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Sampling from Dense Streams without Penalty

Improved Bounds for Frequency Moments and Heavy Hitters

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Computing and Combinatorics (COCOON 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

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Abstract

We investigate the ability to sample relatively small amounts of data from a stream and approximately calculate statistics on the original stream. McGregor et al. [29] provide worst case theoretical bounds that show space costs for sampling that are inversely correlated with the sampling rate. Indeed, while the lower bound of McGregor et al. cannot be improved in the general case, we show it is possible to improve the space bound for stream D of domain n, when the average positive frequency μ = F 1/F 0 is sufficiently large. We consider the following range of parameters: μ ≥ log(n) and sample rate p ≥ C k μ − 1log(n), where C k is a constant. On these streams we improve the bound from \(\tilde{O} ({1 \over p} n^{1-2/k})\) to \( \tilde{O} (n^{1-2/k})\) thus giving polynomial improvement in space for sufficiently large μ and p − 1.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Johns Hopkins University, Baltimore, Maryland, USA

    Vladimir Braverman & Gregory Vorsanger

Authors
  1. Vladimir Braverman
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  2. Gregory Vorsanger
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Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

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Braverman, V., Vorsanger, G. (2014). Sampling from Dense Streams without Penalty. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-08783-2_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

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