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Order statistics and estimating cardinalities of massive data sets

Author:

Frédéric GiroireAuthors Info & Claims

Discrete Applied Mathematics, Volume 157, Issue 2

Pages 406 - 427

https://doi.org/10.1016/j.dam.2008.06.020

Published: 20 January 2009 Publication History

Abstract

A new class of algorithms to estimate the cardinality of very large multisets using constant memory and doing only one pass on the data is introduced here. It is based on order statistics rather than on bit patterns in binary representations of numbers. Three families of estimators are analyzed. They attain a standard error of 1M using M units of storage, which places them in the same class as the best known algorithms so far. The algorithms have a very simple internal loop, which gives them an advantage in terms of processing speed. For instance, a memory of only 12 kB and only few seconds are sufficient to process a multiset with several million elements and to build an estimate with accuracy of order 2 percent. The algorithms are validated both by mathematical analysis and by experimentations on real internet traffic.

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Cited By

Qi YLi RWang PSun YXing RBaeza-Yates RBonchi F(2024)QSketch: An Efficient Sketch for Weighted Cardinality Estimation in StreamsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671695(2432-2443)Online publication date: 25-Aug-2024
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Sultan SShakiba KLee AChen PStumm M(2024)TTLs Matter: Efficient Cache Sizing with TTL-Aware Miss Ratio Curves and Working Set SizesProceedings of the Nineteenth European Conference on Computer Systems10.1145/3627703.3650066(387-404)Online publication date: 22-Apr-2024
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Hehir JTing DCormode GKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Sketch-flip-mergeProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3618930(12846-12865)Online publication date: 23-Jul-2023
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Order statistics and estimating cardinalities of massive data sets

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cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 157, Issue 2

January, 2009

240 pages

ISSN:0166-218X

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2008.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 20 January 2009

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Cited By

Qi YLi RWang PSun YXing RBaeza-Yates RBonchi F(2024)QSketch: An Efficient Sketch for Weighted Cardinality Estimation in StreamsProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671695(2432-2443)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671695
Sultan SShakiba KLee AChen PStumm M(2024)TTLs Matter: Efficient Cache Sizing with TTL-Aware Miss Ratio Curves and Working Set SizesProceedings of the Nineteenth European Conference on Computer Systems10.1145/3627703.3650066(387-404)Online publication date: 22-Apr-2024
https://dl.acm.org/doi/10.1145/3627703.3650066
Hehir JTing DCormode GKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Sketch-flip-mergeProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3618930(12846-12865)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3618930
Wang DPettie SGeerts FNgo HSintos S(2023)Better Cardinality Estimators for HyperLogLog, PCSA, and BeyondProceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3584372.3588680(317-327)Online publication date: 18-Jun-2023
https://dl.acm.org/doi/10.1145/3584372.3588680
Harris DRinberg ARottenstreich O(2023)Compressing Distributed Network Sketches With Traffic-Aware SummariesIEEE Transactions on Network and Service Management10.1109/TNSM.2022.317229920:2(1962-1975)Online publication date: 1-Jun-2023
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Lin YXu ZZhang YLi YZhang J(2023)Cardinality estimation with smoothing autoregressive modelsWorld Wide Web10.1007/s11280-023-01195-726:5(3441-3461)Online publication date: 28-Jul-2023
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Dickens CThaler JTing DKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Order-invariant cardinality estimators are differentially privateProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3601376(15204-15216)Online publication date: 28-Nov-2022
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Zhou XLi GChai CFeng J(2022)A learned query rewrite system using Monte Carlo tree searchProceedings of the VLDB Endowment10.14778/3485450.348545615:1(46-58)Online publication date: 14-Jan-2022
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Wu YFan ZShi QZhang YYang TChen CZhong ZLi JShtul ATu Y(2022)SHE: A Generic Framework for Data Stream Mining over Sliding WindowsProceedings of the 51st International Conference on Parallel Processing10.1145/3545008.3545009(1-12)Online publication date: 29-Aug-2022
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Karppa MPagh RZhang ARangwala H(2022)HyperLogLogLogProceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3534678.3539246(753-761)Online publication date: 14-Aug-2022
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