Fully Dynamic Data Structure for Top-k Queries on Uncertain Data

Top-k queries allow end-users to focus on the most important (top-k) answers amongst those which satisfy the query. In traditional databases, a user defined score function assigns a score value to each tuple and a top-k query returns k tuples with the highest score. In uncertain database, top-k answer depends not only on the scores but also on the membership probabilities of tuples. Several top-k definitions covering different aspects of score-probability interplay have been proposed in recent past [10], [4], [2], [8]. Most of the existing work in this research field is focused on developing efficient algorithms for answering top-k queries on static uncertain data. Any change (insertion, deletion of a tuple or change in membership probability, score of a tuple) in underlying data forces re-computation of query answers. Such re-computations are not practical considering the dynamic nature of data in many applications. In this paper, we propose a fully dynamic data structure that uses ranking function PRF (α) proposed by Li et al. [8] under the generally adopted model of x-relations [11]. PRF e can effectively approximate various other top-k definitions on uncertain data based on the value of parameter α. An x-relation consists of a number of xtuples, where x-tuple is a set of mutually exclusive tuples (up to a constant number) called alternatives. Each x-tuple in a relation randomly instantiates into one tuple from its alternatives. For an uncertain relation with N tuples, our structure can answer top-k queries in O(k logN) time, handles an update in O(logN) time and takes O(N) space. Finally, we evaluate practical efficiency of our structure on both synthetic and real data.