Unifying Cluster-Tree Decompositions for Automated Reasoning

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as jointree clustering for constraint-satisfaction and the clique-tree algorithm for probabilistic reasoning. By following the framework introduced by Shenoy [16], we then introduce a new algorithm, called buckettree elimination (BTE), that extends Bucket Elimination (BE) [5] to trees, and show that it is also an instance of tree-decomposition. Moreover, our analysis shows that the new extension, BTE, can provide a speed-up of n over BE for important reasoning tasks. Finally, time-space tradeoffs are shown to be cast naturally within the treedecomposition framework.