Reporting all intersection points, line segments: Difference between revisions
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, line segments - Time.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, line segments - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, line segments - Space.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, line segments - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Line segment intersection - Reporting all intersection points, line segments - Pareto Frontier.png|1000px]] | [[File:Line segment intersection - Reporting all intersection points, line segments - Pareto Frontier.png|1000px]] | ||
Revision as of 13:04, 15 February 2023
Description
The line segment intersection problem supplies a list of line segments in the Euclidean plane and asks about the points where they intersect (cross), if any. In this case, we wish to report all points of intersection.
Related Problems
Generalizations: Reporting all intersection points, generalized segments
Subproblem: Counting number of intersection points, line segments
Related: Reporting all intersection points, convex polygons, Reporting all intersection points, general polygons
Parameters
n: number of line segments
k: number of points of intersection
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naive | 1940 | $O(n^{2})$ | $O(n+k)$ total ($O({1})$ auxiliary if excluding input and output) | Exact | Deterministic | |
| Bentley–Ottmann algorithm | 1979 | $O( n log n + k log n)$ | $O(n)$ auxiliary | Exact | Deterministic | Time & Space |
| Chazelle & Edelsbrunner | 1992 | $O( nlog n + k )$ | $O(n+k)$ total? | Exact | Deterministic | Time & Space |
| CHAZELLE | 1986 | $O( n*log^{2}(n)/(log log n) + k)$ | $O(n+k)$ total (and possibly auxiliary as well?) | Exact | Deterministic | Time & Space |
| Goodrich | 1989 | $O(log^{2}(n))$ | $O(n+k)$ total? | Exact | Parallel | Time |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
