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].
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Received January 30, 1997; revised May 14, 1998.
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Alstrup, S., Lauridsen, P. & Thorup, M. Generalized Dominators for Structured Programs . Algorithmica 27, 244–253 (2000). https://doi.org/10.1007/s004530010018
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DOI: https://doi.org/10.1007/s004530010018