## Partial Constraint Satisfaction (1992)

Citations: | 443 - 23 self |

### BibTeX

@MISC{Freuder92partialconstraint,

author = {Eugene C. Freuder and Richard J. Wallace},

title = {Partial Constraint Satisfaction},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...

### Citations

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Decisions with multiple objectives: preferences and value trade-offs
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Citation Context ...more specific objectives, which are then associated with measurable attributes. After that, preference functions are constructed that take into account priorities and tradeoffs among these attributes =-=[KR93]-=- [vWE86]. In this paper we describe an approach that represents such decision problems as a kind of constraint satisfaction problem (CSP). We model preferences in terms of orderings among solutions to... |

1052 | Consistency in Networks of Relations - Mackworth - 1977 |

1016 | Temporal Constraint Networks - Dechter, I, et al. - 1991 |

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Citation Context ... usual pattern of difficulty: easy, hard, (relatively) easy, with respect to finding a feasible solution as either density or constraint tightness is varied while the other parameter is held constant =-=[CKT91]-=-. Although we are interested in finding the best acceptable solution, since the number of feasible solutions changes dramatically as either density or tightness increases, we may still see a crossover... |

482 |
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Citation Context ...er, for purposes of presentation representative values were chosen for density 0.5, so a slice of the plane can be shown that spans the entire range of tightness. Algorithms for forward checking (FC) =-=[HE80]-=- and maintained arc consistency using AC-3 (MAC-3) [SF94] were written in C, and experiments were run on a Dell Work Station PWS 330 with 4 CPUs running at 1800 MHz. The measures taken were time and n... |

402 | Constraint Satisfaction in Logic Programming - Hentenryck - 1989 |

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Citation Context ...ecific objectives, which are then associated with measurable attributes. After that, preference functions are constructed that take into account priorities and tradeoffs among these attributes [KR93] =-=[vWE86]-=-. In this paper we describe an approach that represents such decision problems as a kind of constraint satisfaction problem (CSP). We model preferences in terms of orderings among solutions to a CSP. ... |

294 | Valued Constraint Satisfaction Problems: Hard and Easy Problems
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(Show Context)
Citation Context ...tright exclusion. At present, the leading formalisms are the valued and semiring CSPs, in which evaluations are attached to domain values as well as to either constraints or constraint tuples [BMR97] =-=[SFV95]-=-. These evaluations can be used to represent preferences (in the form of utilities) as well as other scalable features like importance or likelihood. The resulting problems are constraint optimization... |

290 |
and easy distributions of SAT problems
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Citation Context ...ce. The phase transition curve for lexical ordering shown in these figures does not represent quite the same phenomenon (or variant) as do complexity peaks with ordinary CSP or SAT algorithms [CKT91] =-=[MSL92]-=-. It is more closely related to the demonstraMedian Nodes 1e+06 100000 10000 1000 100 n=10 n=20 n=30 n=40 10 0 10 20 30 40 50 Tightness 60 70 80 90 100 Fig. 3. Effort required by MAC-3 with lexical o... |

284 | Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition - Dechter - 1990 |

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241 |
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Citation Context ...ct support in the psychology of choice, which has produced evidence that people process complex decisions by successively eliminating attributes (called “aspects”) according to some priority ordering =-=[Tve72]-=-. In this case, it may even be possible to establish a lexicographic preference ordering during the course of problem solving, by allowing the user to follow his or her natural strategy of eliminating... |

223 |
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Citation Context ...k does not allow one to express conditional preferences as can be done with CP-nets, it may be possible to combine the present framework with that of conditional CSPs (sometimes called “dynamic CSPs” =-=[MF90]-=-) to achieve the same representational capacities. The virtue of such an approach, in contrast to TCP-nets, is that it does not require any additional representational elements; instead it associates ... |

215 | Contradicting conventional wisdom in constraint satisfaction
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(Show Context)
Citation Context ...re chosen for density 0.5, so a slice of the plane can be shown that spans the entire range of tightness. Algorithms for forward checking (FC) [HE80] and maintained arc consistency using AC-3 (MAC-3) =-=[SF94]-=- were written in C, and experiments were run on a Dell Work Station PWS 330 with 4 CPUs running at 1800 MHz. The measures taken were time and numbers of backtracks, search nodes, and constraint checks... |

189 |
Semiring-based Constraint Solving and Optimization
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Citation Context ...ad to outright exclusion. At present, the leading formalisms are the valued and semiring CSPs, in which evaluations are attached to domain values as well as to either constraints or constraint tuples =-=[BMR97]-=- [SFV95]. These evaluations can be used to represent preferences (in the form of utilities) as well as other scalable features like importance or likelihood. The resulting problems are constraint opti... |

