topological sorting

Make can decide where to start through topological sorting.

Otherwise, the graph must have at least one cycle and therefore a topological sorting is impossible.

An alternative algorithm for topological sorting is based on depth-first search.

In computer science, algorithms for finding linear extensions of partial orders are called topological sorting.

Reverse postordering produces a topological sorting of any directed acyclic graph.

He related this problem to problems in other areas of mathematics including linear algebra and topological sorting of graphs.

Topological sorting.

Many topological sorting algorithms will detect cycles too, since those are obstacles for topological order to exist.

Topological sorting is the algorithmic problem of finding topological orderings; it can be solved in linear time.

The usual algorithms for topological sorting have running time linear in the number of nodes plus the number of edges ().

If a dependency graph does not have any circular dependencies, it forms a directed acyclic graph, and an evaluation order may be found by topological sorting.

D. E. Knuth, The Art of Computer Programming, Volume 1, section 2.2.3, which gives an algorithm for topological sorting of a partial ordering, and a brief history.

A major feature in APT is the way it calls dpkg - it does topological sorting of the list of packages to be installed or removed and calls dpkg in the best possible sequence.

The algorithmic problem of constructing a linear extension of a partial order on a finite set, represented by a directed acyclic graph with the set's elements as its vertices, is known as topological sorting; several algorithms solve it in linear time.

Most topological sorting algorithms are also capable of detecting cycles in their inputs, however, it may be desirable to perform cycle detection separately from topological sorting in order to provide appropriate handling for the detected cycles.

The canonical application of topological sorting (topological order) is in scheduling a sequence of jobs or tasks based on their dependencies; topological sorting algorithms were first studied in the early 1960s in the context of the PERT technique for scheduling in project management .