On the application of sheared retrieval to orthogonal range queries
SCG '86 Proceedings of the second annual symposium on Computational geometry
Small sets supporting fary embeddings of planar graphs
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Quasi-Valid range querying and its implications for nearest neighbor problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
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We establish new upper bounds on the complexity of several "rectangle" problems. Our results include, for instance, optimal algorithms for range counting and rectangle searching in two dimensions. These involve linear space implementations of range trees and segment trees. The algorithms we give are simple and practical; they can be dynamized and taken into higher dimensions. Also of interest is the nonstandard approach which we follow to obtain these results: it involves transforming data structures on the basis of functional specifications.