d-dimensional Convex Hull (Convex Hull)

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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


$n$: 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