- Published 2002 in Theory of Computing Systems

This paper presents algorithms for estimating aggregate functions over a "sliding window" of the <i>N</i> most recent data items in one or more streams. Our results include:<ol><li>For a <i>single stream</i>, we present the first ε-approximation scheme for the number of 1's in a sliding window that is optimal in both worst case time and space. We also present the first ε for the sum of integers in [<i>0</i>..<i>R</i>] in a sliding window that is optimal in both worst case time and space (assuming <i>R</i> is at most polynomial in <i>N</i>). Both algorithms are deterministic and use only logarithmic memory words.</li><li>In contrast, we show that <i>an </i> deterministic algorithm that estimates, to within a small constant relative error, the number of 1's (or the sum of integers) in a sliding window over the <i>union of distributed streams</i> requires &OHgr;(<i>N</i>) space.</li><li> We present the first randomized (ε,&sgr;)-approximation scheme for the number of 1's in a sliding window over the <i>union of distributed streams</i> that uses only logarithmic memory words. We also present the first (ε,&sgr;)-approximation scheme for the number of distinct values in a sliding window over distributed streams that uses only logarithmic memory words.</li></olOur results are obtained using a novel family of synopsis data structures.

Citations per Year

Semantic Scholar estimates that this publication has **161** citations based on the available data.

See our **FAQ** for additional information.

@article{Gibbons2002DistributedSA,
title={Distributed Streams Algorithms for Sliding Windows},
author={Phillip B. Gibbons and Srikanta Tirthapura},
journal={Theory of Computing Systems},
year={2002},
volume={37},
pages={457-478}
}