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COMPGEOM
2010
ACM

Orthogonal range reporting: query lower bounds, optimal structures in 3-d, and higher-dimensional improvements

8 years 8 months ago
Orthogonal range reporting: query lower bounds, optimal structures in 3-d, and higher-dimensional improvements
Orthogonal range reporting is the problem of storing a set of n points in d-dimensional space, such that the k points in an axis-orthogonal query box can be reported efficiently. While the 2-d version of the problem was completely characterized in the pointer machine model more than two decades ago, this is not the case in higher dimensions. In this paper we provide a space optimal pointer machine data structure for 3-d orthogonal range reporting that answers queries in O(log n + k) time. Thus we settle the complexity of the problem in 3-d. We use this result to obtain improved structures in higher dimensions, namely structures with a log n/ log log n factor increase in space and query time per dimension. Thus for d ≥ 3 we obtain a structure that both uses optimal O(n(log n/ log log n)d−1 ) space and answers queries in the best known query bound O(log n(log n/ log log n)d−3 + k). Furthermore, we show that any data structure for the d-dimensional orthogonal range reporting proble...
Peyman Afshani, Lars Arge, Kasper Dalgaard Larsen
Added 10 Jul 2010
Updated 10 Jul 2010
Type Conference
Year 2010
Where COMPGEOM
Authors Peyman Afshani, Lars Arge, Kasper Dalgaard Larsen
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