Probabilistic Skylines

Definition

Given an arbitrary set P of points in the positive orthant $\mathbb{R}_{+}^{d}$, we say that a point p Pareto-dominates a point q ($p \succ q$) if p is no worse than q in all the d dimensions and strictly better in at least one dimension. Without lack of generality, we can assume that a point p is better than a point q over the dimension i if p is smaller than q when both are projected on the i-coordinate. The skyline of P is the subset of points that are not dominated by any other point in P. The goal of probabilistic skylines is to compute the skyline over uncertain data, i.e. when there is no perfect information about the location of each point in P. There are several ways to define probabilistic skylines; the most appropriate definition usually depends on the task at hand. The first, original definition is due to Jiang et al. [1]: given a probability threshold τ, the probabilistic skyline is the set of...