Mergeable summaries

We study the mergeability of data summaries. Informally speaking, mergeability requires that, given two summaries on two data sets, there is a way to merge the two summaries into a single summary on the union of the two data sets, while preserving the error and size guarantees. This property means that the summaries can be merged in a way like other algebraic operators such as sum and max, which is especially useful for computing summaries on massive distributed data. Several data summaries are trivially mergeable by construction, most notably all the sketches that are linear functions of the data sets. But some other fundamental ones like those for heavy hitters and quantiles, are not (known to be) mergeable. In this paper, we demonstrate that these summaries are indeed mergeable or can be made mergeable after appropriate modifications. Specifically, we show that for ε-approximate heavy hitters, there is a deterministic mergeable summary of size O(1/ε); for εapproximate quantiles...

• Type: Journal
• Year: 2012
• Where: PODS
• Authors: Pankaj K. Agarwal, Graham Cormode, Zengfeng Huang, Jeff M. Phillips, Zhewei Wei, Ke Yi
• Keywords: Algebraic Operators, Database, Faculty Research Award, PODS 2012, Size Guarantees