Faster upper bounding of intersection sizes

Abstract

There is a long history of developing efficient algorithms for set intersection, which is a fundamental operation in information retrieval and databases. In this paper, we describe a new data structure, a Cardinality Filter, to quickly compute an upper bound on the size of a set intersection. Knowing an upper bound of the size can be used to accelerate many applications such as top-k query processing in text mining. Given finite sets A and B, the expected computation time for the upper bound of the size of the intersection |A cap B| is O( (|A| + |B|) w), where w is the machine word length. This is much faster than the current best algorithm for the exact intersection, which runs in O((|A| + |B|) / √w + |A cap B|) expected time. Our performance studies show that our implementations of Cardinality Filters are from 2 to 10 times faster than existing set intersection algorithms, and the time for a top-k query in a text mining application can be reduced by half.