Computing graph dominators

Here is my attempt at summarizing the computing dominators algorithm without reproducing any text from the source:

Graph dominators can be computed using an algorithm described in a 2001 paper that claims to be both useful for learning and about 2.5 times faster in practice than the Lengauer-Tarjan algorithm. This Simple Fast Dominance Algorithm works by representing the computation of dominators as a data-flow equation. For each node n, dom[n] is defined as the set of dominators including n itself and the intersection of the dominators of n's predecessors. The algorithm iteratively updates each node's dominator set until it stops changing.

A key technique is using a reverse postorder traversal of the graph to compute dominators efficiently. Reverse postorder differs from standard preorder traversal in that each node is visited before its children. This ordering property allows the algorithm to converge on the correct dominator sets in relatively few iterations, although the paper shows it is guaranteed to converge fast enough without detailed proof.

The core idea is that the dominator sets can be thought of as representing paths from the root of the graph, with intersections of sets giving the common ancestors along all paths. By traversing the graph in reverse postorder, the algorithm efficiently computes these dominator sets for each node. The result is an algorithm that is both conceptually simple to understand and empirically fast in practice for typical graphs encountered in computing applications.