Stabbing the Sky: Efficient Skyline Computation over Sliding Windows

Abstract

We consider the problem of efficiently computing the skyline against the most recent N elements in a data stream seen so far. Specifically, we study the n-of-N skyline queries; that is, computing the skyline for the most recent n (/spl forall/n/spl les/N) elements. Firstly, we developed an effective pruning technique to minimize the number of elements to be kept. It can be shown that on average storing only O(log/sup d/ N) elements from the most recent N elements is sufficient to support the precise computation of all n-of-N skyline queries in a d-dimension space if the data distribution on each dimension is independent. Then, a novel encoding scheme is proposed, together with efficient update techniques, for the stored elements, so that computing an n-of-N skyline query in a d-dimension space takes O(log N+s) time that is reduced to O(d log log N+s) if the data distribution is independent, where s is the number of skyline points. Thirdly, a novel trigger based technique is provided to process continuous n-of-N skyline queries with O(/spl delta/) time to update the current result per new data element and O(log s) time to update the trigger list per result change, where /spl delta/ is the number of element changes from the current result to the new result. Finally, we extend our techniques to computing the skyline against an arbitrary window in the most recent N element. Besides theoretical performance guarantees, our extensive experiments demonstrated that the new techniques can support on-line skyline query computation over very rapid data streams.