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

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## Description

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

## Parameters

$n$: 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 |