Nearly optimal distinct elements and heavy hitters on sliding windows

Vladimir Braverman; Elena Grigorescu; Harry Lang; David P. Woodruff; Samson Zhou

doi:10.4230/LIPIcs.APPROX-RANDOM.2018.7

Nearly optimal distinct elements and heavy hitters on sliding windows

Vladimir Braverman
, Elena Grigorescu
, Harry Lang
, David P. Woodruff
, Samson Zhou

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

14 Scopus citations

Abstract

We study the distinct elements and p-heavy hitters problems in the sliding window model, where only the most recent n elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the exponential (Datar et al., SODA 2002) and smooth histograms (Braverman and Ostrovsky, FOCS 2007) that may be of independent interest. We then show that the composable histogram along with a careful combination of existing techniques to track either the identity or frequency of a few specific items suffices to obtain algorithms for both distinct elements and p-heavy hitters that are nearly optimal in both n and. Applying our new composable histogram framework, we provide an algorithm that outputs a (1 + ϵ)-approximation to the number of distinct elements in the sliding window model and uses [EQUATION PRESENTED].

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018
Editors	Eric Blais, Jose D. P. Rolim, David Steurer, Klaus Jansen
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)	9783959770859
DOIs	https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.7
State	Published - 1 Aug 2018
Externally published	Yes
Event	21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018 - Princeton, United States Duration: 20 Aug 2018 → 22 Aug 2018

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	116
ISSN (Print)	1868-8969

Conference

Conference	21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018
Country/Territory	United States
City	Princeton
Period	20/08/18 → 22/08/18

Keywords

Distinct Elements
Heavy Hitters
Sliding Windows
Streaming Algorithms

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.APPROX-RANDOM.2018.7

Cite this

Braverman, V., Grigorescu, E., Lang, H., Woodruff, D. P., & Zhou, S. (2018). Nearly optimal distinct elements and heavy hitters on sliding windows. In E. Blais, J. D. P. Rolim, D. Steurer, & K. Jansen (Eds.), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018 Article 7 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 116). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.7

Braverman, Vladimir ; Grigorescu, Elena ; Lang, Harry et al. / Nearly optimal distinct elements and heavy hitters on sliding windows. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018. editor / Eric Blais ; Jose D. P. Rolim ; David Steurer ; Klaus Jansen. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs).

@inproceedings{0711f24a5e06422c890009a23bb218da,

title = "Nearly optimal distinct elements and heavy hitters on sliding windows",

abstract = "We study the distinct elements and p-heavy hitters problems in the sliding window model, where only the most recent n elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the exponential (Datar et al., SODA 2002) and smooth histograms (Braverman and Ostrovsky, FOCS 2007) that may be of independent interest. We then show that the composable histogram along with a careful combination of existing techniques to track either the identity or frequency of a few specific items suffices to obtain algorithms for both distinct elements and p-heavy hitters that are nearly optimal in both n and. Applying our new composable histogram framework, we provide an algorithm that outputs a (1 + ϵ)-approximation to the number of distinct elements in the sliding window model and uses [EQUATION PRESENTED].",

keywords = "Distinct Elements, Heavy Hitters, Sliding Windows, Streaming Algorithms",

author = "Vladimir Braverman and Elena Grigorescu and Harry Lang and Woodruff, \{David P.\} and Samson Zhou",

note = "Publisher Copyright: {\textcopyright} 2018 Aditya Bhaskara and Srivatsan Kumar.; 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018 ; Conference date: 20-08-2018 Through 22-08-2018",

year = "2018",

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doi = "10.4230/LIPIcs.APPROX-RANDOM.2018.7",

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series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Eric Blais and Rolim, \{Jose D. P.\} and David Steurer and Klaus Jansen",

booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018",

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Braverman, V, Grigorescu, E, Lang, H, Woodruff, DP & Zhou, S 2018, Nearly optimal distinct elements and heavy hitters on sliding windows. in E Blais, JDP Rolim, D Steurer & K Jansen (eds), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018., 7, Leibniz International Proceedings in Informatics, LIPIcs, vol. 116, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018, Princeton, United States, 20/08/18. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.7

Nearly optimal distinct elements and heavy hitters on sliding windows. / Braverman, Vladimir; Grigorescu, Elena; Lang, Harry et al.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018. ed. / Eric Blais; Jose D. P. Rolim; David Steurer; Klaus Jansen. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 7 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 116).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Nearly optimal distinct elements and heavy hitters on sliding windows

AU - Braverman, Vladimir

AU - Grigorescu, Elena

AU - Lang, Harry

AU - Woodruff, David P.

AU - Zhou, Samson

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We study the distinct elements and p-heavy hitters problems in the sliding window model, where only the most recent n elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the exponential (Datar et al., SODA 2002) and smooth histograms (Braverman and Ostrovsky, FOCS 2007) that may be of independent interest. We then show that the composable histogram along with a careful combination of existing techniques to track either the identity or frequency of a few specific items suffices to obtain algorithms for both distinct elements and p-heavy hitters that are nearly optimal in both n and. Applying our new composable histogram framework, we provide an algorithm that outputs a (1 + ϵ)-approximation to the number of distinct elements in the sliding window model and uses [EQUATION PRESENTED].

AB - We study the distinct elements and p-heavy hitters problems in the sliding window model, where only the most recent n elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the exponential (Datar et al., SODA 2002) and smooth histograms (Braverman and Ostrovsky, FOCS 2007) that may be of independent interest. We then show that the composable histogram along with a careful combination of existing techniques to track either the identity or frequency of a few specific items suffices to obtain algorithms for both distinct elements and p-heavy hitters that are nearly optimal in both n and. Applying our new composable histogram framework, we provide an algorithm that outputs a (1 + ϵ)-approximation to the number of distinct elements in the sliding window model and uses [EQUATION PRESENTED].

KW - Distinct Elements

KW - Heavy Hitters

KW - Sliding Windows

KW - Streaming Algorithms

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U2 - 10.4230/LIPIcs.APPROX-RANDOM.2018.7

DO - 10.4230/LIPIcs.APPROX-RANDOM.2018.7

M3 - Conference contribution

AN - SCOPUS:85052466791

SN - 9783959770859

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018

A2 - Blais, Eric

A2 - Rolim, Jose D. P.

A2 - Steurer, David

A2 - Jansen, Klaus

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018

Y2 - 20 August 2018 through 22 August 2018

ER -

Braverman V, Grigorescu E, Lang H, Woodruff DP, Zhou S. Nearly optimal distinct elements and heavy hitters on sliding windows. In Blais E, Rolim JDP, Steurer D, Jansen K, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 7. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.APPROX-RANDOM.2018.7

Nearly optimal distinct elements and heavy hitters on sliding windows

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Keywords

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