Algorithm for finding nearby points?

Question

Given a set of several million points with x,y coordinates, what is the algorithm of choice for quickly finding the top 1000 nearest points from a location? \"Quickly\" here mea

Answer 1

You want to use a structure like a Quad tree, or an RTree. These are multidimensional index structures.

The key is using a good "space filling curve", which is what helps define the nearness of points. A simple space filling curve is a Zorder, but you would be more interested in something like a hilbert curve.

http://en.wikipedia.org/wiki/Space_filling_curve

I don't know of any prepackaged implementations of this stuff. I recently implemented my own RTree in 2 dimensions that only supports bulk loading and searches (via a provided bounding box).

One drawback here is that your points have to be contained in a finite region. There know there are space filling curves that work for spaces that are not finite, but I do not know anything about them.