Approximating Multidimensional Range Counts with Maximum Error Guarantees

We address the problem of compactly approximating multidimensional range counts with a guaranteed maximum error and propose a novel histogram-based summary structure, termed SliceHist. The key idea is to operate a grid histogram in an approximately rank-transformed space, where the data points are more uniformly distributed and each grid slice contains only a small number of points. Then, the points of each slice are summarised again using the same technique. As each query box partially intersects only few slices and each grid slice has few data points, the summary is able to achieve tight error guarantees. In experiments and through analysis of non-asymptotic formulas we show that SliceHist is not only competitive with existing heuristics in terms of performance, but additionally offers tight error guarantees.