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

Maybe I'm misunderstanding the question, but wouldn't it be easiest to just reverse the sign on all the coordinates in one data set (i.e. multiply one set of coordinates by -1), then find the first nearest neighbour (which would be the farthest neighbour)? You can use your favourite knn algorithm with k=1.