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.ESA.2021.42
URN: urn:nbn:de:0030-drops-146230
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14623/
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Fichtenberger, Hendrik ; Henzinger, Monika ; Ost, Wolfgang

Differentially Private Algorithms for Graphs Under Continual Observation

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LIPIcs-ESA-2021-42.pdf (0.8 MB)


Abstract

Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the solution to a problem (e.g., a matching) on an evolving input, i.e., a graph where nodes or edges are inserted or deleted over time. They output the value of the solution after each update operation, i.e., continuously. We study (event-level and user-level) differentially private algorithms for graph problems under continual observation, i.e., differentially private dynamic graph algorithms. We present event-level private algorithms for partially dynamic counting-based problems such as triangle count that improve the additive error by a polynomial factor (in the length T of the update sequence) on the state of the art, resulting in the first algorithms with additive error polylogarithmic in T.
We also give ε-differentially private and partially dynamic algorithms for minimum spanning tree, minimum cut, densest subgraph, and maximum matching. The additive error of our improved MST algorithm is O(W log^{3/2}T / ε), where W is the maximum weight of any edge, which, as we show, is tight up to a (√{log T} / ε)-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error (1+β) for any constant β > 0 and additive error O(W log(nW) log(T) / (ε β)). Finally, we show that the additive error for a broad class of dynamic graph algorithms with user-level privacy must be linear in the value of the output solution’s range.

BibTeX - Entry

@InProceedings{fichtenberger_et_al:LIPIcs.ESA.2021.42,
  author =	{Fichtenberger, Hendrik and Henzinger, Monika and Ost, Wolfgang},
  title =	{{Differentially Private Algorithms for Graphs Under Continual Observation}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{42:1--42:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14623},
  URN =		{urn:nbn:de:0030-drops-146230},
  doi =		{10.4230/LIPIcs.ESA.2021.42},
  annote =	{Keywords: differential privacy, continual observation, dynamic graph algorithms}
}

Keywords: differential privacy, continual observation, dynamic graph algorithms
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021


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