Multi-dimensional Histograms with Tight Bounds for the Error

Histograms are being used as non-parametric selectivity estimators for one-dimensional data. For high-dimensional data it is common to either compute one-dimensional histograms for each attribute or to compute a multi-dimensional equi-width histogram for a set of attributes. This either yields small low-quality or large high-quality histograms. In this paper we introduce HIRED (high-dimensional histograms with dimensionality reduction): small high-quality histograms for multi-dimensional data. HIRED histograms are adaptive, and they are based on the shape error and directional splits. The shape error permits a precise control of the estimation error of the histogram and, together with directional splits, yields a memory complexity that does not depend on the number of uniform attributes in the dataset. We provide extensive experimental results with synthetic and real world datasets. The experiments confirm that our method is as precise as state-of-the-art techniques and uses orders of magnitude less memory