Time- and Space-Efficient Sliding Window Top-k Query Processing

Abstract

A sliding window top-k (top-k/w) query monitors incoming data stream objects within a sliding window of size w to identify the k highest-ranked objects with respect to a given scoring function over time. Processing of such queries is challenging because, even when an object is not a top-k/w object at the time when it enters the processing system, it might become one in the future. Thus a set of potential top-k/w objects has to be stored in memory while its size should be minimized to efficiently cope with high data streaming rates. Existing approaches typically store top-k/w and candidate sliding window objects in a k-skyband over a two-dimensional score-time space. However, due to continuous changes of the k-skyband, its maintenance is quite costly. Probabilistic k-skyband is a novel data structure storing data stream objects from a sliding window with significant probability to become top-k/w objects in future. Continuous probabilistic k-skyband maintenance offers considerably improved runtime performance compared to k-skyband maintenance, especially for large values of k, at the expense of a small and controllable error rate. We propose two possible probabilistic k-skyband usages: (i) When it is used to process all sliding window objects, the resulting top-k/w algorithm is approximate and adequate for processing random-order data streams. (ii) When probabilistic k-skyband is used to process only a subset of most recent sliding window objects, it can improve the runtime performance of continuous k-skyband maintenance, resulting in a novel exact top-k/w algorithm. Our experimental evaluation systematically compares different top-k/w processing algorithms and shows that while competing algorithms offer either time efficiency at the expanse of space efficiency or vice-versa, our algorithms based on the probabilistic k-skyband are both time and space efficient.