Nearest Point Query on 184,088,599 Points in E with a Uniform Grid

Nearpt3 is an algorithm and implementation to preprocess more than 10 fixed points in E and then perform nearest point queries against them. With fixed and query points drawn from the same distribution, Nearpt3’s expected preprocessing and query time are θ(1), per point, with a very small constant factor. The data structure is a uniform grid in E, typically with the same number of grid cells as points. The storage budget for Nearpt3, in addition to the space to store the points themselves, is only 4 bytes per grid cell plus 4 bytes per point. Running on a laptop computer, Nearpt3 can process these large datasets: the UNC complete powerplant (Nf = 5, 413, 053 fixed points), Lucy (Nf = 14, 012, 961), David (Nf = 28, 158, 109) and St Matthew (Nf = 184, 088, 599). Nonuniform data can be as quick to process as uniform data, although the optimal grid size is larger. Nearpt3 demonstrates that simple data structures and algorithms can be quite competitive for processing large datasets in E.