Abstract
The control dependence relation is used extensively in restructuring compilers. This relation is usually represented using the control dependence graph ; unfortunately, the size of this data structure can be quadratic in the size of the program, even for some structured programs. In this paper, we introduce a data structure called the augmented post-dominator tree (APT) which is constructed in space and time proportional to the size of the program, and which can answer control dependence queries in time proportional to the size of the output. Therefore, APT is an optimal representation of control dependence . We also show that using APT , we can compute SSA graphs, as well as sparse dataflow evaluator graphs, in time proportional to the size of the program. Finally, we put APT in perspective by showing that it can be viewed as a factored representation of control dependence graph in which filtered search is used to answer queries.
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