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## Nogood Recording for Static and Dynamic Constraint Satisfaction Problems (1993)

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Venue: | International Journal of Artificial Intelligence Tools |

Citations: | 120 - 5 self |

### Citations

2802 | Computational Complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ...Recherches et Estudes Techniques" of the French "Delegation Generale de l'Armement" under contract 89.002.109. 1 This simply follows form the fact that the GRAPH k-COLORABILITY problem =-=is NP-complete [Pap94]-=- and is an obvious restriction of the CONSTRAINT SATISFACTION problem : variables correspond to vertices, domains contain all the available colours and one difference constraint appears instead of eac... |

1137 |
Consistency in networks of relations
- Mackworth
- 1977
(Show Context)
Citation Context ...s are binary i.e., involve at most two variables. The methods proposed in this paper are not restricted to binary CSPs. Let us consider for instance the CSP graph presented in Figure 1 (modified from =-=[Mac77]-=-). Each node represents a variable whose domain is explicitly indicated, each arc is labeled with the set of tuples permitted by the constraint (note that the constraint between connected variables is... |

672 | Where the really hard problems are
- Cheeseman, Kanefsky, et al.
- 1991
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Citation Context ... sometimes consistent, sometimes inconsistent (\Sigma). The hardest problems occur at the transition between inconsistent and consistent CSP. A similar remark was made for various NP-hard problems in =-=[CKT91]-=-. It is on these hard problems and on highly inconsistent ones that nogood recording is especially useful. As previously observed, NR and NR-FC algorithms outperform the FSL algorithms both in number ... |

454 | P.: Minimizing conflicts: A heuristic repair method for constraint satisfaction and scheduling problems - Minton, Johnston, et al. - 1992 |

384 | Dynamic Backtracking
- Ginsberg
- 1993
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Citation Context ...sed in [Bes91, PCM92] directly on CSP. This is far from satisfaction, but could be useful for pre-processing however. Another related algorithm is the Dynamic Backtracking algorithm (DBT) proposed in =-=[Gin93]-=-, related to the Intelligent Backtracking of [Bru81]. In spite of its name, DBT can not deal with dynamic CSP since it only records induced constraints (called eliminating explanations in [Gin93] and ... |

379 | Hybrid algorithms for the constraint satisfaction problem
- Prosser
- 1993
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Citation Context ...ump to the lowest variable in V J = [ j2J X J . The backjumping obtained is a dependency-directed backtracking closely related to the conflict-directed backjumping algorithm independently proposed in =-=[Pro93]-=-. the constraint forbidding A #X J being induced by (X; J); J ae C, it is also induced by (X; C). It is therefore possible to immediately add this new constraint to the CSP, during the backtrack tree ... |

330 | de Kleer. Foundations of assumption-based truth maintenance systems: Preliminary report - Reiter, Johan - 1987 |

280 | Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition
- Dechter
- 1990
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Citation Context ...states that the CSP is inconsistent and its justification is a (here minimal) justification of the CSP inconsistency. On the same problem, using the same ordering, the full shallow learning algorithm =-=[Dec90]-=- explores 35 nodes and performs 49 constraint checks. a b a b a b a b a b a b a b a b a b a b c a b c a b a b a b a b a b a b a b a b a b x5 x4 x3 x2 x1 x4 x3 x3 x3 x3 {c32, c34, c45} {x2=b} {x3=b} {c... |

194 | Performance measurement and analysis of certain search algorithms
- GASCHNIG
- 1979
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Citation Context ...t be extended to a consistent assignment on the complete set of n CSP variables (this may strictly include the dead-end situations). In essence, the difference is similar to the difference between BJ =-=[Gas79]-=- and CBJ [Pro93]. This is why full shallow learning, when limited to the i th order, only enforces a subset of strong (i; 1)-consistency (or strong (i + 1)-consistency). 3. the full shallow learning a... |

95 | Arc-consistency in dynamic constraint satisfaction problems - Bessière - 1991 |

95 | Solution reuse in dynamic constraint satisfaction problems - Verfaillie, Schiex - 1994 |

80 | R.: Dead-end driven learning
- Frost, Dechter
- 1994
(Show Context)
Citation Context ... a high quality BT than a high quality sophisticated NR-FC 2 . Moreover, further improvement could also be obtained by not maintaining justifications (this is a static problem) as it has been done in =-=[FD94]. Ho-=-wever, the timings show that the overhead for building and recording nogoods is not only reasonable but obviously balanced by the improvement obtained. Algorithm �� oe Y Z FSL 1 1.3 0.7 0.2 2.8 FS... |

61 | A comparison of ATMS and CSP techniques
- Kleer
- 1989
(Show Context)
Citation Context ...h modification with any of these algorithms, we will probably rediscover many identical failures at each satisfaction. Another approach, embodied in the ATMS and related to k-consistency enforcing in =-=[dK89], is to st-=-ore, in a "concise" way, the whole frontier of the solution space explored along with justifications for its existence. However, the space needed may grow exponentially with the size of the ... |

