## Algorithms for Constraint Satisfaction Problems: A Survey (1992)

Venue: | AI MAGAZINE |

Citations: | 398 - 0 self |

### BibTeX

@ARTICLE{Kumar92algorithmsfor,

author = {Vipin Kumar},

title = {Algorithms for Constraint Satisfaction Problems: A Survey},

journal = {AI MAGAZINE},

year = {1992},

volume = {13},

number = {1},

pages = {32--44}

}

### Years of Citing Articles

### OpenURL

### Abstract

A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.

### Citations

2489 | Maintaining Knowledge about Temporal Intervals
- Allen
- 1983
(Show Context)
Citation Context ...b; Montanari 1974; Rosenfeld 1976), belief maintenance (Dechter 1987; Dechter 1988a; Dhar 1990a), scheduling (Dhar 1990b; Fox 1987; Fox 1989; Petrie 1989; Prosser 1989; Rit 1986), temporal reasoning (=-=Allen 1983-=-; Allen 1984; Dechter 1989b; Vilain 1986; Tsang 1987), graph problems (McGregor 1979; Bruynooghe 1 Figure 1: An example map-coloring problem and its equivalent constraintsatisfaction problem 1985), fl... |

1013 | Temporal constraint network - Dechter, Meiri, et al. - 1991 |

924 |
Towards a general theory of action and time
- Allen
- 1984
(Show Context)
Citation Context ... 1974; Rosenfeld 1976), belief maintenance (Dechter 1987; Dechter 1988a; Dhar 1990a), scheduling (Dhar 1990b; Fox 1987; Fox 1989; Petrie 1989; Prosser 1989; Rit 1986), temporal reasoning (Allen 1983; =-=Allen 1984-=-; Dechter 1989b; Vilain 1986; Tsang 1987), graph problems (McGregor 1979; Bruynooghe 1 Figure 1: An example map-coloring problem and its equivalent constraintsatisfaction problem 1985), floor plan des... |

652 |
A truth maintenance system
- Doyle
- 1979
(Show Context)
Citation Context ...ing based method that eliminates both of these drawbacks of backtracking. This method is traditionally called dependencydirected backtracking (Stallman 1977) and is used in truth maintenance systems (=-=Doyle 1979-=-; McDermott 1991). A CSP can be solved by Doyle's RMS (Doyle 1979; Stallman 1977) as follows. A variable is assigned some value, and a justification for this is noted (the justification is simply that... |

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

469 | An assumption-based TMS - Kleer - 1986 |

443 | Partial constraint satisfaction
- Freuder, Wallace
- 1992
(Show Context)
Citation Context ...d one assignment to the variables such that the assignment satisfies all the constraints. In some problems, the goal is to find all such assignments. More general formulations of CSP can be found in (=-=Freuder 1989-=-; Gu 1889; Mackworth 1985b; Mittal 1987; Mittal 1990; Freeman-Benson 1990; Navinchandra 1987; Shapiro 1981; Ricci 1990). In this paper, we further restrict the discussion to the CSPs in which each con... |

401 | Network-based heuristics for constraint satisfaction problems - Dechter, Pearl - 1987 |

365 | Scene labeling by relaxation operations - Rosenfeld, Hummel, et al. - 1976 |

284 |
Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition
- Dechter
- 1990
(Show Context)
Citation Context ...etermined in advance. For other techniques that take advantage of the structure of the constraint graphs to reduce search, see (Dechter 1988a; Dechter 1988c; Dechter 1986; Freuder 1985; Freuder 1990; =-=Dechter 1990-=-b; 10 Figure 5: A tree-structured constraint graph and one of its width-1 orderings Zabih 1990; Perlin 1991; Montanari 1991). 4 How Much Constraint Propagation is Useful? So far we have considered two... |

187 | Performance measurement and analysis of certain search algorithms
- Gaschnig
- 1979
(Show Context)
Citation Context ...han generate-and-test, its runtime complexity for most nontrivial problems is still exponential. One of the reasons for this poor performance is that the backtracking paradigm suffers from thrashing (=-=Gaschnig 1979-=-); i.e., search in different parts of the space keeps failing for the same reasons. The simplest cause of thrashing concerns the unary predicates, and is referred to as node inconsistency (Mackworth 1... |

