2-dimensional space, Euclidean metric (Closest Pair Problem)
Revision as of 10:19, 15 February 2023 by Admin (talk | contribs) (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...")
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 Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Khuller; Matias Randomized Sieve | 1995 | $O(n)$ | $O(n)$, not sure if this is auxiliary | Exact | Randomized | Time & Space |
| Shamos; Hoey | 1975 | $O(n logn)$ | $O(n)$ | Exact | Deterministic | Time |
Time Complexity graph
Space Complexity graph
Pareto Decades graph
