The closest pair of points problem deals with the task to find a pair of points with the global minimum distance. There is a problem, when all points share the same x-coordinate, or at least a large number of points.
I just don't know why, I heard the running time becomes $n^2$
What about it? What is the problem, since the proof for the algorithm shows, that at max. 8 points can reside in the $2 \delta \times \delta$ area.