Structure-Aware Sampling: Flexible and Accurate Summarization

In processing large quantities of data, a fundamental problem isto obtain a summary which supports approximate query answer-ing. Random sampling yields flexible summaries which naturallysupport subset-sum queries with unbiased estimators and well-understood confidence bounds. Classic sample-based summaries,however, are designed for arbitrary subset queries and are oblivi-ous to the structure in the set of keys. The particular structure, suchas hierarchy, order, or product space (multi-dimensional), makesrange queries much more relevant for most analysis of the data.Dedicated summarization algorithms for range-sum queries havealso been extensively studied. They can outperform existing sam-pling schemes in terms of accuracy on range queries per summarysize. Their accuracy, however, rapidly degrades when, as is of-ten the case, the query spans multiple ranges. They are also lessflexible—being targeted for range sum queries alone—and are of-ten quite costly to build and use.In this paper we propose and evaluate variance optimal samplingschemes that are structure-aware. These summaries improve overthe accuracy of existing structure-oblivious sampling schemes onrange queries while retaining the benefits of sample-based sum-maries: flexible summaries, with high accuracy on both rangequeries and arbitrary subset queries.