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Bucket Elimination: A Unifying Framework for Reasoning

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by Rina Dechter
Citations:298 - 58 self
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BibTeX

@MISC{Dechter_bucketelimination:,
    author = {Rina Dechter},
    title = {Bucket Elimination: A Unifying Framework for Reasoning},
    year = {}
}

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Abstract

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 satisfiability, 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, finding 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 class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucket-elimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade space for time.

Keyphrases

bucket elimination    unifying framework    constraint satisfaction    combinatorial optimization    dynamic programming    probable explanation    extensive demand    elimination strategy    space exponential    interaction graph    unifying theme    bucket elimination framework    linear equality    search algorithm    utility maximization    conditioning set    deterministic reasoning task    bucket-elimination framework    belief updating    bucket-elimination algorithm    performance guarantee    typical example    gaussian elimination    algorithmic framework    linear space    many probabilistic inference task    propositional satisfiability    conditioning search   

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