SORTaki: A Framework to Integrate Sorting with Differential Private Histogramming Algorithms

Differential privacy has been established as the primary framework for privacy preserving data-sharing. In the context of query answering through histograms, most of the datadependent solutions are composed of two steps: a partitioning phase that splits the histogram into bins and a finalizing step that approximates each bin with its average frequency or other similar statistics. Solutions that sort the histograms' values prior to the partitioning phase can improve the utility of the final output. In this paper, we build SORTaki, a framework that integrates sorting with any partitioning and finalizing mechanism. Using SORTaki, we modify existing partitioning and finalizing solutions, as well as propose new ones, that mitigate the error of the final approximation up to 70% over existing sorting or nonsorting based algorithms. Additionally, we perform a principled and thorough empirical evaluation of current and proposed techniques, that highlights the right settings to use sorting and when to avoid it.