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## A Generic Arc-Consistency Algorithm and its Specializations (1992)

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### Other Repositories/Bibliography

Venue: | Artificial Intelligence |

Citations: | 212 - 7 self |

### Citations

10437 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2009
(Show Context)
Citation Context ...s a hash table to test membership in the domain. Although the time complexity of membership is theoretically not O(1), under reasonable assumptions, the expected time to search for an element is O(1) =-=[-=-1]. For ease of presentation, we assume in the rest of the paper that AC-5 stops as soon as a domain becomes empty. 5 Functional Constraints Denition 10 A constraint C is functional wrt a domain D i f... |

1137 |
Consistency in networks of relations
- Mackworth
- 1977
(Show Context)
Citation Context ...omplete, which means that backtracking search is an important technique in their solution. Many search algorithms (e.g. [2, 5, 6, 7, 10, 18]), preprocessing techniques and constraint algorithms (e.g. =-=[26, 17, 11, 13, 15]-=-) have been designed and analyzed for this class of problems; see the reviews [12, 19] for a comprehensive overview of this area. In this paper, we are mainly concerned with (network) consistency tech... |

521 | Increasing tree search efficiency for constraint satisfaction problems - Haralick, Elliott - 1980 |

484 |
Networks of constraints: Fundamental properties and applications to picture processing
- Montanari
(Show Context)
Citation Context ...P-complete, which means that backtracking search isanimportanttechnique in their solution. Many search algorithms (e.g. [2, 6, 7, 8, 11, 19]), preprocessing techniques and constraint algorithms (e.g. =-=[27, 18, 12, 14, 16]-=-) have been designed and analyzed for this class of problems� see the reviews [13, 20] for a comprehensiveoverview of this area. In this paper, we are mainly concerned with (network) consistency techn... |

407 |
Network-based heuristics for constraint satisfaction problems
- Dechter, Pearl
- 1987
(Show Context)
Citation Context ...blem amounts tosnding one or all solutions. Most problems in this class are NP-complete, which means that backtracking search is an important technique in their solution. Many search algorithms (e.g. =-=[2, 5, 6, 7, 10, 18]-=-), preprocessing techniques and constraint algorithms (e.g. [26, 17, 11, 13, 15]) have been designed and analyzed for this class of problems; see the reviews [12, 19] for a comprehensive overview of t... |

288 |
The complexity of some polynomial network consistency algorithms for constraint satisfaction problems
- Mackworth, Freuder
- 1985
(Show Context)
Citation Context ...omplete, which means that backtracking search is an important technique in their solution. Many search algorithms (e.g. [2, 5, 6, 7, 10, 18]), preprocessing techniques and constraint algorithms (e.g. =-=[26, 17, 11, 13, 15]-=-) have been designed and analyzed for this class of problems; see the reviews [12, 19] for a comprehensive overview of this area. In this paper, we are mainly concerned with (network) consistency tech... |

266 |
The constraint logic programming language CHIP
- Dincbas, Hentenryck, et al.
- 1988
(Show Context)
Citation Context ... size of the largest domain. Consistency techniques have recently 2 been applied in the design of constraint logic programming (CLP) languages, more precisely in the design and implementation of CHIP =-=[23, 4-=-]. CHIP allows the solving of a variety of constraints oversnite domains, including numerical, symbolic, and user-dened constraints. It has been applied to a variety of industrial problems and preserv... |

263 | Constraint satisfaction
- Mackworth
- 1992
(Show Context)
Citation Context ...arch algorithms (e.g. [2, 5, 6, 7, 10, 18]), preprocessing techniques and constraint algorithms (e.g. [26, 17, 11, 13, 15]) have been designed and analyzed for this class of problems; see the reviews =-=[12, 19]-=- for a comprehensive overview of this area. In this paper, we are mainly concerned with (network) consistency techniques, and arc consistency in particular. Consistency techniques are constraint algor... |

256 |
Synthesizing constraint expressions
- Freuder
- 1978
(Show Context)
Citation Context ...blem amounts tosnding one or all solutions. Most problems in this class are NP-complete, which means that backtracking search is an important technique in their solution. Many search algorithms (e.g. =-=[2, 5, 6, 7, 10, 18]-=-), preprocessing techniques and constraint algorithms (e.g. [26, 17, 11, 13, 15]) have been designed and analyzed for this class of problems; see the reviews [12, 19] for a comprehensive overview of t... |

