We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a combination of multiplicative and additive approximation to the query results. We examine known mechanisms in differential privacy (DP) and prove their optimality, under this measure, in the pure-DP setting. In the approximate-DP setting, we design new algorithms achieving significant improvements over known ones.

翻译：我们研究了在层级结构中执行不同层次计数查询同时保护个体隐私的问题。受实际应用启发，我们针对该问题提出了一种新的误差度量，通过结合查询结果的乘法近似与加法近似来进行评估。在纯差分隐私框架下，我们检验了已知的差分隐私机制，并证明它们在此度量下具有最优性。在近似差分隐私框架下，我们设计了新算法，较已知方法取得了显著改进。