On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization (Extended Abstract)

The size of Ordered Binary Decision Diagrams (OBDDs) is determined by the chosen variable ordering. A poor choice may cause an OBDD to be too large to fit into the available memory. The decision variant of the variable ordering problem is known to be -complete. We strengthen this result by showing that there in no polynomial time approximation scheme for the variable ordering problem unless . We also prove a small lower bound on the performance ratio of a polynomial time approximation algorithm under the assumption .