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Near-Optimal Differentially Private k-Core Decomposition (2312.07706v2)
Published 12 Dec 2023 in cs.DS, cs.CR, and cs.SI
Abstract: Recent work by Dhulipala et al. \cite{DLRSSY22} initiated the study of the $k$-core decomposition problem under differential privacy via a connection between low round/depth distributed/parallel graph algorithms and private algorithms with small error bounds. They showed that one can output differentially private approximate $k$-core numbers, while only incurring a multiplicative error of $(2 +\eta)$ (for any constant $\eta >0$) and additive error of $\poly(\log(n))/\eps$. In this paper, we revisit this problem. Our main result is an $\eps$-edge differentially private algorithm for $k$-core decomposition which outputs the core numbers with no multiplicative error and $O(\text{log}(n)/\eps)$ additive error. This improves upon previous work by a factor of 2 in the multiplicative error, while giving near-optimal additive error. Our result relies on a novel generalized form of the sparse vector technique, which is especially well-suited for threshold-based graph algorithms; thus, we further strengthen the connection between distributed/parallel graph algorithms and differentially private algorithms.
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