summary. The space complexity of our scheme is O((1/ε) log R) if the points lie in the domain [0, R]d, where d is assumed to be a constant. The scheme extends to the sliding window model with a log (ε n) factor increase in space, where n is the size of the sliding window. Our sketch can also be used to answer ε-approximate rectangular range queries over a stream of d-dimensional points.

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Authors and Affiliations

  1. Mentor Graphics Corp., 8005 SW Boeckman Road, Wilsonville, OR 97070, USA

    John Hershberger

  2. Department of Computer Science, University of California at Santa Barbara, Santa Barbara, CA 93106, USA

    Nisheeth Shrivastava & Subhash Suri

  3. Department of Mathematics, Room 2-336, MIT, Cambridge, MA 02139, USA

    Csaba D. Toth

Authors
  1. John Hershberger
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  2. Nisheeth Shrivastava
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  3. Subhash Suri
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  4. Csaba D. Toth
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Corresponding authors

Correspondence to John Hershberger, Nisheeth Shrivastava, Subhash Suri or Csaba D. Toth.

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Hershberger, J., Shrivastava, N., Suri, S. et al. Adaptive Spatial Partitioning for Multidimensional Data Streams. Algorithmica 46, 97–117 (2006). https://doi.org/10.1007/s00453-006-0070-3

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  • DOI: https://doi.org/10.1007/s00453-006-0070-3

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