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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 y can be started (for example, when washing clothes, the washing machine must finish before we put the clothes in the dryer).
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.
Topological sorting is the algorithmic problem of finding a topological ordering of a given DAG. It can be solved in linear time. [16] Kahn's algorithm for topological sorting builds the vertex ordering directly.
A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces , and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology.
A topological space X is called orderable or linearly orderable [1] if there exists a total order on its elements such that the order topology induced by that order and the given topology on X coincide. The order topology makes X into a completely normal Hausdorff space. The standard topologies on R, Q, Z, and N are the order topologies.
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. 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 ...
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Topological sorting. Finding 2-(edge or vertex)-connected components. Finding 3-(edge or vertex)-connected components. Finding the bridges of a graph. Generating words in order to plot the limit set of a group. Finding strongly connected components. Determining whether a species is closer to one species or another in a phylogenetic tree ...