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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== Parameters == | == Parameters == | ||
$n$: number of vertices | |||
$m$: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Ioannidou; Kyriaki; Mertzios; George B.; Nikolopoulos; Stavros D. (Longest Path on Interval Graphs Longest Path Problem)|Ioannidou; Kyriaki; Mertzios; George B.; Nikolopoulos; Stavros D.]] || 2011 || $O(n^{4})$ || $O(n^{3})$ || Exact || Deterministic || | | [[Ioannidou; Kyriaki; Mertzios; George B.; Nikolopoulos; Stavros D. (Longest Path on Interval Graphs Longest Path Problem)|Ioannidou; Kyriaki; Mertzios; George B.; Nikolopoulos; Stavros D.]] || 2011 || $O(n^{4})$ || $O(n^{3})$ || Exact || Deterministic || [https://link.springer.com/content/pdf/10.1007/s00453-010-9411-3.pdf Time & Space] | ||
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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]] | ||
Latest revision as of 09:10, 28 April 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
$n$: number of vertices
$m$: number of edges
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
