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Orthogonal Range Reporting in Three and Higher Dimensions

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3 Author(s)
Afshani, P. ; Dept. of Comput. Sci., Aarhus Univ., Aarhus, Denmark ; Arge, L. ; Larsen, K.D.

In orthogonal range reporting we are to preprocess N points in d-dimensional space so that the points inside a d-dimensional axis-aligned query box can be reported efficiently. This is a fundamental problem in various fields, including spatial databases and computational geometry. In this paper we provide a number of improvements for three and higher dimensional orthogonal range reporting: In the pointer machine model, we improve all the best previous results, some of which have not seen any improvements in almost two decades. In the I/O-model, we improve the previously known three-dimensional structures and provide the first (non-trivial) structures for four and higher dimensions.

Published in:

Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on

Date of Conference:

25-27 Oct. 2009