Finding Dominators Revisited

A Linear-Time Algorithm for Finding All Double-Vertex Dominators of a Given Vertex

Dominators provide a general mechanism for identifying reconverging paths in graphs. This is useful for a number of applications in ComputerAided Design (CAD) including signal probability computation in biased random simulation, switching activity estimation in power and noise analysis, and cut points identification in equivalence checking. However, traditional single-vertex dominators are too ...

Finding dominators via disjoint set union

The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-lineartime algorithms exist, they use sophisticated data structures. We develop an algorithm for finding dominators that uses only a “static tree” disjoint set data structure in addition to simple lists and maps. The algorithm runs in n...

Finding Dominators in Practice

The computation of dominators in a flowgraph has applications in several areas, including program optimization, circuit testing, and theoretical biology. Lengauer and Tarjan [30] proposed two versions of a fast algorithm for finding dominators and compared them experimentally with an iterative bit-vector algorithm. They concluded that both versions of their algorithm were much faster even on gr...

Finding Dominators in Directed Graphs

Computing Frequency Dominators and Related Problems

We consider the problem of finding frequency dominators in a directed graph with a single source vertex and a single terminal vertex. A vertex x is a frequency dominator of a vertex y if and only if in each source to terminal path, the number of occurrences of x is at least equal to the number of occurrences of y. This problem was introduced in a paper by Lee et al. [11] in the context of dynam...