Achieve privacy-preserving simplicial depth query over collaborative cloud servers

The simplicial depth (SD) of a query point q∈ℝd$$q\in \mathbb {R}^{d}$$ with respect to a dataset S⊂ℝd$$S\subset \mathbb {R}^{d}$$ is defined based on counting all (d + 1)-dimensional simplices obtained from S that contain q. The simplicial depth is a ranking function which is frequently used in order to sort a multivariate dataset. In the higher dimension d, no better algorithm is known than the brute force method which takes Θ(nd+ 1) time, …