Haralick, R., Elliott, G.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14 (1980) 263--313  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has dramatically increased. It appears that the more constraint networks are used, the simpler the constraint satisfaction techniques involved in the applications are. In fact, a great part of real life applications using constraint networks are limited to a forward checking search procedure [HE80], or use an arc consistency filtering algorithm before or during the search. This is one of the reasons why arc consistency remains a hot area in the CSP community [Bes94a, BC93, Per92, VDT92] Improving the efficiency of arc consistency algorithms improves in the same way the efficiency of all ....

R.M. Haralick and G.L. Elliot. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....via labeling: which variable is to be fixed (variable ordering) and which value it should be fixed at (value ordering) Choosing the proper ordering strategies can greatly improve efficiency of the search. One of the most commonly used strategies for variable ordering is the fail first strategy [HE,80] Here the decision variables with the fewest possible remaining 21 alternatives (the fewest elements in their domains) are selected first. These variables usually are the most difficult to satisfy and can cause failure early and often in the search. The rationale here is that detecting early ....

Haralick, R.; Elliott, G.: Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence, 1980.

....since it can only start at time 2. This example suggests a simple rule of thumb for choosing which observation to schedule next: prefer observations having the fewest remaining opportunities. This heuristic resembles the Minimum Remaining Values (MRV) heuristic commonly used in the CSP community [7] . Calculating the number of remaining opportunities for an observation is appealing because it is simple to compute, and provides at least some estimate of how easy it is to schedule that particular observation. However, it does not give any estimate of how much contention there is for those ....

R. Haralick and G. Elliot. Increasing tree search efficiency for constraint satisfaction. Journal of Artificial Intelligence, 14:263--313, 1980.

....Which can then eventually start a new forward step. A7 A5 A3 A2 A4 A1 A6 forward step Figure 2. IDIBT: forward steps Figure 2 represents possible forwards steps for the problem of figure 1. Since children share a constraint relation, IDIBT is closer to forward checking search (FC) [8] than to classical backtracking. Here the direct peers connections allow the receiver to prune its subspace according to incoming choices. That is what sequential FC make pro actively between successive instantiations. 3.2.2 Backtrack steps When an agent is unable to perform the first step of a ....

R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. AI, 14:263--314, 1980.

....this algorithm was removed from the solver system. Node consistency and Regin s mutex filtering algorithm are the two stand alone constraint propagation algorithms that we ve implemented and used in this system. Other methods for constraint propagation that we have tested are forward checking [6], and forward checking for non binary constraints [2] These methods are used during search; they will be covered in the next section. 4.2 Solution techniques We utilize systematic search techniques based on depth first search to solve the GTA assignment problem. In order to cope with the ....

Robert M. Haralick and Gordon L. Elliott. Increasing Tree Search Efficiency for Constraint Satisfaction Problems. Artificial Intelligence, 14:263--313, 1980.

....works in the literature of graph matching, where graphs do not have attribute descriptors (labels) for vertices or arcs. This problem has been studied for over 30 years [19] Various state space search approaches were reported including exact subgraph isomorphism [20] and heuristic techniques [21]. Domain specific heuristic methods have been neglected in the literature for a period due to the development of modern metaheuristic methods [22] such as simulated annealing [23] genetic algorithms [24] and memetic algorithms [25] In [22] Williams and Wilson implement a heuristic method for ....

Haralick, R.M., and Elliott, G., `Increasing tree search efficiency for constraint satisfaction problems', Artificial Intelligence, 14, 263-313, (1980).

....constraint networks. The generic backtracking algorithm was first described more than a century ago, and since then has been rediscovered many times It] In recent years, many new backtracking algorithms have been proposed. The basic ones include Backmarking [3] Backjumping [4] Forward Checking [5], and Conflict Directed Backjumping It0] Several hybrid algorithms, which combine two or more basic algorithms, have also been developed It0] There is no simple answer to the question which backtracking algorithm is the best one. First, the performance of backtracking algorithms depends heavily ....

