On Differentially Private Counting on Trees

We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. We propose a new error measure for this setting 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 in the pure-DP setting. In the approximate-DP setting, we design new algorithms achieving significant improvement over known ones.