A Theoretical Evaluation of Selected Backtracking Algorithms

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A Theoretical Evaluation of Selected Backtracking Algorithms (1997)

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by Grzegorz Kondrak , Peter Van Beek

Venue:	Artificial Intelligence
Citations:	123 - 3 self

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@ARTICLE{Kondrak97atheoretical,
    author = {Grzegorz Kondrak and Peter Van Beek},
    title = {A Theoretical Evaluation of Selected Backtracking Algorithms},
    journal = {Artificial Intelligence},
    year = {1997},
    volume = {89},
    pages = {541--547}
}

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Abstract

In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on characterizations of the sets of search treenodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such well-known concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove the correctness of Backjumping and Con ict-Directed Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modi cation to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Con ict-Directed Backjumping (BM-CBJ), so that they always perform fewer consistency checks than the original algorithms. 1

Keyphrases

selected backtracking algorithm theoretical evaluation con ict-directed backjumping consistency check di erent original algorithm constraint satisfaction problem modi cation recent year forward checking useful tool search treenodes domain annihilation standard performance measure empirical testing theoretical approach well-known concept backtracking algorithm

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