On sampling edges almost uniformly

Talya Eden; Will Rosenbaum

doi:10.4230/OASIcs.SOSA.2018.7

On sampling edges almost uniformly

Talya Eden
, Will Rosenbaum

Tel Aviv University

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

15 Scopus citations

Abstract

We consider the problem of sampling an edge almost uniformly from an unknown graph, G = (V,E). Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe a new simple algorithm that returns a random edge e ∈ E using O(n/√ϵm) queries in expectation, such that each edge e is sampled with probability (1 ± ϵ)/m. Here, n = |V| is the number of vertices, and m = |E| is the number of edges. Our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform Ω(n/√m) queries.

Original language	English
Title of host publication	1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Editors	Raimund Seidel
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959770644
DOIs	https://doi.org/10.4230/OASIcs.SOSA.2018.7
State	Published - 1 Jan 2018
Externally published	Yes
Event	1st Symposium on Simplicity in Algorithms, SOSA 2018 - New Orleans, United States Duration: 7 Jan 2018 → 10 Jan 2018

Publication series

Name	OpenAccess Series in Informatics
Volume	61
ISSN (Print)	2190-6807

Conference

Conference	1st Symposium on Simplicity in Algorithms, SOSA 2018
Country/Territory	United States
City	New Orleans
Period	7/01/18 → 10/01/18

Bibliographical note

Publisher Copyright:
© Talya Eden and William B. Rosenbaum.

Keywords

Graph algorithms
Query complexity
Sampling edges
Sublinear algorithms

Access to Document

10.4230/OASIcs.SOSA.2018.7

Cite this

Eden, T., & Rosenbaum, W. (2018). On sampling edges almost uniformly. In R. Seidel (Ed.), 1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 Article 7 (OpenAccess Series in Informatics; Vol. 61). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/OASIcs.SOSA.2018.7

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title = "On sampling edges almost uniformly",

abstract = "We consider the problem of sampling an edge almost uniformly from an unknown graph, G = (V,E). Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe a new simple algorithm that returns a random edge e ∈ E using O(n/√ϵm) queries in expectation, such that each edge e is sampled with probability (1 ± ϵ)/m. Here, n = |V| is the number of vertices, and m = |E| is the number of edges. Our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform Ω(n/√m) queries.",

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Eden, T & Rosenbaum, W 2018, On sampling edges almost uniformly. in R Seidel (ed.), 1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018., 7, OpenAccess Series in Informatics, vol. 61, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 1st Symposium on Simplicity in Algorithms, SOSA 2018, New Orleans, United States, 7/01/18. https://doi.org/10.4230/OASIcs.SOSA.2018.7

On sampling edges almost uniformly. / Eden, Talya; Rosenbaum, Will.
1st Symposium on Simplicity in Algorithms, SOSA 2018 - Co-located with the 29th ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. ed. / Raimund Seidel. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 7 (OpenAccess Series in Informatics; Vol. 61).

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

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KW - Query complexity

KW - Sampling edges

KW - Sublinear algorithms

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On sampling edges almost uniformly

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Keywords

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