Generalized Dominators for Structured Programs

. Recently it has been discovered that control flow graphs of structured programs have bounded treewidth. In this paper we show that this knowledge can be used to design fast algorithms for control flow analysis. We give a linear time algorithm for the problem of finding the immediate multiple-vertex dominator set for all nodes in a control flow graph. The problem was originally proposed by Gupta (Generalized dominators and post-dominators, ACM Symp. on Principles of Programming Languages, 1992). Without the restriction of bounded treewidth the fastest algorithm runs in O(jV j jEj) on a graph with jV j nodes and jEj edges and is due to Alstrup, Clausen and Jørgensen (An O(jV j jEj) Algorithm for Finding Immediate Multiple-Vertex Dominators, accepted to Information Processing Letters). 1 Introduction Constructing dominator trees for control flow graphs G(V; E; s) has been investigated in many papers (see e.g. [8, 9, 11, 13, 14]) in connection with global flow analysis and program op..