Differentially Private Range Subgraph Counting
Keywords: Differential privacy, subgraph, range query
Abstract: Subgraph counting is a fundamental problem in graph analysis. Motivated by the practical need to perform graph analytics on subgraphs defined by selected vertices (or edges) rather than the entire graph, as well as privacy concerns, we initiate the study of private range subgraph counting. Given an $n$-vertex graph $G$, where each vertex (or edge) has a $d$-dimensional attribute vector, a pattern graph $H$, and a set $Q$ of range queries $q$, our goal is to count the occurrences of $H$ in the subgraph of $G$ induced by vertices (or edges) whose attributes fall within $q$, all while preserving privacy. We give the first $\varepsilon$-differentially private algorithm for range subgraph counting, achieving near-optimal accuracy (up to a polylogarithmic factor of $n$) for constant privacy parameter $\varepsilon$ and dimension $d$, with no additional computational overhead compared to non-private algorithms.
We also demonstrate that by relaxing to $(\varepsilon, \delta)$-DP, we can achieve smaller additive errors. Furthermore, our results generalize the subgraph counting results of the partially dynamic model in [FHO21]. Empirical evaluations demonstrate that our algorithm significantly outperforms baseline methods in accuracy while ensuring strong privacy guarantees.
Primary Area: alignment, fairness, safety, privacy, and societal considerations
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Submission Number: 13694
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