36 |
Backtrack-Free and BacktrackBounded Search
- Freuder
- 1988
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Citation Context ... inferred by strong (i; n \Gamma k)-consistency enforcing. Furthermore, it is possible that some of these nogoods would not have been inferred by strong (i; n \Gamma k \Gamma 1)-consistency enforcing =-=[Fre88]-=-. Proof: Let (A #XJ ; J) be a nogood built at level k (A is an assignment on x 1 ; : : : ; xk ). We know that A may not be extended to a full solution by assigning values to variables (xk+1 ; : : : ; ... |

34 |
Solving combinatorial search problems by intelligent backtracking
- Bruynooghe
- 1981
(Show Context)
Citation Context ...rom satisfaction, but could be useful for pre-processing however. Another related algorithm is the Dynamic Backtracking algorithm (DBT) proposed in [Gin93], related to the Intelligent Backtracking of =-=[Bru81]-=-. In spite of its name, DBT can not deal with dynamic CSP since it only records induced constraints (called eliminating explanations in [Gin93] and cause-lists in [Bru81]) which are not justified in t... |

17 |
Itay Meiri. Experimental Evaluation of Preprocessing Techniques in Constraint Satisfaction Problems
- Dechter
- 1989
(Show Context)
Citation Context ...nd attempts to append to it a new instantiation such that the whole set is consistent. The order by which variables get instantiated has usually an important effect on the efficiency of the algorithm =-=[DM89]-=- since each ordering defines how soon a constraint may be checked. The ordering used may be either pre-computed or may vary dynamically during the execution. The methods proposed in this paper are not... |

17 | A constraint maintenance system for the distributed resource allocation problem - Prosser, Conway, et al. - 1992 |

16 |
Dechter and Avi Dechter. Belief maintenance in Dynamic Constraint Networks
- Rina
- 1988
(Show Context)
Citation Context ...traints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The notion of dynamic CSP(DCSP)=-=[DD88]-=- has been proposed to represent such evolutions. The problem we consider here is the solution maintenance problem in a DCSP. Naively applying usual satisfaction algorithms to this problem results in r... |

14 | Maintenance of solution in a dynamic constraint satisfaction problem - Bellicha - 1994 |

9 |
How to Solve the Zebra Problem, or Path Consistency the Easy Way
- Smith
- 1992
(Show Context)
Citation Context ...and FSL 2 ) [Dec90]. 4.1 The zebra is back! The first experimentation will try to estimate the price paid for building and recording nogoods and the amount of pruning obtained. The Zebra problem (see =-=[Smi92]-=-) has been solved using 50 random vertical orderings. No heuristics has been used. For each ordering, the Zebra problem has been solved twice (the second resolution uses all the nogoods built on the f... |

6 | Two approaches to the solution maintenance problem in dynamic constraint satisfaction problems - SCHIEX, VERFAILLIE - 1993 |

6 | The Computational Complexity of Multiple-Context Truth Maintenance Systems - Provan - 1990 |

6 |
Hentenryck and Thierry Le Provost. Incremental Search in Constraint Logic Programming
- Van
- 1991
(Show Context)
Citation Context ...roposals for the solution maintenance problem: the first remark is used by [Ver93, VS94] in a local changes satisfaction algorithm applied to the previous solution if any. Remarks 1 and 2 are used by =-=[vHP91]-=- oracles scheme: using a static order on variables and values, the space explored by a tree search algorithm is totally and strictly ordered and the space explored before the occurrence of a first sol... |

5 |
Stubborness: an enhancement scheme for backjumping and nogood recording
- Schiex, Verfaillie, et al.
- 1994
(Show Context)
Citation Context ...is variety of algorithms could possibly be used to adapt to temporal pressure. We are currently investigating approaches that should offer a wider choice for trading time versus learning quality (see =-=[SV94]-=-). 4.2 Using random dynamic CSP The next experimentation aims at evaluating the impact of nogood recording after a non trivial relaxation or restriction (relaxing an inconsistent CSP and restricting a... |

2 | the ATMS and search reduction, Reason Maintenance Systems and their Applications - Smith, Forward-checking - 1988 |

2 | CCMA*: a semi-Complete Constraint Maintenance Algorithm using constraint programming - Trombettoni - 1993 |

2 | Probl`emes de satisfaction de contraintes : production et r'evision de solution par modifications locales, Under submission - Verfaillie - 1993 |

1 | de Kleer, "A comparison of ATMS and CSP techniques - Johan - 1989 |

1 |
No-good recording for static and dynamic
- Schiex, Verfaillie
- 1993
(Show Context)
Citation Context ...w solution of the constraint network after each modification of the problem. This will be called the solution maintenance problem in a dynamic CSP [SV93b, SV93a]. This paper is an extended release of =-=[SV93a] that appe-=-ars in the Proc. of the 5 th International Conference on Tools with Artificial Intelligence. This work has been supported by the "Direction des Recherches et Estudes Techniques" of the Frenc... |

1 |
Schiex andGerard Verfaillie, Stubborness: an enhancement scheme for backjumping and nogood recording
- Thomas
- 1994
(Show Context)
Citation Context ...is variety of algorithms could possibly be used to adapt to temporal pressure. We are currently investigating approaches that should offer a wider choice for trading time versus learning quality (see =-=[SV94]-=-). 4.2 Using random dynamic CSP The next experimentation aims at evaluating the impact of nogood recording after a non trivial relaxation or restriction (relaxing an inconsistent CSP and restricting a... |