A fast algorithm for finding dominators in a flowgraph

Abstract

A fast algorithm for finding dominators in a flowgraph is presented. The algorithm uses depth-first search and an efficient method of computing functions defined on paths in trees. A simple implementation of the algorithm runs in O ( m log n ) time, where m is the number of edges and n is the number of vertices in the problem graph. A more sophisticated implementation runs in O ( m α( m , n )) time, where α( m , n ) is a functional inverse of Ackermann's function. Both versions of the algorithm were implemented in Algol W, a Stanford University version of Algol, and tested on an IBM 370/168. The programs were compared with an implementation by Purdom and Moore of a straightforward O ( mn )-time algorithm, and with a bit vector algorithm described by Aho and Ullman. The fast algorithm beat the straightforward algorithm and the bit vector algorithm on all but the smallest graphs tested.