Differentially private algorithms for graphs under continual observation LIPIcs Fichtenberger, Hendrik Henzinger, Monika H ; https://orcid.org/0000-0002-5008-6530 Ost, Wolfgang 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 Informatik 2021 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/11814 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> eng info:eu-repo/semantics/altIdentifier/doi/10.4230/LIPIcs.ESA.2021.42 info:eu-repo/semantics/altIdentifier/issn/1868-8969 info:eu-repo/semantics/altIdentifier/isbn/9783959772044 info:eu-repo/semantics/altIdentifier/arxiv/2106.14756 info:eu-repo/semantics/openAccess