Evaluating MAX and MIN over Sliding Windows with Various Size Using the Exemplary Sketch

MAX and MIN are two important aggregates offered by the original SQL specification. In the paper, we propose a novel mechanism, i.e. the exemplary sketch, to evaluate MAX and MIN over sliding windows with various size in the data stream environment. Performance analysis shows that evaluating MAX or MIN over w sliding windows with various size using the exemplary sketch takes O(ln n) expected amortized space and O(w) expected amortized evaluation time, where n is the number of the tuples fall into the maximal size sliding window. Moreover, the slidingwindow semantics can also be integrated into the exemplary sketch, which means that we no longer need to buffer all the tuples fall into current sliding windows separately for implementing the sliding-window semantics all alone. Experimental results show that the sketch scheme yields very good performance on both space and time cost.