New Metrics for Static Variable Ordering in Decision Diagrams

We investigate a new class of metrics to find good variable orders for decision diagrams in symbolic state-space generation. Most of the previous work on static ordering is centered around the concept of minimum variable span, which can also be found in the literature under several other names. We use a similar concept, but applied to event span, and generalize it to a family of metrics parameterized by a moment, where the metric of moment 0 is the combined event span. Finding a good variable order is then reduced to optimizing one of these metrics, and we design extensive experiments to evaluate them. First, we investigate how the actual optimal order performs in state-space generation, when it can be computed by evaluating all possible permutations. Then, we study the performance of these metrics on selected models and compare their impact on two different state-space generation algorithms: classic breadth-first and our own saturation strategy. We conclude that the new metric of moment 1 is the best choice. In particular, the saturation algorithm seems to benefit the most from using it, as it achieves the better performance in nearly 80% of the cases.