Longest Path on Interval Graphs (Longest Path Problem)

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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 $G$.


$n$: 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

Longest Path Problem - Longest Path on Interval Graphs - Time.png