D-dimensional Convex Hull: Difference between revisions
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(Created page with "{{DISPLAYTITLE:d-dimensional Convex Hull (Convex Hull)}} == 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 == <pre>n: number of line segments h: number of points on the convex hull f_1: number of facets on the con...") |
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== Parameters == | == Parameters == | ||
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 == | ||
Revision as of 12:02, 15 February 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 |