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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.
It is also possible to check whether a given directed graph is a DAG in linear time, either by attempting to find a topological ordering and then testing for each edge whether the resulting ordering is valid [18] or alternatively, for some topological sorting algorithms, by verifying that the algorithm successfully orders all the vertices ...
1 Examples and types of graphs. 2 Graph coloring. 3 Paths and cycles. 4 Trees. ... Topological sorting. Pre-topological order; Other topics. Adjacency list; Adjacency ...
This is a list of useful examples in general topology, a field of mathematics. Alexandrov topology; Cantor space; Co-kappa topology Cocountable topology; Cofinite topology; Compact-open topology; Compactification; Discrete topology; Double-pointed cofinite topology; Extended real number line; Finite topological space; Hawaiian earring; Hilbert cube
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
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 ...
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.