Nearly optimal edge estimation with independent set queries

Xi Chen; Amit Levi; Erik Waingarten

Nearly optimal edge estimation with independent set queries

Xi Chen
, Amit Levi
, Erik Waingarten

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

Abstract

We study the problem of estimating the number of edges of an unknown, undirected graph G = ([n], E) with access to an independent set oracle. When queried about a subset S ⊆ [n] of vertices, the independent set oracle answers whether S is an independent set in G or not. Our first main result is an algorithm that computes a (1 + ε)-approximation of the number of edges m of the graph using min(^√m, n/√m) · poly(log n, 1/ε) independent set queries. This improves the upper bound of min(^√m, n²/m) · poly(log n, 1/ε) by Beame et al. [3]. Our second main result shows that min(^√m, n/√m)/polylog(n) independent set queries are necessary, thus establishing that our algorithm is optimal up to a factor of poly(log n, 1/∈).

Original language	English
Title of host publication	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Editors	Shuchi Chawla
Publisher	Association for Computing Machinery
Pages	2916-2935
Number of pages	20
ISBN (Electronic)	9781611975994
State	Published - 2020
Externally published	Yes
Event	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020 - Salt Lake City, United States Duration: 5 Jan 2020 → 8 Jan 2020

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	2020-January

Conference

Conference	31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Country/Territory	United States
City	Salt Lake City
Period	5/01/20 → 8/01/20

Bibliographical note

Publisher Copyright:
Copyright © 2020 by SIAM

ASJC Scopus subject areas

Software
General Mathematics

Cite this

@inproceedings{260e89db1efd4a56a0291e7fd49913a0,

title = "Nearly optimal edge estimation with independent set queries",

abstract = "We study the problem of estimating the number of edges of an unknown, undirected graph G = ([n], E) with access to an independent set oracle. When queried about a subset S ⊆ [n] of vertices, the independent set oracle answers whether S is an independent set in G or not. Our first main result is an algorithm that computes a (1 + ε)-approximation of the number of edges m of the graph using min(√m, n/√m) · poly(log n, 1/ε) independent set queries. This improves the upper bound of min(√m, n2/m) · poly(log n, 1/ε) by Beame et al. [3]. Our second main result shows that min(√m, n/√m)/polylog(n) independent set queries are necessary, thus establishing that our algorithm is optimal up to a factor of poly(log n, 1/∈).",

author = "Xi Chen and Amit Levi and Erik Waingarten",

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year = "2020",

language = "English",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "2916--2935",

editor = "Shuchi Chawla",

booktitle = "31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020",

address = "United States",

}

Chen, X, Levi, A & Waingarten, E 2020, Nearly optimal edge estimation with independent set queries. in S Chawla (ed.), 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020-January, Association for Computing Machinery, pp. 2916-2935, 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, United States, 5/01/20.

Nearly optimal edge estimation with independent set queries. / Chen, Xi; Levi, Amit; Waingarten, Erik.
31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. ed. / Shuchi Chawla. Association for Computing Machinery, 2020. p. 2916-2935 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2020-January).

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

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T1 - Nearly optimal edge estimation with independent set queries

AU - Chen, Xi

AU - Levi, Amit

AU - Waingarten, Erik

PY - 2020

Y1 - 2020

N2 - We study the problem of estimating the number of edges of an unknown, undirected graph G = ([n], E) with access to an independent set oracle. When queried about a subset S ⊆ [n] of vertices, the independent set oracle answers whether S is an independent set in G or not. Our first main result is an algorithm that computes a (1 + ε)-approximation of the number of edges m of the graph using min(√m, n/√m) · poly(log n, 1/ε) independent set queries. This improves the upper bound of min(√m, n2/m) · poly(log n, 1/ε) by Beame et al. [3]. Our second main result shows that min(√m, n/√m)/polylog(n) independent set queries are necessary, thus establishing that our algorithm is optimal up to a factor of poly(log n, 1/∈).

AB - We study the problem of estimating the number of edges of an unknown, undirected graph G = ([n], E) with access to an independent set oracle. When queried about a subset S ⊆ [n] of vertices, the independent set oracle answers whether S is an independent set in G or not. Our first main result is an algorithm that computes a (1 + ε)-approximation of the number of edges m of the graph using min(√m, n/√m) · poly(log n, 1/ε) independent set queries. This improves the upper bound of min(√m, n2/m) · poly(log n, 1/ε) by Beame et al. [3]. Our second main result shows that min(√m, n/√m)/polylog(n) independent set queries are necessary, thus establishing that our algorithm is optimal up to a factor of poly(log n, 1/∈).

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M3 - Conference contribution

AN - SCOPUS:85084087124

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 2916

EP - 2935

BT - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020

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PB - Association for Computing Machinery

T2 - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020

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ER -

Nearly optimal edge estimation with independent set queries

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

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Cite this