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Approximate Histogram and Wavelet Summaries of Streaming Data

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Data Stream Management

Part of the book series: Data-Centric Systems and Applications ((DCSA))

Abstract

We study a synopsis abstract data structure similar to an array abstract data type commonly seen in textbooks. Specifically, we model an array \(\mathbf{A}\) of \(N\) real values, \(\{i: 0\le i < N\}=[0,N)\). Like to an array, a user can pose point and range queries; in addition, the data is dynamic (i.e., continuously updated) and can be multidimensional. We study approximate versions of this abstract data structure that provide only an approximate representation of \(\mathbf{A}\), using much less space than the full data set. Our focus is on two related types of sparse summaries, histograms and Haar wavelets.

S. Muthukrishnan supported by NSF ITR 0220280. M. Strauss supported in part by NSF DMS-0354600 and NSF DMS-0510203.

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Authors and Affiliations

  1. Department of Computer Science, Rutgers University, Piscataway, NJ, USA

    S. Muthukrishnan

  2. Department of Computer Science and Engineering, University of Michigan, Ann Arbor, MI, USA

    Martin Strauss

Authors
  1. S. Muthukrishnan
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  2. Martin Strauss
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Corresponding author

Correspondence to S. Muthukrishnan .

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Editors and Affiliations

  1. University Campus - Kounoupidiana, School of ECE, Techn. Univ. of Crete University Campus - Kounoupidiana, Chania, Greece

    Minos Garofalakis

  2. Microsoft Corporation, Redmond, Washington, USA

    Johannes Gehrke

  3. Amazon India , Bangalore, India

    Rajeev Rastogi

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Muthukrishnan, S., Strauss, M. (2016). Approximate Histogram and Wavelet Summaries of Streaming Data. In: Garofalakis, M., Gehrke, J., Rastogi, R. (eds) Data Stream Management. Data-Centric Systems and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28608-0_13

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  • DOI: https://doi.org/10.1007/978-3-540-28608-0_13

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  • Print ISBN: 978-3-540-28607-3

  • Online ISBN: 978-3-540-28608-0

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