Interactive LEDP improves subgraph counting accuracy by factor of sqrt n
Original title: The Power of Interaction in Locally Edge-Private Subgraph Counting
A two-round interactive algorithm for subgraph counting under local edge differential privacy improves additive error by a factor of sqrt n compared to noninteractive approaches.
We study non-induced subgraph counting under interactive local edge differential privacy. For every fixed pattern graph H we give Linear Noise Cancellation a two-round ε-LEDP algorithm with additive error O(n^{k-3/2}/ε^ℓ). This improves the optimal noninteractive additive error for triangles by a factor of sqrt n. We also determine accuracy improvements when the graph has maximum degree at most a public bound d and prove matching lower bounds.
- First separation between interactive and noninteractive LEDP subgraph counting
- Polynomial improvement in worst-case accuracy with one additional round
- Matching lower bounds up to logarithmic factors at fixed privacy
From the original article
1 min read at arxiv.orgWe study (non-induced) subgraph counting under interactive local edge differential privacy (LEDP). Given a fixed pattern graph $H$ with $k$ vertices, $\ell\ge1$ 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.
By Xian Chen · arxiv.org
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