Ranking queries on uncertain data

Abstract

Uncertain data is inherent in a few important applications. It is far from trivial to extend ranking queries (also known as top-k queries), a popular type of queries on certain data, to uncertain data. In this paper, we cast ranking queries on uncertain data using three parameters: rank threshold k, probability threshold p, and answer set size threshold l. Systematically, we identify four types of ranking queries on uncertain data. First, a probability threshold top-k query computes the uncertain records taking a probability of at least p to be in the top-k list. Second, a top-(k, l) query returns the top-l uncertain records whose probabilities of being ranked among top-k are the largest. Third, the p-rank of an uncertain record is the smallest number k such that the record takes a probability of at least p to be ranked in the top-k list. A rank threshold top-k query retrieves the records whose p-ranks are at most k. Last, a top-(p, l) query returns the top-l uncertain records with the smallest p-ranks. To answer such ranking queries, we present an efficient exact algorithm, a fast sampling algorithm, and a Poisson approximation-based algorithm. To answer top-(k, l) queries and top-(p, l) queries, we propose PRist+, a compact index. An efficient index construction algorithm and efficacious query answering methods are developed for PRist+. An empirical study using real and synthetic data sets verifies the effectiveness of the probabilistic ranking queries and the efficiency of our methods.