The massive data streams observed in network monitoring, data processing and scientific studies are typically too large to store. For many applications over such data, we must obtain compact summaries of the stream. These summaries should allow accurate answering of post hoc queries with estimates which approximate the true answers over the original stream. The data often has an underlying structure which makes certain subset queries, in particular range queries, more relevant than arbitrary subsets. Applications such as access control, change detection, and heavy hitters typically involve subsets that are ranges or unions thereof. Random sampling is a natural summarization tool, being easy to implement and flexible to use. Known sampling methods are good for arbitrary queries but fail to optimize for the common case of range queries. Meanwhile, specialized summarization algorithms have been proposed for range-sum queries and related problems. These can outperform sampling giving ...
Edith Cohen, Graham Cormode, Nick G. Duffield