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 n). By definition, every node dominates itself.
There are a number of related concepts:
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 the problem of efficiently computing the placement of φ functions, which are used in static single assignment form.
Dominators, and dominance frontiers particularly, have applications in compilers for computing static single assignment form. A number of compiler optimizations can also benefit from dominators. The flow graph in this case comprises basic blocks.
Automatic parallelization benefits from postdominance frontiers. This is an efficient method of computing control dependence, which is critical to the analysis.
Memory usage analysis can benefit from the dominator tree to easily find leaks and identify high memory usage.
In hardware systems, dominators are used for computing signal probabilities for test generation, estimating switching activities for power and noise analysis, and selecting cut points in equivalence checking. In software systems, they are used for reducing the size of the test set in structural testing techniques such as statement and branch coverage.
The dominators of a node n are given by the maximal solution to the following data-flow equations:
...
Wikipedia