184 | Structural descriptions and inexact matching - Shapiro, Haralick - 1981 |

179 | Combinatorial algorithm: theory and practice - Reingold, Nievergelt, et al. - 1982 |

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148 | Constraint hierarchies
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(Show Context)
Citation Context ...rast, soft constraint representations require some form of branch and bound to solve to completion. (This is true even when hard constraints are represented within a soft constraints framework, as in =-=[BFBW92]-=- [SFV95].) It is to be expected that at least in certain parts of the problem space ordinary CSP algorithms will outperform branch and bound algorithms. (Of course, branch and bound techniques are als... |

125 | Constraint satisfaction algorithms - Nadel - 1989 |

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Citation Context ...assignments.) 2.3 Ordinal CSPs and CP-nets. Another formalism for representing certain kinds of preference structures is the conditional preference network with ceteris paribus assumptions, or CP-net =-=[BBHP99]-=-. Here, the preference ordering for one attribute depends on the value chosen for other attributes. The CP-net formalism cannot represent lexicographic orderings (as noted by the authors). In addition... |

113 | Good Old Discrete Relaxation - Mohr, Masini - 1988 |

100 | Backtrack programming - Golomb, Baumert - 1965 |

81 | Complexity of k-tree structured constraint satisfaction problems - Freuder - 1990 |

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74 | Look-ahead value ordering for constraint satisfaction problems
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(Show Context)
Citation Context ...domains, and (dynamic) minimum-conflicts value ordering, where values with a smaller sum of conflicts with values in adjacent future domains are chosen before values with a larger number of conflicts =-=[FD95]-=-. (Although value ordering cannot make the all-solutions problem more efficient, it was of interest to determine whether such heuristics can be used to find good solutions more quickly.) For experimen... |

69 | Constraint hierarchies and logic programming - Borning, Maher, et al. - 1989 |

59 | Enhancement Schemes for Constraint Processing - Dechter - 1990 |

54 | A general Backtracking algorithm that eliminates most redundant tests - Gaschnig - 1977 |

51 | Constraint Satisfaction Problems: An Overview - Meseguer - 1989 |

36 | Backtrack-free and backtrack-bounded search - Freuder - 1988 |

34 | Making Compromises among Antagonist Constraints in a Planner - Descotte, Latombe - 1985 |

26 | Improved relaxation and search methods for approximate constraint satisfaction with a maximin criterion - Snow, Freuder - 1990 |

23 |
Utility theory
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(Show Context)
Citation Context ...tegy. These indications are borne out, as shown later in the paper. Although lexicographic orderings have a venerable history in the study of preference in such areas as economics and decision making =-=[Fis68]-=-, there has been very little work on applying this idea to constraint satisfaction problems, and little work on algorithms for solving these problems. In the context of symmetry breaking, [FHK 02] hav... |

23 | Analysis of heuristic methods for partial constraint satisfaction problems - Wallace - 1996 |

20 |
Phase transition in max-csp
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(Show Context)
Citation Context ...3. Effort required by MAC-3 with lexical ordering, for 10, 20, 30 and 40-variable problems with density = 0.5 and tightness varying in steps of 0.05. Sample size at each step was 50 problems. tion by =-=[LM96]-=- of an algorithm-dependent phase transition with increasing constraint tightness for MAX-CSPs. In their situation, as in the present case, problems can become more and more difficult across a paramete... |

13 | Optimization algorithms for student scheduling via constraint satis ability - Feldman, Golumbic - 1990 |

13 | Tree Decompositions with Applications to Constraint Processing - Meiri, Dechter, et al. - 1990 |

7 |
The emergence of ordered belief from initial ignorance
- Snow
- 1994
(Show Context)
Citation Context ...the atom-bound probability formalism used to model credibility or belief is also based on the notion of “overwhelming advantage” of higher-priority elements over any set of elements of lower priority =-=[Sno94]-=- [BDP97]. As our introductory example indicates, combining this idea with constraint based reasoning gives a useful representation for many decision problems that is also amenable to a variety of algo... |

6 | A debugging assistant for incompletely specified constraint network knowledge bases - Huard, Freuder - 1993 |

5 | Visual Occlusion and the Interpretation of Ambiguous Pictures - Cooper - 1992 |

3 | Experimental Design: Brooks/Cole - Kirk - 1968 |

2 | Tcp-nets for preference-based product configuration
- Brafman, Domshlak
- 2002
(Show Context)
Citation Context ...rence since an optical zoom can be combined with either weight, while the same ordering given a digital zoom is due to a constraint restriction). A more recent extension of CP-nets, called “TCP-nets” =-=[BD02]-=-, is capable of representing lexicographic orderings. However, even this framework does not allow one to clearly specify hard constraints as well as preference orderings, and so it does not allow one ... |