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The Computer Journal 1986 29(1):76-82; doi:10.1093/comjnl/29.1.76
© 1986 by British Computer Society
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Rectangular Point Location in d Dimensions with Applications

H. Edelsbrunner1 *, G. Haring1 * and D. Hilbert2 §

1 Institutes for Information Processing, Technical University of Graz, Schiessstattagasse 4a, A-8010 Graz, Austria, 2 Institute for Applied Mathematics, Technical University of Graz, Steyregasse 17, A-8010, Graz, Austria

Rectangle location search in d dimensions is finding the d-dimensional axis-parallel box of a non-overlapping collection C that contains a query point. A new data structure is proposed that requires optimal space and 0(logd|C|) time for a search. The significance of this data structure in practical applications is substantiated by empirical examinations of its behaviour.

Received January 1984.

* Institutes for Information Processing, Technical University of Graz, SchieBstattagasse 4a, A-8010 Graz/Austria.(Address for Correspondence.)

§ Institute for Applied Mathematics, Technical University of Graz, Steyregasse 17, A-8010, Graz, Austria.


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