Integrating a Variable Ordering Heuristic with BDDs and CSP Decomposition Techniques for Interactive Configurators

The Binary Decision Diagram (BDD) based compilation schemes are quite suitable for representing configuration knowledge bases. It is well-known that the size of BDDs are very sensitive to the variable order. In this paper, we study the variable ordering problem of BDDs when they represent a configuration knowledge. Such a study is crucial to better understand the BDD-based compilation schemes. We introduce a small variant of a classical variable ordering heuristic, that proves empirically useful. It is surprising since such a heuristic is known to fail when BDDs are used in formalverification. We show that a compilation scheme using CSP tree-decomposition is less dependent on the variable order. We also show that, for a good variable order the benefit of tree-decomposition, which reduces space, can drastically diminish.