Finding Probabilistic k-Skyline Sets on Uncertain Data

ABSTRACT Skyline is a set of points that are not dominated by any other point. Given uncertain objects, probabilistic skyline has been studied which computes objects with high probability of being skyline. While useful for selecting individual objects, it is not sufficient for scenarios where we wish to compute a subset of skyline objects, i.e., a skyline set. In this paper, we generalize the notion of probabilistic skyline to probabilistic k-skyline sets (Pk-SkylineSets) which computes k-object sets with high probability of being skyline set. We present an efficient algorithm for computing probabilistic k-skyline sets. It uses two heuristic pruning strategies and a novel data structure based on the classic layered range tree to compute the skyline set probability for each instance set with a worst-case time bound. The experimental results on the real NBA dataset and the synthetic datasets show that Pk-SkylineSets is interesting and useful, and our algorithms are efficient and scalable

Skyline Probability over Uncertain Preferences

Skyline analysis is a key in a wide spectrum of real applications involving multi-criteria optimal decision making. In recent years, a considerable amount of research has been contributed on efficient computation of skyline probabilities over uncertain environment. Most studies if not all, assume uncertainty lies only in attribute values. To the extent of our knowledge, only one study addresses the skyline probability computation problem in scenarios where uncertainty resides in attribute preferences, instead of values. However this study takes a problematic approach by assuming independent object dominance, which we find is not always true in uncertain preference scenarios. In fact this assumption has already been shown to be not necessarily true in uncertain value scenarios. Motivated by this, we revisit the skyline probability computation over uncertain preferences in this paper. We first show that the problem of skyline probability computation over uncertain preferences is ♯P-complete. Then we propose efficient exact and approximate algorithms to tackle this problem. While the exact algorithm remains exponential in the worst case, our experiments demonstrate its efficiency in practice. The approximate algorithm achieves ɛ-approximation by the confidence (1 − δ) with time complexity O(dn 1 ɛ2 ln 1), where n is the number of objects and δ d is the dimensionality. The efficiency and effectiveness of our methods are verified by extensive experimental results on real and synthetic data sets. 1