  The paper deals with optimality issues in connection with updating beliefs in
networks. We address two processes: triangulation and construction of junction
trees. In the first part, we give a simple algorithm for constructing an
optimal junction tree from a triangulated network. In the second part, we argue
that any exact method based on local calculations must either be less efficient
than the junction tree method, or it has an optimality problem equivalent to
that of triangulation.