174 |
Constraint-Directed Search: A Case Study of Job-Shop Scheduling
- Fox
- 1983
(Show Context)
Citation Context ...Some examples are machine vision (Chakravarty 1979; Davis 1981; Mackworth 1977b; Montanari 1974; Rosenfeld 1976), belief maintenance (Dechter 1987; Dechter 1988a; Dhar 1990a), scheduling (Dhar 1990b; =-=Fox 1987-=-; Fox 1989; Petrie 1989; Prosser 1989; Rit 1986), temporal reasoning (Allen 1983; Allen 1984; Dechter 1989b; Vilain 1986; Tsang 1987), graph problems (McGregor 1979; Bruynooghe 1 Figure 1: An example ... |

147 | Belief Maintenance in Dynamic Constraint Networks - Dechter, Dechter - 1988 |

120 | Backtrack Programming Techniques - Bitner, Reingold - 1975 |

120 | An incremental constraint solver - Freeman-Benson, Maloney, et al. - 1990 |

81 |
Complexity of k-tree structured constraint satisfaction problems
- Freuder
- 1990
(Show Context)
Citation Context ...ng it can be determined in advance. For other techniques that take advantage of the structure of the constraint graphs to reduce search, see (Dechter 1988a; Dechter 1988c; Dechter 1986; Freuder 1985; =-=Freuder 1990-=-; Dechter 1990b; 10 Figure 5: A tree-structured constraint graph and one of its width-1 orderings Zabih 1990; Perlin 1991; Montanari 1991). 4 How Much Constraint Propagation is Useful? So far we have ... |

80 | Taking advantage of stable sets of variables in constraint satisfaction problems - Freuder, Quinn - 1985 |

77 |
Experimental case studies of backtrack vs waltz-type vs new algorithms for satisficing assignment problems
- Gaschnig
- 1978
(Show Context)
Citation Context ... to be the best algorithm. Experiments of other researchers with a variety of problems also indicate it is better to apply constraint propagation only in a limited form (Haralick 1980; McGregor 1979; =-=Gaschnig 1978-=-; Gaschnig 1979; Dechter 1989a; Prosser 1991). 5 Intelligent Backtracking and Truth Maintenance There are two major drawbacks of the standard backtracking scheme. One, discussed earlier, is thrashing;... |

76 |
An optimal k-consistency algorithm
- Cooper
- 1989
(Show Context)
Citation Context ...onsistency discussed earlier is equivalent to strong 1-consistency. Arc-consistency is equivalent to strong 2-consistency. Algorithms exist to make a constraint graph strongly K-consistent for K ? 2 (=-=Cooper 1989-=-; Freuder 1988). Clearly, if a constraint graph containing n nodes is strongly n-consistent, then a solution to the CSP can be found without any search. But the worst-case complexity of the algorithm ... |

66 | Problem solving with the ATMS - Kleer - 1986 |

59 | A comparison of ATMS and CSP techniques - Kleer - 1989 |

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

58 | Constrained Heuristic Search - Fox, Sadeh, et al. - 1989 |

56 | Experimental evaluation of preprocessing techniques in constraint satisfaction problems - Dechter, Meiri - 1989 |

54 | General Backtrack Algorithm that Eliminates Most Redundant Tests
- Gaschnig, “A
- 1977
(Show Context)
Citation Context ...for a variety of problems. Hence a number of simplifications to this scheme have been developed by various researchers (e.g., Bruynooghe 1981; Rosiers 1986; Dechter 1986; Dechter 1990; Haralick 1980; =-=Gaschnig 1977-=-). For example, a scheme developed by Dechter and Pearl is much simpler and less precise than the original dependency-directed backtracking scheme of Stallman and Sussman. Even the schemes that perfor... |

52 | Deduction Revision by Intelligent backtracking - Bruynooghe, Pereira - 1984 |

