Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Histograms on Streams

  • Martin J. Strauss
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_191

Synonyms

Piecewise-constant approximations

Definition

A B-bucket histogram of length N is a partition of the set [0 , N) of N integers into intervals [b0 , b1) ∪ [b1 , b2) ∪ … ∪ [bB − 1 , bB), where b0 = 0 and bB = N, together with a collection of B heights hj, for 0 ≤ j < B, one for each bucket. On point query i, the histogram answer is hj, where j is the index of the interval (or “bucket”) containing i; that is, the unique j with bji < bj + 1. In vector notation, χS is the vector that is 1 on the set S and zero elsewhere and the answer vector of a histogram is \( \overrightarrow{H}={\displaystyle {\sum}_{0\le j<B^h_j}{\chi}_{\left[{b}_j,{b}_{j+1}\right).}} \)

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Recommended Reading

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    Cormode G, Muthukrishnan S. An improved data stream summary: the count-min sketch and its applications. In: Proceedings of the 6th Latin American Symposium Theoretical Informatics; 2004, p. 29–38.CrossRefGoogle Scholar
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    Gilbert A, Guha S, Indyk P, Kotidis Y, Muthukrishnan S, Strauss M. Fast, small-space algorithms for approximate histogram maintenance. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing; 2002. p. 389–98.Google Scholar
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    Guha S, Koudas N, Shim K. Approximation and streaming algorithms for histogram construction problems. ACM Trans Database Syst. 2006;31(1):396–438.CrossRefGoogle Scholar
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    Ioannidis Y. The history of histograms (abridged). In: Proceedings of the 29th International Conference on Very Large Data Bases; 2003, p. 19–30.CrossRefGoogle Scholar
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    Jagadish H, Koudas N, Muthukrishnan S, Poosala V, Sevcik K, Suel T. Optimal histograms with quality guarantees. In: Proceedings of the 24th International Conference on Very Large Data Bases; 1998, p. 275–86.Google Scholar
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    Muthukrishnan S, Strauss M. Approximate histogram and wavelet summaries of streaming data. In: Data-stream management – processing high-speed data streams. New York: Springer; 2009 (Data-Centric Systems and Applications Series).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

Section editors and affiliations

  • Divesh Srivastava
    • 1
  1. 1.AT&T Labs - ResearchAT&TBedminsterUSA