Finding Dominators in Practice

Loukas Georgiadis, Renato F. Werneck, Robert E. Tarjan, Spyridon Triantafyllis and David I. August

Abstract

The computation of dominators in a flowgraph has applications in program optimization, circuit testing, and other areas. Lengauer and Tarjan 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 than the bit-vector algorithm even on graphs of moderate size. Recently Cooper et al.have proposed a new, simple, tree-based iterative algorithm. Their experiments suggested that it was faster than the simple version of the Lengauer-Tarjan algorithm on graphs representing computer program control flow. Motivated by the work of Cooper et al., we present an experimental study comparing their algorithm (and some variants) with careful implementations of both versions of the Lengauer-Tarjan algorithm and with a new hybrid algorithm. Our results suggest that, although the performance of all the algorithms is similar, the most consistently fast are the simple Lengauer-Tarjan algorithm and the hybrid algorithm, and their advantage increases as the graph gets bigger or more complicated.