Finding the Optimal Variable Ordering for Binary Decision Diagrams

The ordered binary decision diagram is a canonical representation for Boolean functions, presented by Bryant as a compact representation for a broad class of interesting functions derived from circuits. However, the size of the diagram is very sensitive to the choice of ordering on the variables; hence for some applications, such as Differential Cascode Voltage Switch (DCVS) trees, it becomes extremely important to find the ordering leading to the most compact representation. We present an algorithm for this problem with time complexity O(n²3ⁿ), an improvement over the previous best, which required O(n!2ⁿ).