Efficient variable ordering and partial representation algorithm

In this paper we introduce some new methods for constructing Ordered Partial Decision Diagrams (OPDDs), The algorithms are effective in capturing a significant fraction of a given function's truth table using only a very small space. Using such data structures the importance of a variable in a Boolean function can be computed. Such methods can easily be used for computing effective variable orders to construct BDDs. The measures of a variable's importance are based on information-theoretic criteria, and require computation of the entropy of a variable for a given function. We have found that entropy measures can be quite efficient in distinguishing the importance of variables, and at times provide very effective variable order. The results show an encouraging approach towards the understanding and the solution of this well known problem.