2-dimensional Convex Hull: Difference between revisions
Jump to navigation
Jump to search
(Created page with "{{DISPLAYTITLE:2-dimensional Convex Hull (Convex Hull)}} == Description == The convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or; more generally; in an affine space over the reals) is the smallest convex set that contains X. Here, we are looking at the 2-dimensional case. == Related Problems == Generalizations: d-dimensional Convex Hull Subproblem: 2-dimensional Convex Hull, Online, 2...") |
No edit summary |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 14: | Line 14: | ||
== Parameters == | == Parameters == | ||
$n$: number of line segments | |||
h: number of points on the convex hull | |||
$h$: number of points on the convex hull | |||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 25: | Line 26: | ||
|- | |- | ||
| [[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] | ||
|- | |||
| [[Online 2-d Convex Hull, Preparata (2-dimensional Convex Hull, Online Convex Hull)|Online 2-d Convex Hull, Preparata]] || 1979 || $O(logn)$ per operation, $O(n*log(n)$) total || $O(n)$ || Exact || Deterministic || [https://dl-acm-org.ezproxy.canberra.edu.au/doi/abs/10.1145/359131.359132 Time] | |||
|- | |||
| [[Dynamic 2-d Convex Hull, Overmars and van Leeuwen (2-dimensional Convex Hull, Dynamic Convex Hull)|Dynamic 2-d Convex Hull, Overmars and van Leeuwen]] || 1980 || $O(log^{2}(n)$) per operation, $O(n*log^{2}(n)$) total || || Exact || Deterministic || [https://www-sciencedirect-com.ezproxy.canberra.edu.au/science/article/pii/002200008190012X?via%3Dihub Time] | |||
|- | |||
| [[(many more...) (2-dimensional Convex Hull, Dynamic Convex Hull)|(many more...)]] || || || || Exact || Deterministic || | |||
|- | |- | ||
|} | |} | ||
Latest revision as of 09:19, 10 April 2023
Description
The convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or; more generally; in an affine space over the reals) is the smallest convex set that contains X. Here, we are looking at the 2-dimensional case.
Related Problems
Generalizations: d-dimensional Convex Hull
Subproblem: 2-dimensional Convex Hull, Online, 2-dimensional Convex Hull, Dynamic
Related: 3-dimensional Convex Hull, 2-dimensional Convex Hull, Dynamic
Parameters
$n$: number of line segments
$h$: number of points 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 | |
| Online 2-d Convex Hull, Preparata | 1979 | $O(logn)$ per operation, $O(n*log(n)$) total | $O(n)$ | Exact | Deterministic | Time |
| Dynamic 2-d Convex Hull, Overmars and van Leeuwen | 1980 | $O(log^{2}(n)$) per operation, $O(n*log^{2}(n)$) total | Exact | Deterministic | Time | |
| (many more...) | Exact | Deterministic |