  In recent years, there have been intense research efforts to develop
efficient methods for probabilistic inference in probabilistic influence
diagrams or belief networks. Many people have concluded that the best methods
are those based on undirected graph structures, and that those methods are
inherently superior to those based on node reduction operations on the
influence diagram. We show here that these two approaches are essentially the
same, since they are explicitly or implicity building and operating on the same
underlying graphical structures. In this paper we examine those graphical
structures and show how this insight can lead to an improved class of directed
reduction methods.
