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DOI: 10.4230/LIPIcs.STACS.2010.2453

Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

Authors: Ho-Leung Chan, Tak-Wah Lam, Lap-Kei Lee, and Hing-Fung Ting

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

Abstract

The past decade has witnessed many interesting algorithms for maintaining statistics over a data stream. This paper initiates a theoretical study of algorithms for monitoring distributed data streams over a time-based sliding window (which contains a variable number of items and possibly out-of-order items). The concern is how to minimize the communication between individual streams and the root, while allowing the root, at any time, to be able to report the global statistics of all streams within a given error bound. This paper presents communication-efficient algorithms for three classical statistics, namely, basic counting, frequent items and quantiles. The worst-case communication cost over a window is $O(\frac{k}{\varepsilon} \log \frac{\varepsilon N}{k})$ bits for basic counting and $O(\frac{k}{\varepsilon} \log \frac{N}{k})$ words for the remainings, where $k$ is the number of distributed data streams, $N$ is the total number of items in the streams that arrive or expire in the window, and $\varepsilon < 1$ is the desired error bound. Matching and nearly matching lower bounds are also obtained.

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Ho-Leung Chan, Tak-Wah Lam, Lap-Kei Lee, and Hing-Fung Ting. Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 179-190, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chan_et_al:LIPIcs.STACS.2010.2453,
  author =	{Chan, Ho-Leung and Lam, Tak-Wah and Lee, Lap-Kei and Ting, Hing-Fung},
  title =	{{Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{179--190},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2453},
  URN =		{urn:nbn:de:0030-drops-24536},
  doi =		{10.4230/LIPIcs.STACS.2010.2453},
  annote =	{Keywords: Algorithms, distributed data streams, communication efficiency, frequent items}
}

Document

DOI: 10.4230/LIPIcs.STACS.2009.1815

Nonclairvoyant Speed Scaling for Flow and Energy

Authors: Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

Abstract

We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is $P(s)=s^\alpha$. We give a nonclairvoyant algorithm that is shown to be $O(\alpha^3)$-competitive. We then show an $\Omega( \alpha^{1/3-\epsilon} )$ lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be $O(1)$-competitive.

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Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs. Nonclairvoyant Speed Scaling for Flow and Energy. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 255-264, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{chan_et_al:LIPIcs.STACS.2009.1815,
  author =	{Chan, Ho-Leung and Edmonds, Jeff and Lam, Tak-Wah and Lee, Lap-Kei and Marchetti-Spaccamela, Alberto and Pruhs, Kirk},
  title =	{{Nonclairvoyant Speed Scaling for Flow and Energy}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{255--264},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1815},
  URN =		{urn:nbn:de:0030-drops-18151},
  doi =		{10.4230/LIPIcs.STACS.2009.1815},
  annote =	{Keywords: }
}

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Documents authored by Chan, Ho-Leung

Continuous Monitoring of Distributed Data Streams over a Time-based Sliding Window

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Nonclairvoyant Speed Scaling for Flow and Energy

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