Bucket Elimination: A Unifying Framework for Reasoning

Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problem-solving and reasoning tasks. Algorithms such as directional-resolution for propositional satis ability, adaptive-consistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucket-elimination algorithms. These include: belief updating, nding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees all are time and space exponential in the inducedwidth of the problem's interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called \conditioning search" require only linear space. Algorithms in this clas...

• Type: Journal
• Year: 1999
• Where: AI
• Authors: Rina Dechter
• Keywords: AI 1999, Algorithms, Artificial Intelligence, Bucket Elimination, Dynamic Programming