....variable xi, CBJ backtracks to the highest variable xn in the conflict set of xi. At the same time, the conflict set of xi is absorbed by the conflict set of xn, so that no information about conflicts is lost. In contrast with the above backward checking al gorithms, Forward Checking (FC) [5] performs con sistency checks forward, that is, between the current variable and the future variables. After the current variable has been instantJared, the domains of the future variables are filtered in such a way that all values inconsistent with the current instantiation are removed. If none ....

R. M. Haralick and G. L. Elliot. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263-314, 1980.

....provides a default backtracking search method for solving CSPs. If necessary, new constraint classes and search algorithms can be defined, but these facilities were not required in this case. The default search algorithm is an implementation of full lookahead, as described by Haralick and Elliott [2]. The algorithm repeatedly chooses an unassigned variable, chooses a value for that variable from its current domain and makes a tentative assignment. The constraints are then used to identify the effects of the assignment on future (still unassigned) variables, and any value in the domain of a ....

R. Haralick and G. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....is called the labeling problem. Constraints on these nodes allow one to discard some of these interpretations. The labeling problem includes the graph coloring problem and therefore is NP hard [Garey et al. 1974] Consistency algorithms arose from a backtracking technique called forward checking [Haralick and Elliot, 1980] that prunes the search tree of nodes based upon incompatibility with the partial labeling constructed so far. Consistency algorithms go one step further in removing incompatible future labelings. These inconsistencies would have otherwise been discovered repeatedly by most backtracking ....

....also called discrete relaxation algorithms, were first introduced by Waltz for interpreting polyhedral scenes with shadows [Waltz, 1975] posed as a labeling problem. Traditional techniques for constraint satisfaction include chronological backtracking and backtracking with forward checking [ Haralick and Elliot, 1980] The latter prunes the search tree of nodes based upon incompatibility with the partial labeling constructed so far. Consistency algorithms go one step further in removing incompatible future labelings. These incompatible labelings would have otherwise been discovered repeatedly by most ....

R.M. Haralick and G.L. Elliot. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....intelligence, such as subgraph isomorphism and homomorphism [3] 4] graph coloring [4] school timetabling [2] theorem proving [1] puzzle solving [1] 2] scene labeling [5] line drawing understanding [6] 3D object matching [7] 8] remote sensing [9] 10] etc. Haralick and Elliott [11] proposed some efficient algorithms for finding consistent labelings and McCall et al. [12] and Ullmann [2] considered the computer architectures for solving the CLP. In recent years, some researchers attempted to solve the problems similar to the CLP using neural networks [13] 15] In this paper ....

R. M. Haralick and L. Elliott, "Increasing tree search efficiency for constraint satisfaction problems", Artificial Intelligence, Vol.14, pp. 263-313, (1980)

....the consistency of the assignments generated. The proposed algorithms differ in the heuristics adopted for performing the first step. On the ground of a theoretical analysis and experimental evaluations conducted using variously generated random tests they concluded that forward checking [ Haralick and Elliott, 1980 ] gives the best performance. The forward checking heuristics amounts to valuating to false (and hence eliminating from the problem at hand) each disjunct whose negation is entailed by the assignment generated so far. In the following, we use SK to denote Stergiou and Koubarakis s procedure ....

R. M. Haralick and G. L. Elliott. Increasing Tree Search Efficiency for Constraint Satisfaction Problems. Acta Informatica, 14:263--313, 1980.

....heuristics. As the number of variables increases, the time required to solve the problem grows exponentially. However, since the rate of growing decreases by using dynamic variable ordering, it is better for large scale problems. This is well known by studies of constraint satisfaction problems [20]. In this section, we first describe the outline of an algorithm with dynamic variable ordering heuristics, then explain how to implement such an algorithm on FPGAs, and finally describe two dynamic variable ordering heuristics (EUP heuristic and MOMs heuristic) A. Outline of the Algorithm The ....

R. M. Haralick and G. L. Elliot, "Increasing tree search efficiency for constraint satisfaction problems," Artificial Intelligence, vol. 14, pp. 263--313, 1980.

