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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 cliquetree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can provide a speed-up of n over BE for various reasoning tasks. Time-space tradeoffs of treedecomposition processing are analyzed.doi:10.1016/j.artint.2005.04.004 fatcat:bi5goekuzrccpdzsf3evjv5jv4