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Corresponding dominator tree of the control flow graph. In computer science, a node d of a control-flow graph dominates a node n if every path from the entry 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:
Three dominating sets of the same graph (in red). The domination number of this graph is 2: (b) and (c) show that there is a dominating set with 2 vertices, and there is no dominating set with only 1 vertex. In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D.
There is an arc from Block M to Block N if M is an immediate dominator of N. This graph is a tree, since each block has a unique immediate dominator. This tree is rooted at the entry block. The dominator tree can be calculated efficiently using Lengauer–Tarjan's algorithm. A postdominator tree is analogous to the dominator tree. This tree is ...
Dominator (graph theory), in computer science, a property of certain nodes in control-flow graphs; Dominator culture, a term coined by futurist and writer Riane Eisler; The Dominator, or Inverted Powerbomb, a professional wrestling move
An example control-flow graph, partially converted to SSA It is clear which definition each use is referring to, except for one case: both uses of y in the bottom block could be referring to either y 1 or y 2 , depending on which path the control flow took.
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The connectivity properties are the basic properties of graphs and are useful when testing whether a graph is planar or when determining if two graphs are isomorphic. John Hopcroft and Robert Endre Tarjan (1973) developed an optimal (to within a constant factor) algorithm for dividing a graph into triconnected components. [1]
Graph theory is the branch of mathematics that examines the properties of mathematical graphs. See glossary of graph theory for common terms and their definition. Informally, this type of graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs), which can also have associated directions.