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Topological sorting. In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may ...
Graph. Worst-case performance. Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm.
Directed acyclic graph. In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop ...
Partial orders. A reflexive, weak, [1] or non-strict partial order, [2] commonly referred to simply as a partial order, is a homogeneous relation ≤ on a set that is reflexive, antisymmetric, and transitive. That is, for all it must satisfy: Reflexivity: , i.e. every element is related to itself.
Animated example of a depth-first search For the following graph: a depth-first search starting at the node A, assuming that the left edges in the shown graph are chosen before right edges, and assuming the search remembers previously visited nodes and will not repeat them (since this is a small graph), will visit the nodes in the following ...
1979; 45 years ago (1979) Operating system. Unix, Unix-like, V, Inferno. Platform. Cross-platform. Type. Command. The tsort program is a command line utility on Unix and Unix-like platforms, that performs a topological sort on its input. As of 2017, it is part of the POSIX.1 standard.
The topological spaces ω 1 and its successor ω 1 +1 are frequently used as textbook examples of uncountable topological spaces. For example, in the topological space ω 1 +1, the element ω 1 is in the closure of the subset ω 1 even though no sequence of elements in ω 1 has the element ω 1 as its limit: an element in ω 1 is a countable ...
Selection sort. In computer science, selection sort is an in-place comparison sorting algorithm. It has an O (n2) time complexity, which makes it inefficient on large lists, and generally performs worse than the similar insertion sort. Selection sort is noted for its simplicity and has performance advantages over more complicated algorithms in ...