2-dimensional Convex Hull, Online: 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] | ||
|- | |- | ||
| [[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/doi/abs/10.1145/359131.359132 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/doi/abs/10.1145/359131.359132 Time] | ||
Latest revision as of 09:19, 10 April 2023
Description
Here, we are given the input points one by one, and must maintain the current convex hull after each input point.
Related Problems
Generalizations: 2-dimensional Convex Hull
Related: 3-dimensional Convex Hull, d-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 |
References/Citation
https://dl.acm.org/doi/abs/10.1145/359131.359132
https://link.springer.com/content/pdf/10.1007/978-1-4612-1098-6.pdf