Concepts inOn loops, dominators, and dominance frontiers
Dominator (graph theory)
In computer science, in control flow graphs, a node d dominates a node n if every path from the start node to n must go through d. Notationally, this is written as d dom n (or sometimes d n). By definition, every node dominates itself. There are a number of related concepts: A node d strictly dominates a node n if d dominates n and d does not equal n.
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Loop (graph theory)
In graph theory, a loop (also called a self-loop or a "buckle") is an edge that connects a vertex to itself. A simple graph contains no loops.
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Tree (graph theory)
In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree. A forest is a disjoint union of trees. The various kinds of data structures referred to as trees in computer science are equivalent to trees in graph theory, although such data structures are commonly rooted trees, and may have additional ordering of branches.
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Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context is a collection of "vertices" or "nodes" and a collection of edges that connect pairs of vertices.
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Control flow
In computer science, control flow (or alternatively, flow of control) refers to the order in which the individual statements, instructions or function calls of an imperative or a declarative program are executed or evaluated. Within an imperative programming language, a control flow statement is a statement whose execution results in a choice being made as to which of two or more paths should be followed.
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Vertex (graph theory)
In graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).
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Time complexity
In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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