2-dimensional space, Euclidean metric (Closest Pair Problem)

From Algorithm Wiki
Jump to navigation Jump to search


Given $n$ points in 2-dimensional space equipped with the Eucildean metric, 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 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
Shamos; Hoey 1975 $O(n \log n)$ $O(n)$ Exact Deterministic Time

Time Complexity Graph

Closest Pair Problem - 2-dimensional space, Euclidean metric - Time.png