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An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
Therefore, the order in which the strongly connected components are identified constitutes a reverse topological sort of the DAG formed by the strongly connected components. [7] Donald Knuth described Tarjan's SCC algorithm as one of his favorite implementations in the book The Stanford GraphBase. [8] He also wrote: [9]
Pages in category "Sorting algorithms" The following 48 pages are in this category, out of 48 total. ... Topological sorting; Tournament sort; Tree sort; X.
In computer science, algorithms for finding linear extensions of partial orders (represented as the reachability orders of directed acyclic graphs) are called topological sorting. In category theory [ edit ]
Weak orders have also been used in computer science, in partition refinement based algorithms for lexicographic breadth-first search and lexicographic topological ordering. In these algorithms, a weak ordering on the vertices of a graph (represented as a family of sets that partition the vertices, together with a doubly linked list providing a ...
Many topological sorting algorithms will detect cycles too, since those are obstacles for topological order to exist. Also, if a directed graph has been divided into strongly connected components , cycles only exist within the components and not between them, since cycles are strongly connected.
The traditional ld (Unix linker) requires that its library inputs be sorted in topological order, since it processes files in a single pass. This applies both to static libraries ( *.a ) and dynamic libraries ( *.so ), and in the case of static libraries preferably for the individual object files contained within.
A kind of opposite of a sorting algorithm is a shuffling algorithm. These are fundamentally different because they require a source of random numbers. Shuffling can also be implemented by a sorting algorithm, namely by a random sort: assigning a random number to each element of the list and then sorting based on the random numbers.