  The efficiency of inference in both the Hugin and, most notably, the
Shafer-Shenoy architectures can be improved by exploiting the independence
relations induced by the incoming messages of a clique. That is, the message to
be sent from a clique can be computed via a factorization of the clique
potential in the form of a junction tree. In this paper we show that by
exploiting such nested junction trees in the computation of messages both space
and time costs of the conventional propagation methods may be reduced. The
paper presents a structured way of exploiting the nested junction trees
technique to achieve such reductions. The usefulness of the method is
emphasized through a thorough empirical evaluation involving ten large
real-world Bayesian networks and the Hugin inference algorithm.
