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## Modeling choices in quasigroup completion: SAT vs. CSP (2004)

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Venue: | In AAAI |

Citations: | 10 - 1 self |

### Citations

1350 | Chaff: Engineering an Efficient SAT Solver. In:
- Moskewicz, Madigan, et al.
- 2001
(Show Context)
Citation Context ...lar to the one presented here are discussed at length in (Hnich, Smith, & Walsh 2004). Experimental results: Part 1 We considered four state-of-the art SAT solvers: Satz (Li & Anbulagan 1997), Chaff (=-=Moskewicz et al. 2001-=-), Berkmin (Goldberg & Novikov 2002), and Satzoo (Eén & Sörensson 2003). We chose Satz because some authors have claimed that it is the best option to solve QCPs; our experimental results provide evid... |

284 | BerkMin: a fast and robust SATsolver,
- Goldberg, Novikov
- 2002
(Show Context)
Citation Context ... discussed at length in (Hnich, Smith, & Walsh 2004). Experimental results: Part 1 We considered four state-of-the art SAT solvers: Satz (Li & Anbulagan 1997), Chaff (Moskewicz et al. 2001), Berkmin (=-=Goldberg & Novikov 2002-=-), and Satzoo (Eén & Sörensson 2003). We chose Satz because some authors have claimed that it is the best option to solve QCPs; our experimental results provide evidence of this claim too. We chose Ch... |

163 | Heavy-tailed phenomena in satisfiability and constraint satisfaction problems
- Gomes, Selman, et al.
- 2000
(Show Context)
Citation Context ...Shmoys 2002a). Experimental studies of the problem have confirmed its interest for research, by for example helping to discover important patterns in problem difficulty such as heavy-tailed behavior (=-=Gomes et al. 2000-=-). Among the kind of structure that has been identified in many constraint satisfaction problems, and which is shared by QCPs, is that of permutation problems. These are constraint satisfaction (sub)p... |

105 | CPlan: A constraint programming approach to planning, in: - Beek, Chen - 1999 |

74 | Increasing constraint propagation by redundant modeling: an experience report.
- Cheng, Choi, et al.
- 1999
(Show Context)
Citation Context ...AC) in the CSP channeling model. These results appear easy to extrapolate to other permutation problems (or similar ones with ”channeling constraints”), which have received a lot of recent attention (=-=Cheng et al. 1999-=-; Walsh 2001; Hnich, Smith, & Walsh 2004). Second, empirically, we identify Satz’s UP heuristic as crucial to its success in this domain; as shown by the fact that, when importing the heuristic into o... |

70 | Look-ahead versus look-back for satisfiability problems”, in
- Li, Anbulagan
- 1997
(Show Context)
Citation Context ...cus on the relative conciseness of the 3D model and the pruning power of unit propagation. Empirically, the focus is on the role of the unit-propagation heuristic of the best performing solver, Satz (=-=Li & Anbulagan 1997-=-), which proves crucial to its success, and results in a significant improvement in scalability when imported into the CSP solvers. Our results strongly suggest that SAT encodings of permutation probl... |

67 | Arc consistency in SAT.
- Gent
- 2003
(Show Context)
Citation Context ...ich, Smith, & Walsh 2004)) when compared with the currently preferred channeling models. The reasons for this appear to be twofold. First, we can show that the 3D encoding (which is basically the “SAT channeling model” of (Hnich, Smith, & Walsh 2004) extended to multiple permutations and dual models) exactly captures the channeling models of QCPs as defined e.g. in (Dotu, del Val, & Cebrian 2003), but in a much more concise way, by collapsing primal and dual variables. Further, we can show that the 3D encoding captures the “support SAT encoding” of the channeling model, hence by results of (Gent 2002), that unit propagation on the 3D encoding achieves the same pruning as arc consistency (MAC) in the CSP channeling model. These results appear easy to extrapolate to other permutation problems (or similar ones with ”channeling constraints”), which have received a lot of recent attention (Cheng et al. 1999; Walsh 2001; Hnich, Smith, & Walsh 2004). Second, empirically, we identify Satz’s UP heuristic as crucial to its success in this domain; as shown by the fact that, when importing the heuristic into our CSP solvers, we obtain significant improvements in their scalability. Further, the improve... |

59 | The complexity of completing partial Latin squares - Colbourn - 1984 |

49 | MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems.
- Bessiere, Regin
- 1996
(Show Context)
Citation Context ...titions, and Berkmin because it is often competitive with Chaff. In addition, we tested two CSP solvers, the GAC library described in (van Beek & Chen 1999), and the MAC solver by Regin and Bessiere (=-=Bessière & Régin 1996-=-). Note that for binary CSPs they are simply different implementations of the MAC algorithm. The instances tested in our experiments are of the QWH type (quasigroup with holes (Kautz et al. 2001), gen... |

