Binary-Tree Histograms with Tree Indices

Abstract

In many application contexts, like statistical databases, transaction recording systems, scientific databases, query optimizers, OLAP, and so on, data are summarized as histograms of aggregate values. When the task of reconstructing range queries on original data from aggregate data is performed, a certain estimation error cannot be avoided, due to the loss of information in compressing data. Error size strongly depends both on how histograms partition data domains and on how estimation inside each bucket is done. We propose a new type of histogram, based on an unbalanced binary-tree partition, suitable for providing quick answers to hierarchical range queries, and we use adaptive tree-indexing for better approximating frequencies inside buckets. As the results from our experiments demonstrate, our histogram behaves considerably better than state-of-the-art histograms, showing smaller errors in all considered data sets at the same storage space.