Adaptive Spatial Partitioning for Multidimensional Data Streams

Authors:
John Hershberger;Nisheeth Shrivastava;Subhash Suri;Csaba D. Toth
Affiliations:
Mentor Graphics Corp., 8005 SW Boeckman Road, Wilsonville, OR 97070, USA;Department of Computer Science, University of California at Santa Barbara, Santa Barbara, CA 93106, USA;Department of Computer Science, University of California at Santa Barbara, Santa Barbara, CA 93106, USA;Department of Mathematics, Room 2-336, MIT, Cambridge, MA 02139, USA
Venue:
Algorithmica
Year:
2006

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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.