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Relative error streaming quantiles

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Cormode, Graham, Karnin, Zohar, Liberty, Edo, Thaler, Justin and Veselý, Pavel (2021) Relative error streaming quantiles. In: The 2021 ACM SIGMOD/PODS Conference, Virtual conference, 20-25 Jun 2021. Published in: PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems pp. 96-108. ISBN 9781450383813. doi:10.1145/3452021.3458323

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Official URL: https://doi.org/10.1145/3452021.3458323

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Abstract

Approximating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of n items from a data universe U equipped with a total order, the task is to compute a sketch (data structure) of size poly (log(n), 1/ε). Given the sketch and a query item y ∈ U, one should be able to approximate its rank in the stream, i.e., the number of stream elements smaller than or equal to y. Most works to date focused on additive ε n error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This paper investigates multiplicative (1±ε)$-error approximations to the rank. Practical motivation for multiplicative error stems from demands to understand the tails of distributions, and hence for sketches to be more accurate near extreme values. The most space-efficient algorithms due to prior work store either O(log(ε2 n)/ε2) or O(log3(ε n)/ε) universe items. This paper presents a randomized algorithm storing O(log1.5 (ε n)/ε) items, which is within an O(√log(ε n)) factor of optimal. The algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Relational databases, Query languages (Computer science), Data structures (Computer science), Computer algorithms
Journal or Publication Title: PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
Publisher: ACM
ISBN: 9781450383813
Official Date: 20 June 2021
Dates:
DateEvent
20 June 2021Published
1 May 2021Accepted
Page Range: pp. 96-108
DOI: 10.1145/3452021.3458323
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
ERC-2014-CoG 647557European Research Councilhttp://dx.doi.org/10.13039/501100000781
CCF-1918989National Science Foundationhttp://dx.doi.org/10.13039/501100008982
CCF-1845125National Science Foundationhttp://dx.doi.org/10.13039/501100008982
Conference Paper Type: Paper
Title of Event: The 2021 ACM SIGMOD/PODS Conference
Type of Event: Conference
Location of Event: Virtual conference
Date(s) of Event: 20-25 Jun 2021
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