Structure-Aware Sampling: Flexible and Accurate Summarization
  In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators and well-understood confidence bounds.   Classic sample-based summaries, however, are designed for arbitrary subset queries and are oblivious to the structure in the set of keys. The particular structure, such as hierarchy, order, or product space (multi-dimensional), makes range queries much more relevant for most analysis of the data.   Dedicated summarization algorithms for range-sum queries have also been extensively studied. They can outperform existing sampling schemes in terms of accuracy on range queries per summary size. Their accuracy, however, rapidly degrades when, as is often the case, the query spans multiple ranges. They are also less flexible - being targeted for range sum queries alone - and are often quite costly to build and use.   In this paper we propose and evaluate variance optimal sampling schemes that are structure-aware. These summaries improve over the accuracy of existing structure-oblivious sampling schemes on range queries while retaining the benefits of sample-based summaries: flexible summaries, with high accuracy on both range queries and arbitrary subset queries. 
Edith Cohen, Graham Cormode, Nick Duffield
cs.DS