Bucket Elimination: A Unifying Framework for Reasoning

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Bucket Elimination: A Unifying Framework for Reasoning

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by Rina Dechter

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294 - 58 self

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@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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