We consider a generalization of geometric range searching, with the goal of generating an informative "summary" of the objects contained in a query range via the application of a suitable aggregation function on these objects. We provide some of the first results for functions such as closest pair, diameter, and width that measure the extent (or "spread") of the retrieved set. We discuss a subset of our results, including closest pair queries on point-sets in the plane and on random pointsets in ℝd (d ≥ 2) and guaranteed-quality approximations for diameter and width queries in the plane, all for axes-parallel query rectangles.

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Conference 20th Annual Canadian Conference on Computational Geometry, CCCG 2008
Citation
Gupta, P. (Prosenjit), Janardan, R. (Ravi), Kumar, Y. (Yokesh), & Smid, M. (2008). Data structures for range-aggregate extent queries. Presented at the 20th Annual Canadian Conference on Computational Geometry, CCCG 2008.