232 | Arc and path consistency revisited - Mohr, Henderson - 1986 |

186 | Implementation, and Evaluation of the Constraint Language cc(FD
- HENTENRYCK, SARASWAT, et al.
- 1998
(Show Context)
Citation Context ... is easy to see that the constant factors are in fact small in our algorithms (in general 1 or 2). On the empirical side, most of these classes have been integrated in the cc(FD) programming language =-=[25]-=- improving the computational results of many algorithms compared to the previous versions based on AC-3 and AC-4. This will be discussed in a forthcoming paper. It is however important to note that AC... |

178 |
Generating semantic descriptions from drawings of scenes with shadows.Technical Report AI271
- Waltz
(Show Context)
Citation Context ...d extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arc-consistency algorithms have been proposed, originating from Waltz'ssltering algorithm =-=[26]-=- and culminating in the optimal algorithm AC-4 of Mohr and Henderson [15]. AC-4 runs in O(ed 2 ) in the worst case, where e is the number of arcs (or constraints) and d is the size of the largest doma... |

163 |
Amortized computational complexity
- Tarjan
- 1985
(Show Context)
Citation Context ... possible. Theorem 19 With the revised implementation depicted in Figures 14 and 15, Procedure AC-5 is O(ed) for monotonic constraints wrt D. Proof This proof requires the use of amortized complexity =-=[21]-=- to show that LocalArcConssis O(d) amortized. The number of iterations for a call to the revised version of LocalArcCons is not O(d) in the worst case, since some elements may have been removed from t... |

127 |
Constraint satisfaction algorithms
- Nadel
- 1989
(Show Context)
Citation Context ...arch algorithms (e.g. [2, 5, 6, 7, 10, 18]), preprocessing techniques and constraint algorithms (e.g. [26, 17, 11, 13, 15]) have been designed and analyzed for this class of problems; see the reviews =-=[12, 19]-=- for a comprehensive overview of this area. In this paper, we are mainly concerned with (network) consistency techniques, and arc consistency in particular. Consistency techniques are constraint algor... |

109 |
Good old discrete relaxation
- Mohr, Masini
- 1988
(Show Context)
Citation Context ...mprovements can be obtained for path-consistency algorithms although the algorithms are somewhat more complicated. Non-binary constraints are also being investigated to obtain the equivalent of GAC-4 =-=[14]-=- for AC-5. Preliminary results indicate that the results carry over for some classes of constraints, although once again the algorithms are more involved. Acknowledgments We thank an anonymous IJCAI r... |

98 |
A language and a program for stating and solving combinatorial problems,”Artificial
- Lauriere
- 1978
(Show Context)
Citation Context ...blem amounts tosnding one or all solutions. Most problems in this class are NP-complete, which means that backtracking search is an important technique in their solution. Many search algorithms (e.g. =-=[2, 5, 6, 7, 10, 18]-=-), preprocessing techniques and constraint algorithms (e.g. [26, 17, 11, 13, 15]) have been designed and analyzed for this class of problems; see the reviews [12, 19] for a comprehensive overview of t... |

84 |
Methodology and implementation of a CLP system
- Jaffar, Michaylov
- 1987
(Show Context)
Citation Context ...igure 24: Procedure LocalArcCons for Piecewise Monotonic Constraints 12 Application We describe the application of AC-5 to constraint logic programming oversnite domains. Constraint logic programming =-=[8-=-] is a class of languages whose main operation is constraintsolving over a computation domain. A computation step amounts to checking the satisability of a conjunction of constraints. Constraint logic... |

73 |
On the parallel complexity of discrete relaxation in constraint satisfaction networks
- Kasif
- 1990
(Show Context)
Citation Context ...nt: a functional constraint requires O(d) space with the graph representation and requires constant space in AC-5. Arc consistency of functional constraints can be solved through a reduction to 2-sat =-=[9]-=-, keeping the O(ed) result. However, this algorithm also uses O(d) space per constraint. Finally, it is also interesting to study the evolution of arc-consistency algorithms. The main contribution of ... |

70 | Constraint processing in cc(fd
- Hentenryck, Saraswat, et al.
- 1992
(Show Context)
Citation Context ... is easy to see that the constant factors are in fact small in our algorithms (in general 1 or 2). On the empirical side, most of these classes have been integrated in the cc(FD) programming language =-=[26]-=- improving the computational results of many algorithms compared to the previous versions based on AC-3 and AC-4. This will be discussed in a forthcoming paper. It is however important to note that AC... |

51 |
Increasing tree search eciency for constraint satisfaction problems
- Haralick, Elliott
- 1980
(Show Context)
Citation Context |

48 | The Constraint Logic Programming - Dincbas - 1988 |

44 | An efficient arc consistency algorithm for a class of CSP problems - Deville, Hentenryck - 1991 |

