## Extending forward checking (2000)

Venue: | in Proceedings of CP’00 |

Citations: | 16 - 4 self |

### BibTeX

@INPROCEEDINGS{Bacchus00extendingforward,

author = {Fahiem Bacchus},

title = {Extending forward checking},

booktitle = {in Proceedings of CP’00},

year = {2000},

pages = {35--51},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from the domains of the uninstantiated variables. In this paper we present a general approach to extending constraint propagating algorithms, especially forward checking. In particular, we provide a simple yet flexible mechanism for pruning domain values, and show that with this in place it becomes easy to utilize new mechanisms for detecting inconsistent values during search. This leads to a powerful and uniform technique for designing new CSP algorithms: one simply need design new methods for detecting inconsistent values and then interface them with the domain pruning mechanism. Furthermore, we also show that algorithms following this design can proved to be correct in a simple and uniform way. To demonstrate the utility of these ideas five “new ” CSP algorithms are presented. 1

### Citations

469 |
Increasing tree search efficiency for constraint satisfaction problems
- Haralick, Elliot
- 1980
(Show Context)
Citation Context ... nullifies the reason the values became inconsistent. In terms of simplicity and historical precedence the most basic algorithm in this class is Haralick and Elliott’s forward checking algorithm (FC) =-=[1]-=-. Although conceptually simple, pruning values during search has rather profound computational effects. Different amounts of computation can be devoted to detect inconsistent values. But, once a value... |

394 |
Constraint Satisfaction in Logic Programming
- Hentenryck
- 1989
(Show Context)
Citation Context ...For binary CSPs this means that the domain pruning mechanism must do at least as much pruning as FC. For Ò-ary CSPs, it must do at least as much pruning as the version of FC defined by van Hentenryck =-=[3]-=-.s6 Fahiem Bacchus That is, pruning can only eliminate a value from a subtree when it is certain that the value cannot participate in any further solutions in that subtree. 4 Theorem 1. Subject to the... |

366 | Dynamic Backtracking
- Ginsberg
- 1993
(Show Context)
Citation Context ... 3. prune(val,Ñ�Ü(val.CF)); The basic algorithm CFFC has some similar features to conflict directed backjumping (CBJ) [6], dead-end driven learning [12], and the no-goods used in dynamic backtracking =-=[13]-=-. The conflicts used here are, however, more fine grained: they are value specific conflicts. In addition to CFFC we can define CFFC-. In analogy with EFC-, CFFC- is identical to CFFC except that inst... |

357 | Hybrid algorithms for the constraint satisfaction problem
- Prosser
- 1993
(Show Context)
Citation Context ... found EFC/EFC- to be mostly inferior to MAC. EFC/EFCmay still have some potential on Ò-ary CSPs. 7 Nevertheless, in the binary case both EFC and EFC- can be, like conflict directed backjumping (CBJ) =-=[6]-=-, of considerable assistance to standard FC. Table 1 shows a typical example using 50 random binary CSPs. Each CSP is generated using the standard random CT model, and has 200 variables each having 10... |

278 |
Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition
- Dechter
- 1990
(Show Context)
Citation Context ...sed on using conflicts or no-goods to detect inconsistent values. Conflicts have appeared many times before in CSP algorithms, e.g., in Conflict Directed Backjumping (CBJ) [6] and in no-good learning =-=[11]-=-. One difference here is that we maintain conflicts for values rather than variables. A conflict � for the value Ú is a set of assignments �Î � Ú �����Î� � Ú�� such that no unenumerated solution conta... |

98 | CPlan: A Constraint Programming Approach to Planning
- Beek, Chen
- 1999
(Show Context)
Citation Context ...f J.C. Regin [20] 18 We have also experimented with a preliminary implementation of Ò-ary versions of CFFC, CFFC-, and CFMAC algorithms. The implementation was built on top of van Beek’s CPLAN system =-=[21]-=-. In these experiments we found that on harder logistics, blocks, and grid world planning problem CFMAC out performs the base GACCBJ (generalized arc consistency with conflict directed backtracking) i... |

89 | On the conversion between non-binary and binary constraint satisfaction problems - Bacchus, Beek - 1998 |

84 |
combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems
- MAC
(Show Context)
Citation Context ...m the (200*199/2) possible binary constraints, and the 76 incompatible pairs are chosen at random from the 100 possible pairs. 9 We also tried the current domain size divided by degree as a heuristic =-=[7]-=-. FC showed somewhat better performance with this heuristic but it still failed on many problems, otherwise the results were very similar with both EFC and EFC- still performing better than FCCBJ.s10 ... |

77 | Random constraint satisfaction: A more accurate picture
- Achlioptas, Kirousis, et al.
- 1997
(Show Context)
Citation Context ...are MAC with FC (or even FCCBJ). MAC’s superiority on these problems is not surprising. Achlioptas et al. have shown that the random CT model generates problems that are highly biased in favor of MAC =-=[8]-=-, especially as the number of constraints grows (irrespective of tightness as long as the number of incompatible pairs is greater than the domain size). With 200 constraints and a high tightness of 76... |

77 | Dead-end driven learning
- Frost, Dechter
- 1994
(Show Context)
Citation Context ...[VarAtLevel[level-1]]; 2. val.CF := �1,...,level-2�; 3. prune(val,Ñ�Ü(val.CF)); The basic algorithm CFFC has some similar features to conflict directed backjumping (CBJ) [6], dead-end driven learning =-=[12]-=-, and the no-goods used in dynamic backtracking [13]. The conflicts used here are, however, more fine grained: they are value specific conflicts. In addition to CFFC we can define CFFC-. In analogy wi... |

