Range Thresholding on Streams

Abstract

This paper studies a type of continuous queries called range thresholding on streams (RTS). Imagine the stream as an unbounded sequence of elements each of which is a real value. A query registers an interval, and must be notified as soon as a certain number of incoming elements fall into the interval. The system needs to support multiple queries simultaneously, and aims to minimize the space consumption and computation time. Currently, all the solutions to this problem entail quadratic time O(nm) to process n stream elements and m queries, which severely limits their applicability to only a small number of queries. We propose the first algorithm that breaks the quadratic barrier, by reducing the computation cost dramatically to O(n + m), subject only to a polylogarithmic factor. The algorithm is general enough to guarantee the same on weighted versions of the queries even in d-dimensional space of any constant d. Its vast advantage over the previous methods in practical environments has been confirmed through extensive experimentation.