48 |
Ref-Arf: A System for Solving Problems Stated as Procedures
- Fikes
- 1970
(Show Context)
Citation Context ...usually more expensive than simple backtracking. A number of algorithms for solving CSPs have been investigated by various researcher that essentially fit the above format (Haralick 1980; Nadel 1988; =-=Fikes 1970-=-; Gaschnig 1974; Ullman 1976; Haralick 1978; McGregor 1979; Dechter 1989a). In particular, Nadel (Nadel 1988) empirically compared the performance of the following algorithms: Generate and Test (GT), ... |

36 |
Backtrack-free and backtrack-bounded search
- Freuder
- 1988
(Show Context)
Citation Context ...scussed earlier is equivalent to strong 1-consistency. Arc-consistency is equivalent to strong 2-consistency. Algorithms exist to make a constraint graph strongly K-consistent for K ? 2 (Cooper 1989; =-=Freuder 1988-=-). Clearly, if a constraint graph containing n nodes is strongly n-consistent, then a solution to the CSP can be found without any search. But the worst-case complexity of the algorithm for obtaining ... |

33 |
Solving combinatorial search problems by intelligent backtracking
- Bruynooghe
- 1981
(Show Context)
Citation Context ...ence, overall the scheme may take more time than even simple backtracking for a variety of problems. Hence a number of simplifications to this scheme have been developed by various researchers (e.g., =-=Bruynooghe 1981-=-; Rosiers 1986; Dechter 1986; Dechter 1990; Haralick 1980; Gaschnig 1977). For example, a scheme developed by Dechter and Pearl is much simpler and less precise than the original dependency-directed b... |

30 | Learning while searching in constraintsatisfaction-problems
- Dechter
- 1986
(Show Context)
Citation Context ...d space complexity of applying it can be determined in advance. For other techniques that take advantage of the structure of the constraint graphs to reduce search, see (Dechter 1988a; Dechter 1988c; =-=Dechter 1986-=-; Freuder 1985; Freuder 1990; Dechter 1990b; 10 Figure 5: A tree-structured constraint graph and one of its width-1 orderings Zabih 1990; Perlin 1991; Montanari 1991). 4 How Much Constraint Propagatio... |

27 |
Parallel Algorithms and Architectures for Very Fast
- Gu
- 1989
(Show Context)
Citation Context ...nment of values to variables, and then continue to repair the values of variables until a correct solution is obtained. Sosic and Gu had earlier developed a similar algorithm independently of Minton (=-=Gu 1989-=-). Another heuristic is to prefer the value (from those available) that leads to an easiest to solve CSP. Dechter and Pearl (Dechter 1988a) discuss one way of estimating the difficulty of solving a CS... |

25 | Cooperating processes for low-level vision: a survey - Davis, Rosenfeld - 1980 |

24 | Propagation of Constraints Applied to Circuit Synthesis - DeKleer, Sussman - 1983 |

24 |
A constraint satisfaction method for inference making
- Gaschnig
(Show Context)
Citation Context ... expensive than simple backtracking. A number of algorithms for solving CSPs have been investigated by various researcher that essentially fit the above format (Haralick 1980; Nadel 1988; Fikes 1970; =-=Gaschnig 1974-=-; Ullman 1976; Haralick 1978; McGregor 1979; Dechter 1989a). In particular, Nadel (Nadel 1988) empirically compared the performance of the following algorithms: Generate and Test (GT), Simple Backtrac... |

21 |
A Generalized Line and Junction Labelling Scheme with Applications to Scene Analysis
- Chakravarty
- 1979
(Show Context)
Citation Context ...blems in Artificial Intelligence (AI) and other areas of computer science can be viewed as a special case of the constraint satisfaction problem (CSP) (Nadel 1990a). Some examples are machine vision (=-=Chakravarty 1979-=-; Davis 1981; Mackworth 1977b; Montanari 1974; Rosenfeld 1976), belief maintenance (Dechter 1987; Dechter 1988a; Dhar 1990a), scheduling (Dhar 1990b; Fox 1987; Fox 1989; Petrie 1989; Prosser 1989; Rit... |

21 | An improved constraint propagation algorithm for diagnosis, in - Geffner, Pearl - 1987 |

