Generating optimal contiguous evaluations for expression DAGs

We consider the NP-complete problem of generating contiguous evaluations for expression DAGs with a minimal number of registers. We present two algorithms that generate optimal contiguous evaluation for a given DAG. The first is a modification of a complete search algorithm that omits the generation of redundant evaluations. The second algorithm generates only the most promising evaluations by splitting the DAG into trees with import and export nodes and evaluating the trees with a modified labeling scheme. Experiments with randomly generated DAGs and large DAGs from real application programs confirm that the new algorithms generate optimal contiguous evaluations quite fast.