(Approximate) Uncertain Skylines

Abstract

Given a set of points with uncertain locations, we consider the problem of computing the probability of each point lying on the skyline, that is, the probability that it is not dominated by any other input point. If each point's uncertainty is described as a probability distribution over a discrete set of locations, we improve the best known exact solution. We also suggest why we believe our solution might be optimal. Next, we describe simple, near-linear time approximation algorithms for computing the probability of each point lying on the skyline. In addition, some of our methods can be adapted to construct data structures that can efficiently determine the probability of a query point lying on the skyline.

Efficient computation for probabilistic skyline over uncertain preferences

“…We selected moderate-sized datasets having categorical attributes without missing values from UCI ML repository. 1 Experimental results related to Lenses, Zoo and Balance datasets are presented here. Our empirical study also examines synthetic data wherein datasets of different sizes (number of objects in the range [100, 10000]) with dimensions varying in the range [2,8] are randomly generated with uniform distribution for each dimension and assuming mutual independence of dimensions.…”

“…The domains of dimensions are assumed to be ordered. For instance, given a set of points P in R d , a point p ∈ P is on the skyline of P if for every other point q ∈ P at least one coordinate of p is larger than that of q [1]. Skyline computation exists for both certain and uncertain datasets.…”

Closest pair and the post office problem for stochastic points

“…A number of researchers have recently begun to explore geometric computing over probabilistic data [1,2,14,19]. These studies are fundamentally different from the classical geometric probability that deals with properties of random point sets drawn from some infinite sets, such as points in unit square [11].…”

“…Instead, the recent work in computational geometry is concerned with worst-case set of objects and worst-case probabilities or behavior. In particular, the recent work of Agarwal [1,2] deals with the database problem of skyline computation using a multiple-universe model. The work of van Kreveld and Löffler [14,19] deals with objects whose locations are randomly distributed in some uncertainty regions.…”

On the Most Likely Convex Hull of Uncertain Points

“…The goal there is to achieve robustness under bounded precision, and not to compute structures that are most representative under a probability distribution. There also has been extensive research in the database community on clustering and ranking of uncertain data [4,5,10] and on range searching and indexing [1][2][3].…”