Longest path problem

Longest path problem

In graph theory, the longest path problem is a problem of finding the longest path in a graph. Unlike the shortest path problem, this problem is NP-complete which means that the optimal solution cannot be found in polynomial time unless P=NP.

The longest path problem has an efficient dynamic programming solution in a directed acyclic graph using topological sort. It can also be solved by inverting the weights and using the Bellman-Ford algorithm (this approach does not work in general because it creates negative-weight cycles).

Related problems

* Travelling salesman problem
* Shortest path problem

External links

* [http://www.ics.uci.edu/~eppstein/161/960312.html NP-Completeness]


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