Approaches for algebraic Bayesian networks primary structure cyclicity elimination

One of the conditions for the effectiveness of the algorithms of logical and probabilistic inference in algebraic Bayesian network (ABN) is an acyclicity of its graphical representation. Introduction of hypergraphic representation of ABN structures allowed applying the methods of converting this graph to an acyclic form, basing on the methods of the theory of tree decomposition. The general scheme of the method of converting the network to acyclic one with the help of elimination sequences is considered. The main classes of heuristic elimination sequence search algorithms which are appropriate in the context of the transformation of the ABN, as well as evaluation of their complexity and quality of the results are presented.