Kavli Affiliate: Xian Chen| Summary: We study (non-induced) subgraph counting under interactive local edge differential privacy (LEDP). Given a fixed pattern graph $H$ with $k$ vertices, $ellge1$ edges, and $q$ connected components, our goal is to approximately count its copies in an arbitrary $n$-vertex undirected graph while preserving edge privacy.
We give two complementary accuracy guarantees. First, for every $H$, we give Linear Noise Cancellation (LNC), a two-round $varepsilon$-LEDP algorithm with additive error and root mean square error both $O(n^k-3/2/varepsilon^ell)$ on every $n$-vertex graph. For fixed sufficiently small $varepsilon$, this improves the optimal noninteractive additive error for triangles by a factor of $sqrt n$ and gives the same improvement in worst-case root mean square error for all cliques on at least three vertices. To our knowledge, this is the first separation between interactive and noninteractive LEDP subgraph counting, showing that a single additional round can improve worst-case accuracy polynomially.
Second, we determine how accuracy improves when the graph has maximum degree at most a public bound $d$. Our Predict and Correct (PC) framework gives an $(ell+2)$-round $varepsilon$-LEDP algorithm with additive error $O(n^q-1/2d^k-q-1log^3ell-2n/varepsilon^ell)$. For connected patterns, its polynomial factor is $sqrt n,d^k-2$, giving sublinear error on constant-degree graphs at fixed privacy. We prove matching lower bounds in $n$ and $d$, up to logarithmic factors at fixed privacy, even under arbitrary interaction and approximate privacy with sufficiently small $δ$. At $d=Θ(n)$, the lower bound also establishes the optimality of LNC’s dependence on $n$.| Search Query: arXiv Query: search_query=au:”Chen Xian”&id_list=&start=0&max_results=10Read More