# $k$th closest pair of points

The problem of finding the pair of closest points in a set of points has been a classical example of divide and conquer technique for some decades now. But I could not find any results on finding $k$th closest pair of points; that is the $k$th pair $(p_i, p_j)$ in the list of pairs of distinct points from set $P$, sorted in increasing order of distance.

I could not find anything on that. Do we have any results? More particularly, I am interested in the case of points from a Euclidean plane.

• Try searching Google scholar for "k closest pairs" — there are things to find there. Nov 12 '14 at 15:58
• Thanks. Turns out "distance selection" is also a relevant keyword. Nov 13 '14 at 18:37