Exploiting the hidden structure of junction trees for MPE

The role of decomposition-trees (also known as junction and clique trees) in probabilistic inference is widely known and has been the basis for many well known inference algorithms. Recent approaches have demonstrated that such trees have a "hidden structure", which enables the characterization of tractable problem instances as well as lead to insights that enable boosting the performance of inference algorithms. We consider the MPE problem on a Boolean formula in CNF where each literal in the formula is associated with a weight. We describe techniques for exploiting the junction-tree structure of these formulas in the context of a branch-and-bound algorithm for MPE.