Elsevier

Artificial Intelligence

Volume 14, Issue 3, October 1980, Pages 263-313
Artificial Intelligence

Increasing tree search efficiency for constraint satisfaction problems

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Abstract

In this paper we explore the number of tree search operations required to solve binary constraint satisfaction problems. We show analytically and experimentally that the two principles of first trying the places most likely to fail and remembering what has been done to avoid repeating the same mistake twice improve the standard backtracking search. We experimentally show that a lookahead procedure called forward checking (to anticipate the future) which employs the most likely to fail principle performs better than standard backtracking, Ullman's, Waltz's, Mackworth's, and Haralick's discrete relaxation in all cases tested, and better than Gaschnig's backmarking in the larger problems.

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There are more references available in the full text version of this article.

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    However, finding the optimal ordering, i.e. the one results in a minimal-sized search tree, is at least as hard as solving the CSP (Liberatore, 2000; Rossi et al., 2006). Therefore, current practice mainly relies on hand-crafted variable ordering heuristics obtained from the experience of human experts, such as MinDom (Haralick and Elliott, 1980), Dom/Ddeg (Bessiere and Régin, 1996), and impact-based heuristic (Refalo, 2004). Though they are easy to use and widely adopted, they do not have any formal guarantees on the optimality.

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