69 | On forward checking for nonbinary constraint satisfaction
- Bessière, Meseguer, et al.
- 1999
(Show Context)
Citation Context ... to level 0. This special case is achieved automatically in EFC/EFC-. 7 It is not hard to define EFC for Ò-ary CSPs, and it should be feasible to extend all of the new Ò-ary versions of FC defined in =-=[5]-=- using these ideas. Further empirical evaluation is needed to determine how useful such extensions would be. 8 The particular, in the random CT model the 200 constraints are chosen at random from the ... |

45 |
Domain filtering can degrade intelligent backtracking
- Prosser
- 1993
(Show Context)
Citation Context ... by Prosser in [9]. In particular, Prosser identified that when backing up from a DWO the gains of Prune::Backup could be achieved. However, the algorithm he described uti6 Prosser’s FC-D2C algorithm =-=[4]-=- uses a special test to recognize the case when a value can be pruned back to level 0. This special case is achieved automatically in EFC/EFC-. 7 It is not hard to define EFC for Ò-ary CSPs, and it sh... |

41 | Neighborhood Inverse Consistency Preprocessing
- Freuder, Elfe
- 1996
(Show Context)
Citation Context ... in turn can pass back shorter conflicts and generate better backtracks at the higher levels. Another feature of CFFC is its ability to detect and prune values that have become �-inverse inconsistent =-=[14]-=- for arbitrary �. Thus, CFFC has the potential to achieve exponential savings over an algorithm that continually enforces �-inverse consistency on the values of the future variables for any fixed �. H... |

35 | Using CSP look-back techniques to solve exceptionally hard sat instances
- Bayardo, Schrag
- 1996
(Show Context)
Citation Context ...ucture of the problem. Table 2 shows one type of embedded problem. These problems originated in the work of Bayardo and Schrag and were used to illustrate their CBJ based satisfiability solver RelSat =-=[18]-=-. They took relatively easy random 3-sat problems and embedded in them a small unsatisfiable sat problem. We took the random SAT problems produced by their generator and converted them to binary CSPs ... |

26 | On the Forward Checking Algorithm
- Bacchus, Grove
- 1995
(Show Context)
Citation Context ...cf � val.CF; 4. return(cf); 10 That backmarking (BM) type savings can be a achieved with a domain pruning mechanism is not so surprising given the close relationship between BM and FC demonstrated in =-=[10]-=-. 11 We are using the set of unenumerated solutions to define conflicts. This again allows us to provide a uniform treatment of the case when our algorithms are searching for all solutions. 12 The ini... |

24 | B.M.: The phase transition behaviour of maintaining arc consistency
- Grant, Smith
- 1996
(Show Context)
Citation Context ...immediately detect almost all inconsistent values. Furthermore, this also means that conflicts are unlikely to generate powerful backtracks. Thus, CBJ hardly helps (over MAC) on these problems either =-=[17]-=-. Nevertheless, there are problems on which CFFC is superior. One example, are problems that have a small group of variables participating in an unsolvable subproblem. On these kinds of problems the C... |

14 | Bessière C.: A Generic Customizable Framework for Inverse Local Consistency
- Verfaillie, Martinez
- 1999
(Show Context)
Citation Context ...inary) algorithms. The results are shown in Table 2. 17 One surprising 15 In an interesting recent paper, it has been shown that search is a generic way of implementing �-inverse consistency checking =-=[15]-=-. CFFC can be viewed as an algorithm that does both at the same time. 16 This follows from Mitchell’s recent results showing that these problems have short refutation resolutions [16]. 17 In more deta... |

13 | Forward checking with backmarking
- Prosser
- 1995
(Show Context)
Citation Context ...del) do serve to demonstrate that there exist classes of problems for which EFC is a significant assist to FC. One final point is that EFC- is identical to the algorithm FC-BM described by Prosser in =-=[9]-=-. In particular, Prosser identified that when backing up from a DWO the gains of Prune::Backup could be achieved. However, the algorithm he described uti6 Prosser’s FC-D2C algorithm [4] uses a special... |

6 |
Dynamic variable reordering in CSPs
- Bacchus, Run
- 1995
(Show Context)
Citation Context ...ore important benefit is that domain pruning causes the domain sizes of the uninstantiated variables to vary dynamically, and this provides invaluable input to dynamic variable order (DVO) heuristics =-=[2]-=-. However, popular algorithms like FC and MAC employ domain pruning in a fairly restricted way. In both of these algorithms pruning is done in lock step with search. That is, every time a new assignme... |

3 |
Developpement d’outils alogorithmiques pour l’Intelligence Artificielle. Application a la chimie
- Regin
- 1995
(Show Context)
Citation Context ... current degree as a tie-breaker. The MAC algorithm we used was based on AC3, and in our benchmarking it ran at about 65% of the speed of the more sophisticated AC7 based implementation of J.C. Regin =-=[20]-=- 18 We have also experimented with a preliminary implementation of Ò-ary versions of CFFC, CFFC-, and CFMAC algorithms. The implementation was built on top of van Beek’s CPLAN system [21]. In these ex... |

1 |
Some random csps are hard for resolution. http://http://www.cs.toronto.edu/ ˜mitchell/papers/some.ps
- Mitchell
- 2000
(Show Context)
Citation Context ...istency checking [15]. CFFC can be viewed as an algorithm that does both at the same time. 16 This follows from Mitchell’s recent results showing that these problems have short refutation resolutions =-=[16]-=-. 17 In more detail, the RelSat generator took easy random 3-SAT problems with Æ variables (85 and 90 in our experiment) and ��Æ clauses and added an unsatisfiable subproblem with 10 variables and 40 ... |