A Depth First Search Algorithm for Optimal Triangulation of Bayesian Networks

Abstract

The most popular algorithm for exact inference on Bayesian networks is the junction tree propagation algorithm. To improve the time and space complexity of the junction tree algorithm, we must find an optimal triangulation. For this purpose, Ottosen and Vomlel have proposed a depth-first search (DFS) algorithm for optimal triangulation using branch-and-bound and dynamic clique maintenance techniques. Nevertheless, their method entails heavy computational costs. To mitigate this problem, we propose an extended depth-first search (EDFS) algorithm. The new algorithm EDFS improves the DFS algorithm in the following two ways: (1) reduction of the computational cost of each lower bound calculation, and (2) reduction of the branching factor of each node expansion. Experimental results show that the proposed method is markedly faster than the Ottosen and Vomlel method.