conference paper published yes Hendrik Fichtenberger author Monika H Henzinger author 540c9bbd-f2de-11ec-812d-d04a5be856300000-0002-5008-6530 Wolfgang Ost author ESA: Annual European Symposium on Algorithms 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. Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021Lisbon, Portual eng 1868-8969 9783959772044 2106.1475610.4230/LIPIcs.ESA.2021.42 204 yes Fichtenberger, Hendrik, et al. “Differentially Private Algorithms for Graphs under Continual Observation.” <i>29th Annual European Symposium on Algorithms</i>, vol. 204, 42, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:<a href="https://doi.org/10.4230/LIPIcs.ESA.2021.42">10.4230/LIPIcs.ESA.2021.42</a>. Fichtenberger, H., Henzinger, M., &#38; Ost, W. (2021). Differentially private algorithms for graphs under continual observation. In <i>29th Annual European Symposium on Algorithms</i> (Vol. 204). Lisbon, Portual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href="https://doi.org/10.4230/LIPIcs.ESA.2021.42">https://doi.org/10.4230/LIPIcs.ESA.2021.42</a> Fichtenberger H, Henzinger M, Ost W. 2021. Differentially private algorithms for graphs under continual observation. 29th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 204, 42. H. Fichtenberger, M. Henzinger, and W. Ost, “Differentially private algorithms for graphs under continual observation,” in <i>29th Annual European Symposium on Algorithms</i>, Lisbon, Portual, 2021, vol. 204. Fichtenberger, Hendrik, Monika Henzinger, and Wolfgang Ost. “Differentially Private Algorithms for Graphs under Continual Observation.” In <i>29th Annual European Symposium on Algorithms</i>, Vol. 204. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href="https://doi.org/10.4230/LIPIcs.ESA.2021.42">https://doi.org/10.4230/LIPIcs.ESA.2021.42</a>. Fichtenberger H, Henzinger M, Ost W. Differentially private algorithms for graphs under continual observation. In: <i>29th Annual European Symposium on Algorithms</i>. Vol 204. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:<a href="https://doi.org/10.4230/LIPIcs.ESA.2021.42">10.4230/LIPIcs.ESA.2021.42</a> H. Fichtenberger, M. Henzinger, W. Ost, in:, 29th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. 118142022-08-12T07:04:44Z2024-11-06T08:22:28Z