What’s in a Region? - or - Computing Control Dependence Regions in Linear Time and Space

Regions of control dependence identify the instructions in a program that execute under the same control conditions. They have a variety of applications in parallelizing and optimizing compilers. Two vertices in a control flow graph (which may represent instructions or basic blocks in a program) are in the same region if they have the same set of control dependence predecessors. The best known algorithm for computing regions takes O(V×E) time, where V and E are the number of vertices and edges in the control flow graph, respectively. We present algorithms for finding regions in O (V +E) time and O (V +E) space, without using control dependence. These algorithms are based on alternative definitions of regions, which are easier to reason with than the definitions based on control dependence.