Computing All Restricted Skyline Probabilities for Uncertain Data

Since data uncertainty is inherent in multi-criteria decision making, recent years have witnessed a dramatically increasing amount of attention devoted to conducting advanced analysis on uncertain data. In this paper, we revisit restricted skyline query on uncertain datasets from both complexity and algorithm perspective. Instead of conducting probabilistic restricted skyline analysis under threshold or top-$k$ semantics, we focus on a more general problem that aims to compute the restricted skyline probability of all objects. We prove that the problem can not be solved in truly subquadratic-time unless the Orthogonal Vectors conjecture fails, and propose two algorithms, one with near-optimal time complexity and the other with better expected time complexity. We also propose an algorithm with sublinear query time and polynomial preprocessing time for the case where the preference region is described by $d - 1$ ratio bound constraints. Our thorough experiments over real and synthetic datasets demonstrate the effectiveness of the problem and the efficiency of the proposed algorithms.