30 |
Increasing Tree Search E ciency for Constraint Satisfaction Problems. Arti cial Intelligence 14:263{313
- Haralick, Elliott
- 1980
(Show Context)
Citation Context ...problem amounts to nding one or all solutions. Most problems in this class are NP-complete, which means that backtracking search isanimportanttechnique in their solution. Many search algorithms (e.g. =-=[2, 6, 7, 8, 11, 19]-=-), preprocessing techniques and constraint algorithms (e.g. [27, 18, 12, 14, 16]) have been designed and analyzed for this class of problems� see the reviews [13, 20] for a comprehensiveoverview of th... |

28 |
Arc consistency for factorable relations
- Perlin
- 1992
(Show Context)
Citation Context ...notonic, and anti-functional constraints. They indicate informally how to modify AC-4 to include these constraints, but do not present a uniform and generic algorithm like AC-5. 24 Perlin's algorithm =-=[20]-=- is an arc-consistency algorithm working on a graph representation of the CSP where the values (not the variables) are nodes and the constraints are represented by links between nodes. The algorithm i... |

21 |
A constraint satisfaction method for inference making
- Gaschnig
(Show Context)
Citation Context |

19 | Introduction to Algorithms. The M.I.T - Cormen, Leiserson, et al. - 1990 |

12 |
Consistency Techniques in Logic Programming
- Hentenryck
- 1987
(Show Context)
Citation Context ...intsolving over a computation domain. A computation step amounts to checking the satisability of a conjunction of constraints. Constraint logic programming oversnite domains has been investigated in [=-=24, 22, 23]-=-. This is a computation domain in which constraints are equations, inequalities and disequations over natural number terms or equations and disequations over constants. Natural number terms are constr... |

7 | Running Efficiently Arc Consistency - Mohr, Masini - 1988 |

6 |
An e cient arc consistency algorithm for a class of CSP problems
- Deville, Hentenryck
- 1991
(Show Context)
Citation Context ...a set of basic constraints. We prove that AC-5, in conjunction with node consistency, provides a decision procedure for these constraints running in time O(ed). 1 This paper is an extended version of =-=[3]-=-. 1s1 Introduction Many important problems in areas like arti cial intelligence, operations research and hardware design can be viewed as constraint satisfaction problems (CSP). A CSP is de ned by a n... |

5 |
Methodology and Implementation of a CLP System
- ar, Michaylov
- 1987
(Show Context)
Citation Context ...igure 24: Procedure LocalArcCons for Piecewise Monotonic Constraints 12 Application We describe the application of AC-5 to constraint logic programming over nite domains. Constraint logic programming =-=[9]-=- is a class of languages whose main operation is constraintsolving over a computation domain. A computation step amounts to checking the satis ability of a conjunction of constraints. Constraint logic... |

4 |
An efficient algorithm for the solution of hierarchical networks of constraints
- Montanari, Rossi
- 1986
(Show Context)
Citation Context |

4 | Constraint satisfaction algorithms, Cornput. lntell - Nadel - 1989 |

2 |
Running Eciently Arc Consistency
- Mohr, Masini
- 1988
(Show Context)
Citation Context ...emory requirement. Hence, for memory management reasons, AC-3 may sometimes be preferable. As far as related work are concerned, three closely related papers deserve to be mentioned. Mohr and Mansini =-=[16]-=- also discovered independently the subset of arithmetic constraints that can be solved in O(ed). The constraints considered were binary equations, inequalities, and disequations, which are respectivel... |

2 |
Constraint Satisfaction, volume Encyclopedia of Arti cial Intelligence
- Mackworth
- 1987
(Show Context)
Citation Context ...arch algorithms (e.g. [2, 6, 7, 8, 11, 19]), preprocessing techniques and constraint algorithms (e.g. [27, 18, 12, 14, 16]) have been designed and analyzed for this class of problems� see the reviews =-=[13, 20]-=- for a comprehensiveoverview of this area. In this paper, we are mainly concerned with (network) consistency techniques, and arc consistency in particular. Consistency techniques are constraint algori... |

2 |
Running e - ciently arc consistency
- Mohr, Masini
- 1988
(Show Context)
Citation Context ...emory requirement. Hence, for memory management reasons, AC-3 may sometimes be preferable. As far as related work are concerned, three closely related papers deserve to be mentioned. Mohr and Mansini =-=[17]-=- also discovered independently the subset of arithmetic constraints that can be solved in O(ed). The constraints considered were binary equations, inequalities, and disequations, which are respectivel... |

2 | Hentenryck, A framework for consistency techniques in logic programming - Van - 1987 |

1 | Constraint processing in ce(FD - Hentenryck, Saraswat, et al. - 1992 |