TY - GEN

T1 - Sampling multiple edges efficiently

AU - Eden, Talya

AU - Mossel, Saleet

AU - Rubinfeld, Ronitt

N1 - Publisher Copyright:
© Talya Eden, Saleet Mossel, and Ronitt Rubinfeld; licensed under Creative Commons License CC-BY 4.0

PY - 2021/9/1

Y1 - 2021/9/1

N2 - 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.

AB - 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.

KW - Graph algorithm

KW - Sampling edges

KW - Sublinear algorithms

UR - http://www.scopus.com/inward/record.url?scp=85115648012&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs-APPROX/RANDOM.2021.51

DO - 10.4230/LIPIcs-APPROX/RANDOM.2021.51

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85115648012

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021

A2 - Wootters, Mary

A2 - Sanita, Laura

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Y2 - 16 August 2021 through 18 August 2021

ER -