18 | The Cycle-Cutset Method for Improving Search Performance in AI Applications - Dechter, Pearl - 1987 |

16 | Integer programming vs. Expert Systems: An experimental comparison - Dhar, Ranganathan - 1990 |

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

12 |
A sufficient condition for backtrack free search
- Freuder
- 1982
(Show Context)
Citation Context ... structure. Theorem 1 If a constraint graph is strongly K-consistent, and K ? w where w is the width of the constraint graph, then there exists a search 9 order that is backtrack free. (Freuder 1988; =-=Freuder 1982-=-) The proof of the above theorem is straightforward. If w is the width of the graph, then there exists an ordering of the graph such that the number of constraint arcs that lead from any vertex of the... |

11 | COSSACK: A Constraints-Based Expert System for Configuration - Frayman, Mittal - 1987 |

9 |
Improving Han and Lee’s path consistency algorithm
- Chen
- 1991
(Show Context)
Citation Context ...hieving arc-consistency is O(ed 2 ). Thus Mohr and Handerson 's algorithm is optimal in terms of worst-case complexity. Variations and improvements of this algorithm have been developed in (Han 1988; =-=Chen 1991-=-). Given an arc-consistent constraint graph, is any (complete) instantiation of the variables from current domains a solution to the CSP? In other 6 Figure 3: Examples of arc-consistent constraint gra... |

9 | Reduction operation for constraint satisfaction - Haralick, Davis, et al. - 1978 |

8 | Constraint Satisfiability Algorithms for Interactive Student Scheduling - Feldman, Golumbic - 1989 |

7 |
Preliminary Report on a System for General Space Planning
- Eastman
- 1972
(Show Context)
Citation Context ...hter 1989b; Vilain 1986; Tsang 1987), graph problems (McGregor 1979; Bruynooghe 1 Figure 1: An example map-coloring problem and its equivalent constraintsatisfaction problem 1985), floor plan design (=-=Eastman 1972-=-), planning genetic experiments (Stefik 1981), the satisfiability problem (Zabih 1988), circuit design (de Kleer 1980; Birmingham 1988), machine design and manufacturing (Frayman 1987; Nadel 1990b; Na... |

5 | Graph Coloring and Constraint Satisfaction - Bruynooghe - 1985 |

3 |
A Constraint-Network Approach to Truth Maintenance
- Dechter
- 1987
(Show Context)
Citation Context ... case of the constraint satisfaction problem (CSP) (Nadel 1990a). Some examples are machine vision (Chakravarty 1979; Davis 1981; Mackworth 1977b; Montanari 1974; Rosenfeld 1976), belief maintenance (=-=Dechter 1987-=-; Dechter 1988a; Dhar 1990a), scheduling (Dhar 1990b; Fox 1987; Fox 1989; Petrie 1989; Prosser 1989; Rit 1986), temporal reasoning (Allen 1983; Allen 1984; Dechter 1989b; Vilain 1986; Tsang 1987), gra... |

2 | A Knowledge Representation for Constraint-Satisfaction Problems - Dhar, Croker - 1990 |

2 |
Synthesizing Constrain Expression
- Freuder
- 1978
(Show Context)
Citation Context ...n constraint graph that has minimum width w (Freuder 1988; Freuder 1982). It might appear that all we need to do is to make this constraint graph strongly (w + 1)- consistent using the algorithms in (=-=Freuder 1978-=-). Unfortunately, for K ? 2, the algorithm for obtaining K-consistency adds extra arcs in the constraint graph, which can increase the width of the graph. This means that a higher degree of consistenc... |

2 |
A Perfect Heuristic for the N NonAttacking
- Kale
- 1990
(Show Context)
Citation Context ...aximize the number of options available for future assignments (Haralick 1980). By incorporating such a value-ordering heuristic in Stone and Stone's algorithm for solving the n-queens problem, Kale (=-=Kale 1990-=-) developed a backtrack based algorithm that can be used 16 to solve the problem with very little backtracking even for very large values of n (= 1000). Without incorporating Kale's heuristic, Stone a... |