2-dimensional Convex Hull, Dynamic: 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 | ||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 24: | Line 24: | ||
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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/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/science/article/pii/002001908490084X Time] | ||
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| [[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/science/article/pii/002200008190012X?via%3Dihub 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/science/article/pii/002200008190012X?via%3Dihub Time] | ||
Latest revision as of 08:19, 10 April 2023
Description
Here, the input points may be sequentially inserted or deleted, and the convex hull must be updated after each insert/delete operation.
Related Problems
Generalizations: 2-dimensional Convex Hull
Related: 3-dimensional Convex Hull, d-dimensional Convex Hull, 2-dimensional Convex Hull, Online
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 | |
| 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 |