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Dominator (graph theory) : ウィキペディア英語版
Dominator (graph theory)

In computer science, in control flow graphs, a node d ''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 \gg 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.
* The ''immediate dominator'' or idom of a node ''n'' is the unique node that strictly dominates ''n'' but does not strictly dominate any other node that strictly dominates ''n''. Every node, except the entry node, has an immediate dominator.〔
* The ''dominance frontier'' of a node d is the set of all nodes n such that d dominates an immediate predecessor of n, but d does not strictly dominate n. It is the set of nodes where d's dominance stops.
* A ''dominator tree'' is a tree where each node's children are those nodes it immediately dominates. Because the immediate dominator is unique, it is a tree. The start node is the root of the tree.
== History ==
Dominance was first introduced by Reese T. Prosser in a 1959 paper on analysis of flow diagrams. Prosser did not present an algorithm for computing dominance, which had to wait ten years for Edward S. Lowry and C. W. Medlock. Ron Cytron ''et al.'' rekindled interest in dominance in 1989 when they applied it to efficient computation of φ functions, which are used in static single assignment form.

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