Longest Path on Interval Graphs: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Longest Path on Interval Graphs (Longest Path Problem)}} == Description == The longest path problem is the problem of finding a path of maximum length in a graph. A graph $G$ is called interval graph if its vertices can be put in a one-to-one correspondence with a family $F$ of intervals on the real line such that two vertices are adjacent in $G$ if and only if the corresponding intervals intersect; $F$ is called an intersection model for $G$. == Param...") |
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== Time Complexity | == Time Complexity Graph == | ||
[[File:Longest Path Problem - Longest Path on Interval Graphs - Time.png|1000px]] | [[File:Longest Path Problem - Longest Path on Interval Graphs - Time.png|1000px]] | ||
== Space Complexity | == Space Complexity Graph == | ||
[[File:Longest Path Problem - Longest Path on Interval Graphs - Space.png|1000px]] | [[File:Longest Path Problem - Longest Path on Interval Graphs - Space.png|1000px]] | ||
== Pareto | == Pareto Frontier Improvements Graph == | ||
[[File:Longest Path Problem - Longest Path on Interval Graphs - Pareto Frontier.png|1000px]] | [[File:Longest Path Problem - Longest Path on Interval Graphs - Pareto Frontier.png|1000px]] | ||
Revision as of 13:04, 15 February 2023
Description
The longest path problem is the problem of finding a path of maximum length in a graph.
A graph $G$ is called interval graph if its vertices can be put in a one-to-one correspondence with a family $F$ of intervals on the real line such that two vertices are adjacent in $G$ if and only if the corresponding intervals intersect; $F$ is called an intersection model for $G$.
Parameters
No parameters found.
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Ioannidou; Kyriaki; Mertzios; George B.; Nikolopoulos; Stavros D. | 2011 | $O(n^{4})$ | $O(n^{3})$ | Exact | Deterministic | Time & Space |
Time Complexity Graph
Space Complexity Graph
Pareto Frontier Improvements Graph
