Approximating a data stream for querying and estimation: algorithms and performance evaluation

Obtaining fast and good-quality approximations to data distributions is a problem of central interest to database management. A variety of popular database applications, including approximate querying, similarity searching and data mining in most application domains, rely on such good-quality approximations. Histogram-based approximation is a very popular method in database theory and practice to succinctly represent a data distribution in a space-efficient manner. In this paper, we place the problem of histogram construction into perspective and we generalize it by raising the requirement of a finite data set and/or known data set size. We consider the case of an infinite data set in which data arrive continuously, forming an infinite data stream. In this context, we present single-pass algorithms that are capable of constructing histograms of provable good quality. We present algorithms for the fixed-window variant of the basic histogram construction problem, supporting incremental maintenance of the histograms. The proposed algorithms trade accuracy for speed and allow for a graceful tradeoff between the two, based on application requirements. In the case of approximate queries on infinite data streams, we present a detailed experimental evaluation comparing our algorithms with other applicable techniques using real data sets, demonstrating the superiority of our proposal.