Almost linear time differentially private release of synthetic graphs

TL;DR

This paper introduces nearly linear time algorithms for differentially private synthetic graph release, matching non-private complexities while maintaining high utility, and extends to continual observation scenarios.

Contribution

It presents the first nearly linear time algorithms for differentially private synthetic graph generation with strong utility guarantees.

Findings

Achieves rom ilde{O}(m) time and O(m) space for synthetic graph release.

Provides algorithms that nearly match non-private complexities.

Extends methods to private graph analysis under continual observation.

Abstract

In this paper, we give an almost linear time and space algorithms to sample from an exponential mechanism with an $\ell_1$-score function defined over an exponentially large non-convex set. As a direct result, on input an $n$ vertex $m$ edges graph $G$, we present the \textit{first} $\widetilde{O}(m)$ time and $O(m)$ space algorithms for differentially privately outputting an $n$ vertex $O(m)$ edges synthetic graph that approximates all the cuts and the spectrum of $G$. These are the \emph{first} private algorithms for releasing synthetic graphs that nearly match this task's time and space complexity in the non-private setting while achieving the same (or better) utility as the previous works in the more practical sparse regime. Additionally, our algorithms can be extended to private graph analysis under continual observation.