A Truly Dynamic Data Structure for Top-k Queries on Uncertain Data

Abstract

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 [20, 13, 6, 18]. 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 truly dynamic data structure that uses ranking function PRF ^e(α) proposed by Li et al. [18] under the generally adopted model of x-relations [21]. 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 x-tuples, 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(klogN) 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.

This work is supported in part by US NSF Grant CCF–1017623 (R. Shah).