License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.112
URN: urn:nbn:de:0030-drops-141810
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14181/
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Woodruff, David P. ; Zhou, Samson

Separations for Estimating Large Frequency Moments on Data Streams

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LIPIcs-ICALP-2021-112.pdf (0.8 MB)

Abstract

We study the classical problem of moment estimation of an underlying vector whose n coordinates are implicitly defined through a series of updates in a data stream. We show that if the updates to the vector arrive in the random-order insertion-only model, then there exist space efficient algorithms with improved dependencies on the approximation parameter ε. In particular, for any real p > 2, we first obtain an algorithm for F_p moment estimation using ?̃(1/(ε^{4/p})⋅ n^{1-2/p}) bits of memory. Our techniques also give algorithms for F_p moment estimation with p > 2 on arbitrary order insertion-only and turnstile streams, using ?̃(1/(ε^{4/p})⋅ n^{1-2/p}) bits of space and two passes, which is the first optimal multi-pass F_p estimation algorithm up to log n factors. Finally, we give an improved lower bound of Ω(1/(ε²)⋅ n^{1-2/p}) for one-pass insertion-only streams. Our results separate the complexity of this problem both between random and non-random orders, as well as one-pass and multi-pass streams.

BibTeX - Entry

@InProceedings{woodruff_et_al:LIPIcs.ICALP.2021.112,
  author =	{Woodruff, David P. and Zhou, Samson},
  title =	{{Separations for Estimating Large Frequency Moments on Data Streams}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{112:1--112:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14181},
  URN =		{urn:nbn:de:0030-drops-141810},
  doi =		{10.4230/LIPIcs.ICALP.2021.112},
  annote =	{Keywords: streaming algorithms, frequency moments, random order, lower bounds}
}

Keywords: streaming algorithms, frequency moments, random order, lower bounds
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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