D-dimensional Convex Hull: Difference between revisions
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== Parameters == | == Parameters == | ||
n: number of line segments | $n$: number of line segments | ||
h: number of points on the convex hull | $h$: number of points on the convex hull | ||
f_1: number of facets on the convex hull | $f_1$: number of facets on the convex hull | ||
f_2: number of subfacets on the convex hull | $f_2$: number of subfacets on the convex hull | ||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Incremental convex hull algorithm; Michael Kallay ( Convex Hull)|Incremental convex hull algorithm; Michael Kallay]] || 1984 || $O(n log n)$ || || Exact || Deterministic || [https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/002001908490084X Time] | | [[Incremental convex hull algorithm; Michael Kallay ( Convex Hull)|Incremental convex hull algorithm; Michael Kallay]] || 1984 || $O(n \log n)$ || || Exact || Deterministic || [https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/002001908490084X Time] | ||
|- | |- | ||
| [[Seidel's Shelling Algorithm (d-dimensional Convex Hull Convex Hull)|Seidel's Shelling Algorithm]] || 1986 || $O(n^{2}+f_1*log(n)$) || || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/doi/pdf/10.1145/12130.12172 Time] | | [[Seidel's Shelling Algorithm (d-dimensional Convex Hull Convex Hull)|Seidel's Shelling Algorithm]] || 1986 || $O(n^{2}+f_1*log(n)$) || || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/doi/pdf/10.1145/12130.12172 Time] | ||
Latest revision as of 08:19, 10 April 2023
Description
Here, we are looking at the general d-dimensional case.
Related Problems
Subproblem: 2-dimensional Convex Hull, 3-dimensional Convex Hull
Related: 3-dimensional Convex Hull, 2-dimensional Convex Hull, Online, 2-dimensional Convex Hull, Dynamic
Parameters
$n$: number of line segments
$h$: number of points on the convex hull
$f_1$: number of facets on the convex hull
$f_2$: number of subfacets on the convex hull
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Incremental convex hull algorithm; Michael Kallay | 1984 | $O(n \log n)$ | Exact | Deterministic | Time | |
| Seidel's Shelling Algorithm | 1986 | $O(n^{2}+f_1*log(n)$) | Exact | Deterministic | Time | |
| Chand-Kapur, Gift Wrapping | 1970 | $O(n*f_1)$ | Exact | Deterministic | Time | |
| N-dimensional Quickhull | 1996 | $O(n*f(h)$/h) where f(h) denotes the maximum number of facets with h vertices | Exact | Deterministic | Time |