Histograms are used to summarize the contents of relations into a number of buckets for the estimation of query result sizes. Several techniques have been proposed in the past for determining bucket boundaries which provide accurate estimations. However, while search strategies for optimal bucket boundaries are rather sophisticated, no much attention has been paid for estimating queries inside buckets and all of the above techniques adopt naive methods for such an estimation. This paper focuses on the problem of improving the estimation inside a bucket once its boundaries have been fixed. The proposed technique is based on the addition, to each bucket, of a memory-word additional information (organized into a tree-like index), storing approximate cumulative frequencies in a hierarchical fashion. Both theoretical analysis and experimental results show that the proposed approach improves the accuracy of the estimation inside buckets, w.r.t. both classical approaches (like continuous value assumption and uniform spread assumption) and a number of alternative ways to organize the additional information. The index is later added to state-of-the-art histograms obtaining the non-obvious result that despite the spatial overhead which reduces the number of allowed buckets once the storage space has been fixed, the original methods are strongly improved in terms of accuracy.
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