Differentially Private Quantiles with Smaller Error

In the approximate quantiles problem, the goal is to output mquantile estimates, the ranks of which are as close as possible to m given quantiles 0 q1 qm 1. We present a mechanism for approximate quantiles that satisfies ε-differential privacy for a dataset of n real numbers where the ratio between the distance between the closest pair of points and the size of the domain is bounded by ψ.