k-dimensional space, $l_m$ (or $l_\infty$) norm (Closest Pair Problem)

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Given $n$ points in metric space, typically $k$-dimensional space equipped with $l_m$ (or $l_\infty$) norm, find a pair of points with the smallest distance between them.

Related Problems

Subproblem: 2-dimensional space, $l_m$ (or $l_\infty$) norm

Related: 2-dimensional space, Euclidean metric, 2-dimensional array representation


$n$: 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