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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14623/
Fichtenberger, Hendrik ;
Henzinger, Monika ;
Ost, Wolfgang
Differentially Private Algorithms for Graphs Under Continual Observation
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}
}
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Keywords: |
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differential privacy, continual observation, dynamic graph algorithms |
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Collection: |
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29th Annual European Symposium on Algorithms (ESA 2021) |
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Issue Date: |
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2021 |
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Date of publication: |
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31.08.2021 |
