Relative Error Streaming Quantiles

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10475244" target="_blank" >RIV/00216208:11320/23:10475244 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JDxgW_EUIg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JDxgW_EUIg</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3617891" target="_blank" >10.1145/3617891</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relative Error Streaming Quantiles

Popis výsledku v původním jazyce

Estimating 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 equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in n. Given the sketch and a query item y, 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 en error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This article investigates multiplicative (1 +/- epsilon)-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(epsilon(2)n)/epsilon 2) or O(log(3) (epsilon n)/epsilon) universe items. We present a randomized sketch storing O(log(1.5) (epsilon n)/epsilon) items that can (1 +/- epsilon)-approximate the rank of each universe item with high constant probability; this space bound is within an O(root log(epsilon n)) factor of optimal. Our algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments.

Název v anglickém jazyce

Relative Error Streaming Quantiles

Popis výsledku anglicky

Estimating 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 equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in n. Given the sketch and a query item y, 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 en error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This article investigates multiplicative (1 +/- epsilon)-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(epsilon(2)n)/epsilon 2) or O(log(3) (epsilon n)/epsilon) universe items. We present a randomized sketch storing O(log(1.5) (epsilon n)/epsilon) items that can (1 +/- epsilon)-approximate the rank of each universe item with high constant probability; this space bound is within an O(root log(epsilon n)) factor of optimal. Our algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GX19-27871X" target="_blank" >GX19-27871X: Efektivní aproximační algoritmy a obvodová složitost</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the ACM

ISSN

0004-5411

e-ISSN

1557-735X

Svazek periodika

70

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

48

Strana od-do

30

Kód UT WoS článku

001091490700003

EID výsledku v databázi Scopus

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