## Binary vs. non-binary constraints (2002)

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Venue: | Artificial Intelligence |

Citations: | 23 - 2 self |

### BibTeX

@ARTICLE{Bacchus02binaryvs.,

author = {Fahiem Bacchus and Xinguang Chen and Peter Van Beek and Toby Walsh},

title = {Binary vs. non-binary constraints},

journal = {Artificial Intelligence},

year = {2002},

volume = {140},

pages = {2002}

}

### Years of Citing Articles

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### Abstract

Fellowship program. 1 There are two well known transformations from non-binary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of these two transformations. Our comparison focuses on two backtracking algorithms that maintain a local consistency property at each node in their search tree: the forward checking and maintaining arc consistency algorithms. We first compare local consistency techniques such as arc consistency in terms of their inferential power when they are applied to the original (non-binary) formulation and to each of its binary transformations. For example, we prove that enforcing arc consistency on the original formulation is equivalent to enforcing it on the hidden transformation. We then extend these results to the two backtracking algorithms. We are able to give either a theoretical bound on how much one formulation is better than another, or examples that show such a bound does not exist. For example, we prove that the performance of the forward checking algorithm applied to the hidden transformation of a problem is within a polynomial bound of the performance of the same algorithm applied to the dual transformation of the problem. Our results can be used to help decide if applying one of these transformations to all (or part) of a constraint satisfaction model would be beneficial. 2 1

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Citation Context ...search algorithms that maintain a local consistency property at each node in their search tree. Various types of local consistency have been defined, and algorithms developed for enforcing them (e.g, =-=[5, 13, 14]-=-). Algorithms that maintain a local consistency property during backtracking search (e.g., [8, 10, 15, 16, 20]) can detect dead-ends sooner and thus have the potential of significantly reducing the si... |

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Citation Context ...s types of local consistency have been defined, and algorithms developed for enforcing them (e.g, [5, 13, 14]). Algorithms that maintain a local consistency property during backtracking search (e.g., =-=[8, 10, 15, 16, 20]-=-) can detect dead-ends sooner and thus have the potential of significantly reducing the size of the tree they have to search. Such algorithms have demonstrated significant empirical advantages and are... |

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Citation Context ...he time it takes to find a solution [3, 17, 21], and various modeling techniques have been developed, including adding redundant and symmetry-breaking constraints [9, 22, 25], adding hidden variables =-=[6, 24]-=-, aggregating or grouping variables together [3, 7], and transforming a CSP model into an equivalent representation over a different set of variables [7, 11, 19, 26]. One important modeling decision i... |

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Citation Context ...aints [9, 22, 25], adding hidden variables [6, 24], aggregating or grouping variables together [3, 7], and transforming a CSP model into an equivalent representation over a different set of variables =-=[7, 11, 19, 26]-=-. One important modeling decision is the arity of the constraints used. Constraints can be either binary over pairs of variables, or non-binary over three or more variables. Although a problem may be ... |

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Citation Context ...rsity of Waterloo Ontario, Canada vanbeek@uwaterloo.ca Toby Walsh Department of Computer Science University of York York, England tw@cs.york.ac.uk ¡ This paper includes results that first appeared in=-= [1, 4, 23]-=-. This research has been supported in part by the Canadian Government through their NSERC and IRIS programs, and by the EPSRC Advanced Research Fellowship program. 1sAbstract There are two well known ... |

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Citation Context ...ys of modeling a problem as a CSP. Each model might contain a different set of variables, domains, and constraints. The choice of model can have a large impact on the time it takes to find a solution =-=[3, 17, 21]-=-, and various modeling techniques have been developed, including adding redundant and symmetry-breaking constraints [9, 22, 25], adding hidden variables [6, 24], aggregating or grouping variables toge... |

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Citation Context ...ys of modeling a problem as a CSP. Each model might contain a different set of variables, domains, and constraints. The choice of model can have a large impact on the time it takes to find a solution =-=[3, 17, 21]-=-, and various modeling techniques have been developed, including adding redundant and symmetry-breaking constraints [9, 22, 25], adding hidden variables [6, 24], aggregating or grouping variables toge... |