Algorithm for Detection Algebraic Bayesian Network Primary Structure Acyclicity Based on Number of Minimal Join Graph Edges Estimating

The condition for algebraic Bayesian networks (ABN) global logical-probabilistic inference algorithms performance is the absence of cycles in its secondary structure. The primary structure, on which an acyclic secondary can be synthesized is called acyclic. The goal of work is to propose an algorithm to detect primary structure acyclicity based on estimates of the number of edges in its secondary structure without the direct construction of the secondary structure, and estimation of the algorithm complexity. The algorithm for detection ABN primary structure acyclicity based on number of minimal join graph edges estimating via brute force is formulated, its correctness is proven, its complexity is estimated, improvement in the speed of this algorithm is proposed, the improved algorithm correctness if proven and its performance time is estimated . Also consider the possibility for improving the algorithm performance speed through the use of algorithms for ABN tertiary polystructure elements synthesis is discussed.