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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.

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

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