Orthogonal Range Reporting in Three and Higher Dimensions

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 (nontrivial) structures for four and higher dimensions. Keywords-data structures; computational geometry; orthogonal range searching; external memory;

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Peyman Afshani, Lars Arge, Kasper Dalgaard Larsen
• Keywords: Computational Geometry, Dimensional Orthogonal Range, FOCS 2009, Orthogonal Range, Theoretical Computer Science