  We show that it is possible to significantly improve the accuracy of a
general class of histogram queries while satisfying differential privacy. Our
approach carefully chooses a set of queries to evaluate, and then exploits
consistency constraints that should hold over the noisy output. In a
post-processing phase, we compute the consistent input most likely to have
produced the noisy output. The final output is differentially-private and
consistent, but in addition, it is often much more accurate. We show, both
theoretically and experimentally, that these techniques can be used for
estimating the degree sequence of a graph very precisely, and for computing a
histogram that can support arbitrary range queries accurately.
