Belief updating in Bayesian networks by using a criterion of minimum time

Variable elimination (VE) and clustering algorithms (CAs) are two widely used algorithms for exact inference in Bayesian networks. Both the problem of finding an optimal variable elimination ordering in VE and the problem of finding an optimal graph triangulation in CAs are NP-complete, although greedy algorithms work well in practice. Usually, VE selects the next variable to be eliminated such that a new potential of minimum size is generated during the elimination process. CAs create a variable elimination sequence in order to triangulate the moral graph; usually, the next variable to be eliminated is selected such that a new clique of minimum size is created during the elimination process. This paper presents an approach which makes use of a criterion of minimum time (CMT) for the selection of the next variable to be eliminated in VE or in CAs, and compares its performance with that of the traditional approaches using a criterion of minimum size. The results show that, in general, the CMT introduced in this paper allows inference time to be reduced. Results regarding memory requirements are also reported.