Efficient quantile retrieval on multi-dimensional data

Given a set of N multi-dimensional points, we study the computation of phi-quantiles according to a ranking function F, which is provided by the user at runtime. Specifically, F computes a score based on the coordinates of each point; our objective is to report the object whose score is the phi N-th smallest in the dataset. phi-quantiles provide a succinct summary about the F-distribution of the underlying data, which is useful for online decision support, data mining, selectivity estimation, query optimization, etc. Assuming that the dataset is indexed by a spatial access method, we propose several algorithms for retrieving a quantile efficiently. Analytical and experimental results demonstrate that a branch-and-bound method is highly effective in practice, outperforming alternative approaches by a significant factor.