Ordering Strategies for Removing Redundant Fill Edges

Triangulation is the key step for determining the maximum size of cliques, by which the performances of probabilistic inference algorithms are determined. Obtaining the optimal triangulation is NP-complete. But, triangulation performance can be improved through removing redundant fill edges from the triangulated graph. MinimalChordal and Recursive-Thinning are two popular methods for removing redundant fill edges. It has been validated that if the triangulated graph is minimal, the number of fill edges removed by them is small. In this paper, we shall analyze ordering strategies related to their performance, and propose two ordering algorithms for improving them. However, their performances are determined by triangulation orderings. To make them valuable, some better triangulation ordering method similar to MCS-M is expected even if it is not minimal.