A fast clique maintenance algorithm for optimal triangulation of Bayesian networks

Abstract

The junction tree algorithm is currently the most popular algorithm for exact inference on Bayesian networks. To improve the time and space complexity of the junction tree algorithm, we must find an optimal total table size triangulations. For this purpose, Ottosen and Vomlel proposed a depth-first search (DFS) algorithm for optimal triangulation. They also introduced several techniques for improvement of the DFS algorithm, including dynamic clique maintenance and coalescing map pruning. However, their dynamic clique maintenance might compute some duplicate cliques. In this paper, we propose a new dynamic clique maintenance that only computes the cliques that contain a new edge. The new approach explores less search space and runs faster than the Ottosen and Vomlel method does. Some simulation experiments show that the new dynamic clique maintenance improved the running time of the optimal triangulation algorithm.