  Local Differential Privacy (LDP) protects user privacy from the data
collector. LDP protocols have been increasingly deployed in the industry. A
basic building block is frequency oracle (FO) protocols, which estimate
frequencies of values. While several FO protocols have been proposed, the
design goal does not lead to optimal results for answering many queries. In
this paper, we show that adding post-processing steps to FO protocols by
exploiting the knowledge that all individual frequencies should be non-negative
and they sum up to one can lead to significantly better accuracy for a wide
range of tasks, including frequencies of individual values, frequencies of the
most frequent values, and frequencies of subsets of values. We consider 10
different methods that exploit this knowledge differently. We establish
theoretical relationships between some of them and conducted extensive
experimental evaluations to understand which methods should be used for
different query tasks.
