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.ICALP.2022.26
URN: urn:nbn:de:0030-drops-163674
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16367/
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Blocki, Jeremiah ; Grigorescu, Elena ; Mukherjee, Tamalika

Privately Estimating Graph Parameters in Sublinear Time

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LIPIcs-ICALP-2022-26.pdf (0.8 MB)

Abstract

We initiate a systematic study of algorithms that are both differentially-private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private (1+ρ)-approximation algorithm for the problem of computing the average degree of a graph, for every ρ > 0. The running time of the algorithm is roughly the same (for sparse graphs) as its non-private version proposed by Goldreich and Ron (Sublinear Algorithms, 2005). We also obtain the first differentially-private sublinear-time approximation algorithms for the maximum matching size and the minimum vertex cover size of a graph.
An overarching technique we employ is the notion of coupled global sensitivity of randomized algorithms. Related variants of this notion of sensitivity have been used in the literature in ad-hoc ways. Here we formalize the notion and develop it as a unifying framework for privacy analysis of randomized approximation algorithms.

BibTeX - Entry

@InProceedings{blocki_et_al:LIPIcs.ICALP.2022.26,
  author =	{Blocki, Jeremiah and Grigorescu, Elena and Mukherjee, Tamalika},
  title =	{{Privately Estimating Graph Parameters in Sublinear Time}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{26:1--26:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16367},
  URN =		{urn:nbn:de:0030-drops-163674},
  doi =		{10.4230/LIPIcs.ICALP.2022.26},
  annote =	{Keywords: differential privacy, sublinear time, graph algorithms}
}

Keywords: differential privacy, sublinear time, graph algorithms
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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