## Backjump-based Backtracking for Constraint Satisfaction Problems (2002)

Venue: | Artificial Intelligence |

Citations: | 37 - 2 self |

### BibTeX

@ARTICLE{Dechter02backjump-basedbacktracking,

author = {Rina Dechter and Daniel Frost},

title = {Backjump-based Backtracking for Constraint Satisfaction Problems},

journal = {Artificial Intelligence},

year = {2002},

volume = {136},

pages = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

The performance of backtracking algorithms for solving finite-domain constraint satisfaction problems can be improved substantially by look-back and look-ahead methods. Look-back techniques extract information by analyzing failing search paths that are terminated by dead-ends. Look-ahead techniques use constraint propagation algorithms to avoid such dead-ends altogether. This survey describes a number of look-back variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space. The last portion of the paper gives an overview of look-ahead methods such as forward checking and dynamic variable ordering, and discusses their combination with backjumping.

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Citation Context ...procedure in Figure 13. This routine is particularly simple in that it relies purely on the size of the smallest domain, and breaks ties arbitrarily. More sophisticated DVO schemes have been proposed =-=[37,36,74]. backtra-=-cking38 with-lookahead can be modied to employ dynamic variable ordering by calling selectVariable after the initialization step \is1" and after the forward step \isi + 1." The fc-cbj algori... |

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Citation Context ...nt to x 1 results in an empty domain, and so x 3 = red is rejected, and the algorithm backtracks to x 7 . The information gleaned during the look-ahead phase can also be used to guide value selection =-=[20,72,35,29-=-]. Of course, all look-ahead algorithms perform a coarse version of value selection when they reject values that are shown to lead to a future dead-end, but a more rened approach that ranks the values... |

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Citation Context ...ency. To date, this algorithm is perceived as one of the most successful procedures for that task. Analytical average-case analysis for some backtracking algorithms has been pursued for satisability [=-=69-=-] and for constraint satisfaction [41,63,61]. The value of look-back improvements for solving propositional satisability was initially largely overlooked, as most researchers focused on look-ahead imp... |

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Citation Context ...dea of non-systematic complete backtracking was introduced by Makoto Yokoo who was thesrst to observe that the use of learning in the context of a distributed version of search maintains completeness =-=[81-=-]. This idea caught up recently in the community of SAT-solver developers as well. Many of the current solution methods combine dierent algorithms or exploit nondeterminizm in the randomized version o... |

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Citation Context ...of G. If d is a DFS ordering of G d , then the complexity of graph-based backjumping using ordering d is O(exp(m d )). A proof, that uses somewhat dierent terminology and derivation, is given in [5]=-=-=-. The virtue of Theorem 4 is in allowing a larger set of orderings, each yielding a bound on backjumping's performance as a function of its DFS tree-depth, to be considered. Since every DFS ordering o... |

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Citation Context ... con ict set, minimal relative to prex con ict sets. The obvious candidate is the jumpback set for leaf and internal dead-ends as it was explicated by con ict-directed backjumping. Jumpback learning [=-=27]-=- uses this jumpback set, with the values assigned to the variables, as the con ict set to be learned. Because the con ict set is calculated by the underlying backjumping algorithm, the time complexity... |

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Citation Context ... of arc-consistency; Haralick and Elliott [41], who also added various look-ahead methods; and Nadel [60], who discussed backtracking combined with many variations of partial arcconsistency. Gaschnig =-=[33]-=- has compared Waltz-style look-ahead backtracking with look-back improvements that he introduced, such as backjumping and backmarking. Haralick and Elliot [41] have done a relatively comprehensive stu... |

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An optimal k-consistency algorithm
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Citation Context |

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(Show Context)
Citation Context ...s shown that as larger and more dicult problems are experimented with, higher levels of look-ahead become more useful. The balance between overhead and pruning in constraint propagation is studied in =-=[29,71,4,31-=-]. It is likely that as experiments are conducted with larger and harder problems, look-ahead based on path-consistency will be cost-eective. We end this section by presenting a relationship between t... |

69 | An empirical study of dynamic variable ordering heuristics for the constraint satisfaction problem
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(Show Context)
Citation Context ...procedure in Figure 13. This routine is particularly simple in that it relies purely on the size of the smallest domain, and breaks ties arbitrarily. More sophisticated DVO schemes have been proposed =-=[37,36,74]. backtra-=-cking38 with-lookahead can be modied to employ dynamic variable ordering by calling selectVariable after the initialization step \is1" and after the forward step \isi + 1." The fc-cbj algori... |

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Citation Context ... are used in Lauriere's Alice system [47]. Explicit algorithms employing this idea have been given by Gaschnig [34], who described a backtracking algorithm that incorporates arc-consistency; McGregor =-=[54]-=-, who described backtracking combined with forward checking, which is a truncated form of arc-consistency; Haralick and Elliott [41], who also added various look-ahead methods; and Nadel [60], who dis... |

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Citation Context ...examination of various algorithms uncovered interesting relationships. For instance, as already noted, dynamic variable ordering performs the function of value selection as well as variable selection =-=[2]-=-, and when the order of variables issxed, forward checking eliminates the need for backjumping in leaf nodes, as is done in Gaschnig's backjumping [44]. The idea of non-systematic complete backtrackin... |

58 | Using constraint metaknowledge to reduce arc consistency computation
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Citation Context ...y of arc-consistency algorithms, of which AC-1 is the earliest, perhaps the simplest, and certainly one of the least ecient. Later and more ecient arc-consistency procedures, dubbed AC-2 through AC-7 =-=[48,58,79,65,8,9]-=- can also be used within a selectValue subprocedure. The optimal time complexity for any arc-consistency procedure is O(em r ), where e is the number of constraints in the subproblem, m is the cardina... |