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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.25
URN: urn:nbn:de:0030-drops-90294
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9029/
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Braverman, Vladimir ; Viola, Emanuele ; Woodruff, David P. ; Yang, Lin F.

Revisiting Frequency Moment Estimation in Random Order Streams

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LIPIcs-ICALP-2018-25.pdf (0.6 MB)


Abstract

We revisit one of the classic problems in the data stream literature, namely, that of estimating the frequency moments F_p for 0 < p < 2 of an underlying n-dimensional vector presented as a sequence of additive updates in a stream. It is well-known that using p-stable distributions one can approximate any of these moments up to a multiplicative (1+epsilon)-factor using O(epsilon^{-2} log n) bits of space, and this space bound is optimal up to a constant factor in the turnstile streaming model. We show that surprisingly, if one instead considers the popular random-order model of insertion-only streams, in which the updates to the underlying vector arrive in a random order, then one can beat this space bound and achieve O~(epsilon^{-2} + log n) bits of space, where the O~ hides poly(log(1/epsilon) + log log n) factors. If epsilon^{-2} ~~ log n, this represents a roughly quadratic improvement in the space achievable in turnstile streams. Our algorithm is in fact deterministic, and we show our space bound is optimal up to poly(log(1/epsilon) + log log n) factors for deterministic algorithms in the random order model. We also obtain a similar improvement in space for p = 2 whenever F_2 >~ log n * F_1.

BibTeX - Entry

@InProceedings{braverman_et_al:LIPIcs:2018:9029,
  author =	{Vladimir Braverman and Emanuele Viola and David P. Woodruff and Lin F. Yang},
  title =	{{Revisiting Frequency Moment Estimation in Random Order Streams}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9029},
  URN =		{urn:nbn:de:0030-drops-90294},
  doi =		{10.4230/LIPIcs.ICALP.2018.25},
  annote =	{Keywords: Data Stream, Frequency Moments, Random Order, Space Complexity, Insertion Only Stream}
}

Keywords: Data Stream, Frequency Moments, Random Order, Space Complexity, Insertion Only Stream
Seminar: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 29.06.2018


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