The τ-Skyline for Uncertain Data

In this paper, we introduce the notion of τ -skyline as an alternative representation for uncertain skylines. Given a parameter τ ∈ [0,1] and a set P of n uncertain points in the plane, where each uncertain point Pi is described by a discrete probability distribution defined over k locations, the τ -skyline region of P is the set of points q in the plane such that the probability of any Pi dominating q is at most τ , and the τ -skyline of P is the boundary of the τ -skyline region of P. We present an O(nk log(nk)) time algorithm for computing the τ -skyline of P. The τ -skyline probability of each Pi of P is defined to be the probability of Pi lying inside the τ -skyline region of P. We show that the τ -skyline probabilities of all Pi’s can be computed in O(nk log(nk)) time. Remarkably, our method is very simple and can be easily implemented, a huge potential interest for practice.