Sampling multiple edges efficiently

Talya Eden, Saleet Mossel, Ronitt Rubinfeld

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

We present a sublinear time algorithm that allows one to sample multiple edges from a distribution that is pointwise ϵ-close to the uniform distribution, in an amortized-efficient fashion. We consider the adjacency list query model, where access to a graph G is given via degree and neighbor queries. The problem of sampling a single edge in this model has been raised by Eden and Rosenbaum (SOSA 18). Let n and m denote the number of vertices and edges of G, respectively. Eden and Rosenbaum provided upper and lower bounds of Θ(n/√m) for sampling a single edge in general graphs (where O(·) suppresses poly(1/ϵ) and poly(log n) dependencies). We ask whether the query complexity lower bound for sampling a single edge can be circumvented when multiple samples are required. That is, can we get an improved amortized per-sample cost if we allow a preprocessing phase? We answer in the affirmative. We present an algorithm that, if one knows the number of required samples q in advance, has an overall cost that is sublinear in q, namely, O(√q · (n/√m)), which is strictly preferable to O(q · (n/√m)) cost resulting from q invocations of the algorithm by Eden and Rosenbaum. Subsequent to a preliminary version of this work, Tětek and Thorup (arXiv, preprint) proved that this bound is essentially optimal.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021
EditorsMary Wootters, Laura Sanita
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772075
DOIs
StatePublished - 1 Sep 2021
Externally publishedYes
Event24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021 - Virtual, Seattle, United States
Duration: 16 Aug 202118 Aug 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume207
ISSN (Print)1868-8969

Conference

Conference24th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2021 and 25th International Conference on Randomization and Computation, RANDOM 2021
Country/TerritoryUnited States
CityVirtual, Seattle
Period16/08/2118/08/21

Funding

FundersFunder number
National Science FoundationCCF-1740751
Ben-Gurion University of the NegevDMS 2022448, CCF-2006664

    Keywords

    • Graph algorithm
    • Sampling edges
    • Sublinear algorithms

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