2-dimensional space, Euclidean metric: Difference between revisions
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(Created page with "{{DISPLAYTITLE:2-dimensional space, Euclidean metric (Closest Pair Problem)}} == 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 == No parameters found. == Table of Alg...") |
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== Parameters == | == Parameters == | ||
$n$: number of points | |||
$k$: dimension of space | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Khuller; Matias | | [[Khuller; Matias ( Closest Pair Problem)|Khuller; Matias]] || 1995 || $O(n)$ || $O(n)$, not sure if this is auxiliary || Exact || Randomized || [https://www.sciencedirect.com/science/article/pii/S0890540185710498 Time] & [https://www.sciencedirect.com/science/article/pii/S0890540185710498, Space] | ||
|- | |- | ||
| [[Shamos; Hoey (2-dimensional space, Euclidean metric Closest Pair Problem)|Shamos; Hoey]] || 1975 || $O(n | | [[Shamos; Hoey (2-dimensional space, Euclidean metric Closest Pair Problem)|Shamos; Hoey]] || 1975 || $O(n \log n)$ || $O(n)$ || Exact || Deterministic || [https://ieeexplore.ieee.org/document/4567872 Time] | ||
|- | |- | ||
|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:Closest Pair Problem - 2-dimensional space, Euclidean metric - Time.png|1000px]] | [[File:Closest Pair Problem - 2-dimensional space, Euclidean metric - Time.png|1000px]] | ||
Latest revision as of 09:06, 28 April 2023
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 |
Time Complexity Graph
