All Roads Lead To Rome—New Search Methods for Optimal

To perform efficient inference in Bayesian networks, the network graph needs to be triangulated. The quality of this triangulation largely determines the efficiency of the subsequent inference, but the triangulation problem is unfortunately NP-hard. It is common for existing methods to use the treewidth criterion for optimality of a triangulation. However, this criterion may lead to a somewhat harder inference problem than the total table size criterion. We therefore investigate new methods for depth-first search and best-first search for finding optimal total table size triangulations. The search methods are made faster by efficient dynamic maintenance of the cliques of a graph. The algorithms are mainly supposed to be off-line methods, but they may form the basis for efficient any-time heuristics. Furthermore, the methods make it possible to evaluate the quality of heuristics precisely.