  In this paper, we give efficient algorithms and lower bounds for solving the
heavy hitters problem while preserving differential privacy in the fully
distributed local model. In this model, there are n parties, each of which
possesses a single element from a universe of size N. The heavy hitters problem
is to find the identity of the most common element shared amongst the n
parties. In the local model, there is no trusted database administrator, and so
the algorithm must interact with each of the $n$ parties separately, using a
differentially private protocol. We give tight information-theoretic upper and
lower bounds on the accuracy to which this problem can be solved in the local
model (giving a separation between the local model and the more common
centralized model of privacy), as well as computationally efficient algorithms
even in the case where the data universe N may be exponentially large.
