# Optimal halfspace range reporting in three dimensions

@inproceedings{Afshani2009OptimalHR, title={Optimal halfspace range reporting in three dimensions}, author={P. Afshani and Timothy M. Chan}, booktitle={SODA}, year={2009} }

We give the first optimal solution to a standard problem in computational geometry: three-dimensional halfspace range reporting. We show that n points in 3-d can be stored in a linear-space data structure so that all k points inside a query halfspace can be reported in O(log n + k) time. The data structure can be built in O(n log n) expected time. The previous methods with optimal query time required superlinear (O(n log log n)) space.
We also mention consequences, for example, to higher… Expand

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