We study the fundamental problem of frequency estimation under both privacyand communication constraints . We adopt the model of multiparty differential privacy(MDP), which is more general than local differential privacy (LDP) and centralized) differential privacy . Our protocols achieve optimality (up tologarithmic factors) permissible by the more stringent of the two constraints . In particular, when specialized to the $varepsilon-LDP model, our protocolachieves an error of$\sqrt{k}/(e^{\Theta)-1)$for all$\vareptilon\$

Author(s) : Ziyue Huang, Yuan Qiu, Ke Yi, Graham Cormode