49 | The constrainedness of arc consistency
- Gent, MacIntyre, et al.
- 1997
(Show Context)
Citation Context ...), but in a much more concise way, by collapsing primal and dual variables. Further, we can show that the 3D encoding captures the “support SAT encoding” of the channeling model, hence by results of (=-=Gent 2002-=-), that unit propagation on the 3D encoding achieves the same pruning as arc consistency (MAC) in the CSP channeling model. These results appear easy to extrapolate to other permutation problems (or s... |

42 | Balance and Filtering in Structured Satisfiable Problems
- Kautz, Ruan, et al.
- 2001
(Show Context)
Citation Context ...form a systematic comparison of SAT and CSP models for a challenging combinatorial problem, quasigroup completion (QCP). Our empirical results clearly indicate the superiority of the 3D SAT encoding (=-=Kautz et al. 2001-=-), with various solvers, over other SAT and CSP models. We propose a partial explanation of the observed performance. Analytically, we focus on the relative conciseness of the 3D model and the pruning... |

39 | Permutation problems and channelling constraints.
- Walsh
- 2001
(Show Context)
Citation Context ...is a very challenging benchmark among combinatorial problems, which has been the focus of much recent interest in the area of constraint programming (Gomes & Shmoys 2002b; Dotu, del Val, & Cebrian 2003). It has a broad range of practical applications such as conflict-free wavelength routing in wide band optical networks, statistical design, and error correcting codes (Gomes & Shmoys 2002b); it has been put forward as a benchmark which can bridge the gap between purely random instances and highly structured problems (Gomes & Shmoys 2002a); and its structure as a multiple permutation problem (Walsh 2001; Hnich, Smith, & Walsh 2004) is common to many other important problems in constraint satisfaction. Thus, solutions that prove effective on QCPs have a good chance of being useful in other problems with similar structure. Motivated by earlier results by (Gomes & Shmoys 2002b; 2002a) and (Dotu, del Val, & Cebrian 2003) with integer ∗We thank Carla Gomes for the quasigroup generator lsencode and for computational resources to run the experiments, C. Bessiere for the MAC code, and the authors of all solvers. †This research has been partially supported by projects TIC2001-1577-C03-03 and TIC20... |

35 | Completing quasigroups or latin squares: A structured graph coloring problem.
- Gomes, Shmoys
- 2002
(Show Context)
Citation Context ...solver, Satz (Li & Anbulagan 1997), which proves crucial to its success, and results in a significant improvement in scalability when imported into the CSP solvers. Our results strongly suggest that SAT encodings of permutation problems (Hnich, Smith, & Walsh 2004) may well prove quite competitive in other domains, in particular when compared with the currently preferred channeling CSP models. Introduction The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, which has been the focus of much recent interest in the area of constraint programming (Gomes & Shmoys 2002b; Dotu, del Val, & Cebrian 2003). It has a broad range of practical applications such as conflict-free wavelength routing in wide band optical networks, statistical design, and error correcting codes (Gomes & Shmoys 2002b); it has been put forward as a benchmark which can bridge the gap between purely random instances and highly structured problems (Gomes & Shmoys 2002a); and its structure as a multiple permutation problem (Walsh 2001; Hnich, Smith, & Walsh 2004) is common to many other important problems in constraint satisfaction. Thus, solutions that prove effective on QCPs have a good c... |

30 | Dual modelling of permutation and injection problems - Hnich, Smith, et al. |

24 | Completing Quasigroups or Latin Squares: A Structured Graph Coloring Problem - Gomez, Shmoys |

21 | The promise of LP to boost CSP techniques for combinatorial problems
- Gomes, Shmoys
- 2002
(Show Context)
Citation Context ...solver, Satz (Li & Anbulagan 1997), which proves crucial to its success, and results in a significant improvement in scalability when imported into the CSP solvers. Our results strongly suggest that SAT encodings of permutation problems (Hnich, Smith, & Walsh 2004) may well prove quite competitive in other domains, in particular when compared with the currently preferred channeling CSP models. Introduction The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, which has been the focus of much recent interest in the area of constraint programming (Gomes & Shmoys 2002b; Dotu, del Val, & Cebrian 2003). It has a broad range of practical applications such as conflict-free wavelength routing in wide band optical networks, statistical design, and error correcting codes (Gomes & Shmoys 2002b); it has been put forward as a benchmark which can bridge the gap between purely random instances and highly structured problems (Gomes & Shmoys 2002a); and its structure as a multiple permutation problem (Walsh 2001; Hnich, Smith, & Walsh 2004) is common to many other important problems in constraint satisfaction. Thus, solutions that prove effective on QCPs have a good c... |

13 | Redundant modeling for the quasigroup completion problem. - Dotu, Val, et al. - 2003 |

4 | Solving many-valued SAT encodings with local search - Ansótegui, Manyà, et al. - 2002 |

4 | Simplifying binary propositional theories into connected components twice as fast. - Val, A - 2001 |

1 | The alldifferent constraint: A survey. - Hoere - 2001 |