Abstract
The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas, such as join-tree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. Subsequently, the paper extends the variable-elimination scheme called bucket-elimination (BE) into a two-phase message passing along a bucket-tree (BTE), making it another instance of tree-decomposition. Our analysis shows that the new algorithm BTE may provide a substantial speed-up over BE for important reasoning tasks. Time-space tradeoffs are cast within the tree-decomposition framework.