Given two (large) sets of points, how can I efficiently find pairs that are nearest to each other?

Question

I need to solve a computational problem that boils down to searching for reciprocally-nearest pairs of points between two sets. The problem goes something like this:

Giv

Answer 1

Old thread, but I see there is a pretty recent comment.

I believe for an n dimensional set of points the near point between two sets can be found by finding the near point to the origin of the set difference. You can seek out the paper by Phillip Wolfe of Bell Labs where he lays out the algorithm. You can think of it by taking a random point in set A, finding the closest point in set B, then finding the closest point to the point in set B and so on. http://link.springer.com/article/10.1007%2FBF01580381