Generalized Dominators for Structured Programs

Abstract.

Recently it has been discovered that control flow graphs of structured programs (\equiv goto-free) have bounded treewidth t . Moreover, a bounded tree decomposition can be obtained directly from the parsing of the program [23]. In this paper we show that this knowledge can be used to design a fast algorithms for the generalized dominator problem from control flow analysis: given a digraph G=(V,E) with a start node s∈ V , for every v∈ V find the set of predecessors of v that can be reached from s without passing any other predecessors of v . We give an O(|V|t ⁴ ) algorithm for this problem. The problem was originally proposed by Gupta [12]. Without the restriction to bounded treewidth the fastest algorithm runs in O(|V|*|E|) and is due to Alstrup et al. [2].