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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 $varepsilon$-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 $O(W log^{3/2}T / varepsilon)$, where $W$ is the maximum weight of any edge, which, as we show, is tight up to a $(sqrt{log T} / varepsilon)$-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error $(1+beta)$ for any constant $beta > 0$ and additive error $O(W log(nW) log(T) / (varepsilon beta) )$. 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 solutions range.
The correlations and network structure amongst individuals in datasets today---whether explicitly articulated, or deduced from biological or behavioral connections---pose new issues around privacy guarantees, because of inferences that can be made ab
Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which operate on s
This paper studies the relationship between generalization and privacy preservation in iterative learning algorithms by two sequential steps. We first establish an alignment between generalization and privacy preservation for any learning algorithm.
We introduce a new $(epsilon_p, delta_p)$-differentially private algorithm for the $k$-means clustering problem. Given a dataset in Euclidean space, the $k$-means clustering problem requires one to find $k$ points in that space such that the sum of s
This paper introduces the first provably accurate algorithms for differentially private, top-down decision tree learning in the distributed setting (Balcan et al., 2012). We propose DP-TopDown, a general privacy preserving decision tree learning algo