Editing Directed acyclic graph (section)

=== Path algorithms ===
Some algorithms become simpler when used on DAGs instead of general graphs, based on the principle of topological ordering. For example, it is possible to find [[shortest path]]s and [[longest path problem|longest paths]] from a given starting vertex in DAGs in linear time by [[Topological sorting#Application to shortest path finding|processing the vertices in a topological order]], and calculating the path length for each vertex to be the minimum or maximum length obtained via any of its incoming edges.<ref>Cormen et al. 2001, Section 24.2, Single-source shortest paths in directed acyclic graphs, pp. 592–595.</ref> In contrast, for arbitrary graphs the shortest path may require slower algorithms such as [[Dijkstra's algorithm]] or the [[Bellman–Ford algorithm]],<ref>Cormen et al. 2001, Sections 24.1, The Bellman–Ford algorithm, pp. 588–592, and 24.3, Dijkstra's algorithm, pp. 595–601.</ref> and longest paths in arbitrary graphs are [[NP-hard]] to find.<ref>Cormen et al. 2001, p. 966.</ref>