  There exist two general forms of exact algorithms for updating probabilities
in Bayesian Networks. The first approach involves using a structure, usually a
clique tree, and performing local message based calculation to extract the
belief in each variable. The second general class of algorithm involves the use
of non-serial dynamic programming techniques to extract the belief in some
desired group of variables. In this paper we present a hybrid algorithm based
on the latter approach yet possessing the ability to retrieve the belief in all
single variables. The technique is advantageous in that it saves a NP-hard
computation step over using one algorithm of each type. Furthermore, this
technique re-enforces a conjecture of Jensen and Jensen [JJ94] in that it still
requires a single NP-hard step to set up the structure on which inference is
performed, as we show by confirming Li and D'Ambrosio's [LD94] conjectured
NP-hardness of OFP.
