Computing matchings in graphs is a foundational algorithmic task. Despite extensive interest in differentially private (DP) graph analysis, work on privately computing matching solutions, rather than just their size, has been sparse. The sole prior work in the standard model of pure $\varepsilon$-differential privacy, by Hsu, Huang, Roth, Roughgarden, and Wu [HHR+14, STOC'14], focused on allocations and was thus restricted to bipartite graphs. We present a comprehensive study of DP algorithms for maximum matching and b-matching in general graphs, which also yields techniques that improve upon the bipartite setting. En route to solving these matching problems, we develop a set of novel techniques with broad applicability, including a new symmetry argument for DP lower bounds, the first arboricity-based sparsifiers for node-DP, and the novel Public Vertex Subset Mechanism.

翻译：图匹配计算是基础算法任务。尽管差分隐私图分析受到广泛关注，但针对私有计算匹配解（而非仅其规模）的研究仍较为匮乏。先前在纯ε-差分隐私标准模型中唯一的相关工作由Hsu、Huang、Roth、Roughgarden和Wu [HHR+14, STOC'14]完成，该研究聚焦于分配问题，因而仅限于二分图。本文对一般图中最大匹配与b-匹配的差分隐私算法进行了系统性研究，并提出可改进二分图场景的技术方案。在解决这些匹配问题的过程中，我们开发了一系列具有广泛适用性的创新技术，包括：差分隐私下界证明的新对称性论证方法、首个基于树密度的节点差分隐私稀疏化技术，以及创新的公共顶点子集机制。