2-dimensional array representation: Difference between revisions
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(Created page with "{{DISPLAYTITLE:2-dimensional array representation (Closest Pair Problem)}} == Description == 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 == Parameters == No parameters found. == Table of Algorithms ==...") |
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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.ezproxy.canberra.edu.au/science/article/pii/S0890540185710498, Space] | ||
|- | |- | ||
| [[Dyer (2-dimensional array representation Closest Pair Problem)|Dyer]] || 1980 || $O(n)$ using $O(n^{2})$ processors || $O(n^{2})$ || Exact || Parallel || [https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/0020019080900356 Time & Space] | | [[Dyer (2-dimensional array representation Closest Pair Problem)|Dyer]] || 1980 || $O(n)$ using $O(n^{2})$ processors || $O(n^{2})$ || Exact || Parallel || [https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/0020019080900356 Time & Space] | ||
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Latest revision as of 07:52, 10 April 2023
Description
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
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 |
| Dyer | 1980 | $O(n)$ using $O(n^{2})$ processors | $O(n^{2})$ | Exact | Parallel | Time & Space |