Problem: Find a linear ordering of the vertices of V such that for each edge (i,j) \in E, vertex i is to the left of vertex j.
Excerpt from The Algorithm Design Manual: Topological sorting arises as a natural subproblem in most algorithms on directed acyclic graphs. Topological sorting orders the vertices and edges of a DAG in a simple and consistent way and hence plays the same role for DAGs that depth-first search does for general graphs.
Topological sorting can be used to schedule tasks under precedence constraints. Suppose we have a set of tasks to do, but certain tasks have to be performed before other tasks. These precedence constraints form a directed acyclic graph, and any topological sort (also known as a linear extension) defines an order to do these tasks such that each is performed only after all of its constraints are satisfied.
|Algorithms in Java, Third Edition (Parts 1-4) by Robert Sedgewick and Michael Schidlowsky||Introduction to Algorithms by T. Cormen and C. Leiserson and R. Rivest and C. Stein||Introduction to Algorithms by U. Manber|