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DAG reversal is NP-complete. (English) Zbl 1192.68490
Summary: Runs of numerical computer programs can be visualized as directed acyclic graphs (DAGs). We consider the problem of restoring the intermediate values computed by such a program (the vertices in the DAG) in reverse order for a given upper bound on the available memory. The minimization of the associated computational cost in terms of the number of performed arithmetic operations is shown to be NP-complete. The reversal of the data-flow finds application, for example, in the efficient evaluation of adjoint numerical programs. We derive special cases of numerical programs that require the intermediate values exactly in reverse order, thus establishing the NP-completeness of the optimal adjoint computation problem. Last but not least, we review some state-of-the-art approaches to efficient data-flow reversal taken by existing software tools for automatic differentiation.

68R10 Graph theory (including graph drawing) in computer science
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