k-dimensional space, $l_m$ (or $l_\infty$) norm (Closest Pair Problem)
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Description
Given $n$ points in metric space, typically $k$-dimensional space equipped with $l_m$ (or $l_\infty$) norm, find a pair of points with the smallest distance between them.
Related Problems
Subproblem: 2-dimensional space, $l_m$ (or $l_\infty$) norm
Related: 2-dimensional space, Euclidean metric, 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 Randomized Sieve | 1995 | $O(n)$ | $O(n)$, not sure if this is auxiliary | Exact | Randomized | Time & Space |