ALCOMFT-TR-03-121

Hans L. Bodlaender, Arie M.C.A. Koster and Frank van den Eijkhof
Pre-Processing Rules for Triangulation of Probabilistic Networks
Utrecht. Work package 5. December 2003.

Abstract: The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.

Keywords: probabilistic networks, inference, triangulation, treewidth, pre-processing

Postscript file: ALCOMFT-TR-03-121.ps.gz (80 kb).