The canonical application of topological sorting is in scheduling a sequence of jobs or tasks based on their dependencies. The jobs are represented by vertices, and there is an edge from x to y if job x must be completed before job … 展开

If a topological sort has the property that all pairs of consecutive vertices in the sorted order are connected by edges, then these edges form a directed Hamiltonian path in the 展开

By definition, the solution of a scheduling problem that includes a precedence graph is a valid solution to topological sort (irrespective of the number of machines), however, topological sort in itself is not enough to optimally solve a scheduling optimisation problem. … 展开

The usual algorithms for topological sorting have running time linear in the number of nodes plus the number of edges, asymptotically,
Kahn's algorithm 展开

The topological ordering can also be used to quickly compute shortest paths through a weighted directed acyclic graph. Let V be the list of vertices in … 展开

Topological orderings are also closely related to the concept of a linear extension of a partial order in mathematics. A partially ordered set is just a set of objects together with a definition of the "≤" inequality relation, satisfying the axioms of reflexivity (x ≤ x), … 展开

• tsort, a Unix program for topological sorting
• Feedback arc set, a set of edges whose removal allows the remaining subgraph to be topologically sorted
• Tarjan's strongly connected components algorithm, an … 展开