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

The Skyline of a Probabilistic Relation

In a deterministic relation, tuple u dominates tuple v if u is no worse than v on all attributes, and better than v on at least one attribute. This concept is at the heart of skyline queries, that return the set of undominated tuples. In this paper we extend the notion of skyline to probabilistic relations by generalizing to this context the definition of tuple domination. Our approach is parametric in the semantics for ranking probabilistic tuples and, being it based on order-theoretic principles, preserves the three properties the skyline has in the deterministic case: it equals the union of all top1 results of monotone scoring functions, it requires no additional parameter, and it is insensitive to attribute scales. We then show how domination among probabilistic tuples can be efficiently checked by means of a set of rules. We detail rules for the cases in which tuples are ranked using either the "expected rank" or the "expected score" semantics, and explain how the approach can be applied to other semantics as well. Since computing the skyline of a probabilistic relation is a time-consuming task, we introduce algorithms for checking domination rules in an optimized way. Experiments show that these algorithms can reduce execution times with respect to a naive evaluation

Domination in the Probabilistic World: Computing Skylines for Arbitrary Correlations and Ranking Semantics

In a probabilistic database, deciding if a tuple u is better than another tuple v has not a univocal solution, rather it depends on the specific Probabilistic Ranking Semantics (PRS) one wants to adopt so as to combine together tuples' scores and probabilities. In deterministic databases it is known that skyline queries are a remarkable alternative to (top-k) ranking queries, because they remove from the user the burden of specifying a scoring function that combines values of different attributes into a single score. The skyline of a deterministic relation R is the set of undominated tuples in R -- tuple u dominates tuple v iff on all the attributes of interest u is better than or equal to v and strictly better on at least one attribute. Domination is equivalent to having s(u) 65 s(v) for all monotone scoring functions s(). The skyline of a probabilistic relation Rp can be similarly defined as the set of P-undominated tuples in Rp, where now u P-dominates v iff, whatever monotone scoring function one would use to combine the skyline attributes, u is reputed better than v by the PRS at hand. This definition, which is applicable to arbitrary ranking semantics and probabilistic correlation models, is parametric in the adopted PRS, thus it ensures that ranking and skyline queries will always return consistent results. In this article we provide an overall view of the problem of computing the skyline of a probabilistic relation. We show how, under mild conditions that indeed hold for all known PRSs, checking P-domination can be cast into an optimization problem, whose complexity we characterize for a variety of combinations of ranking semantics and correlation models. For each analyzed case we also provide specific P-domination rules, which are exploited by the algorithm we detail for the case where the probabilistic model is known to the query processor. We also consider the case in which the probability of tuple events can only be obtained through an oracle, and describe another skyline algorithm for this loosely integrated scenario. Our experimental evaluation of P-domination rules and skyline algorithms confirms the theoretical analysis

Getting the Best from Uncertain Data

The skyline of a relation is the set of tuples that are not dominated by any other tuple in the same relation, where tuple u dominates tuple v if u is no worse than v on all the attributes of interest and strictly better on at least one attribute. Previous attempts to extend skyline queries to probabilistic databases have proposed either a weaker form of domination, which is unsuitable to univocally define the skyline, or a definition that implies algorithms with exponential complexity. In this paper we demonstrate how, given a semantics for linearly ranking probabilistic tuples, the skyline of a probabilistic relation can be univocally defined. Our approach preserves the three fundamental properties of skyline: 1) it equals the union of all top-1 results of monotone scoring functions, 2) it requires no additional parameter to be specified, and 3) it is insensitive to actual attribute scales. We also detail efficient sequential and index-based algorithms