Fixed-radius near neighbors

In the fixed-radius near neighbor problem, one is given as input a set of points in d-dimensional Euclidean space and a fixed distance Δ.

The problem has long been studied; Bentley (1975) cites a 1966 paper by Levinthal that uses this technique as part of a system for visualizing molecular structures, and it has many other applications.

However, the constant of proportionality in the linear time bound grows exponentially as a function of the dimension.

Modern parallel methods for GPU are able to efficiently compute all pairs fixed-radius NNS.

Hoetzlein [4] improves this further on modern hardware with counting sorting and atomic operations.