2-dimensional array representation (Closest Pair Problem)

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Given $n$ points in 2-dimensional space in array representation, find a pair of points with the smallest distance between them.

Related Problems

Related: k-dimensional space, $l_m$ (or $l_\infty$) norm, 2-dimensional space, $l_m$ (or $l_\infty$) norm, 2-dimensional space, Euclidean metric


$n$: number of points

$k$: dimension of space

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Khuller; Matias 1995 $O(n)$ $O(n)$, not sure if this is auxiliary Exact Randomized Time & Space
Dyer 1980 $O(n)$ using $O(n^{2})$ processors $O(n^{2})$ Exact Parallel Time & Space