Finding the farthest point in one set from another set

Question

My goal is a more efficient implementation of the algorithm posed in this question.

Consider two sets of points (in N-space. 3-space for the example case of RGB colorsp

Answer 1

The most obvious approach seems to me to be to build a tree structure on one set to allow you to search it relatively quickly. A kd-tree or similar would probably be appropriate for that.

Having done that, you walk over all the points in the other set and use the tree to find their nearest neighbour in the first set, keeping track of the maximum as you go.

It's nlog(n) to build the tree, and log(n) for one search so the whole thing should run in nlog(n).