License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.51
URN: urn:nbn:de:0030-drops-147441
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14744/
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Eden, Talya ; Mossel, Saleet ; Rubinfeld, Ronitt

Sampling Multiple Edges Efficiently

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LIPIcs-APPROX51.pdf (0.8 MB)

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.

BibTeX - Entry

@InProceedings{eden_et_al:LIPIcs.APPROX/RANDOM.2021.51,
  author =	{Eden, Talya and Mossel, Saleet and Rubinfeld, Ronitt},
  title =	{{Sampling Multiple Edges Efficiently}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{51:1--51:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14744},
  URN =		{urn:nbn:de:0030-drops-147441},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.51},
  annote =	{Keywords: Sampling edges, graph algorithm, sublinear algorithms}
}

Keywords: Sampling edges, graph algorithm, sublinear algorithms
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)
Issue Date: 2021
Date of publication: 15.09.2021

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