....algorithms that maintain a local consistency property at each node in their search tree. Various types of local consistency have been defined, and algorithms developed for enforcing them (e. g, 5, 13, 14] Algorithms that maintain a local consistency property during backtracking search (e.g. [8, 10, 15, 16, 20]) can detect dead ends sooner and thus have the potential of significantly reducing the size of the tree they have to search. Such algorithms have demonstrated significant empirical advantages and are the algorithms of choice in practice. Hence, they are the most relevant objects of study. We ....

....empty after enforcing the local consistency, the instantiation of the current variable cannot be extended to a solution and it should be uninstantiated; otherwise, the instantiation of the current variable is accepted and the search continues to the next level. The forward checking algorithm (FC) [10, 15, 25] enforces arc consistency only on the constraints which have exactly one uninstantiated variable. By comparison, on a problem that is not empty after enforcing arc consistency, the maintaining arc consistency or really full lookahead algorithms [8, 16, 20] as their names suggest, enforce full arc ....

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R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....algorithms that maintain a local consistency property at each node in their search tree. Various types of local consistency have been defined, and algorithms developed for enforcing them (e. g, 5, 13, 14] Algorithms that maintain a local consistency property during backtracking search (e.g. [8, 10, 15, 16, 20]) can detect dead ends sooner and thus have the potential of significantly reducing the size of the tree they have to search. Such algorithms have demonstrated significant empirical advantages and are the algorithms of choice in practice. Hence, they are the most relevant objects of study. We ....

....empty after enforcing the local consistency, the instantiation of the current variable cannot be extended to a solution and it should be uninstantiated; otherwise, the instantiation of the current variable is accepted and the search continues to the next level. The forward checking algorithm (FC) [10, 15, 25] enforces arc consistency only on the constraints which have exactly one uninstantiated variable. By comparison, on a problem that is not empty after enforcing arc consistency, the maintaining arc consistency or really full lookahead algorithms [8, 16, 20] as their names suggest, enforce full arc ....

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R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....problem [10, 11] As we have shown in [16] constraint logic programming over finite domains CLP(FD) 25, 13] has proved to be an appropriate platform for representing the different models and performing the search. The application of consistency techniques (forward checking and look ahead) [17, 9, 18] provided an acceptable efficiency. Applied constraints. For the task of building recognition we employ four different types of constraints. Fig. 1 shows the geometric constraints and fig. 2 the topological constraints. P 1 P 2 P 3 P 4 P 5 P 6 L 1 L 2 L 4 L 5 L 6 L 7 1 F F 2 L 3 ....

R. M. Haralick and G. L. Elliott. Increasing Tree Search Efficiency for Constraint Satisfaction Problems. Artificial Intelligence, 14:263--313, 1980.

....Finding the subset of node combinations that is consistent with the input query can be treated as a local CSP at each level in order to avoid exhaustive search. Similarly to WR, ST can be applied with a variety of search algorithms and optimization techniques. Here we employ forward checking (FC) [16], a backtracking based algorithm which prunes the domain of future variables based on the current instantiations. Several studies [2] 31] have shown that it performs very well for a variety of CSPs. Furthermore, we combine FC with a space restriction ordering heuristic that minimizes the number ....

Haralick, R.M., Elliott, G.L. Increasing Tree Search Efficiency for Constraint Satisfaction Problems. Artificial Intelligence, 14: 263--313, 1980.

....On the other hand, iterative improvement algorithms do not construct a consistent partial solution and can revise a bad decision without exhaustive search. However, most of the powerful heuristics obtained through the long history of constraint satisfaction studies (e.g. forward checking (Haralick Elliot 1980)) presuppose the existence of a consistent partial solution. Therefore, these heuristics can not be applied to iterative improvement algorithms. Furthermore, these algorithms are not theoretically complete. In this paper, a new algorithm called weakcommitment search which utilizes the ....

....is difficult. The completeness of the algorithms may have only theoretical importance when solving large scale problems. A more practical drawback is that we can not apply most of the powerful heuristics obtained through the long history of constraint satisfaction studies (e.g. forward checking (Haralick Elliot 1980)) to iterative improvement algorithms, since these heuristics presuppose the existence of a consistent partial solution. In this paper, a new algorithm called weakcommitment search which utilizes the min conflict heuristic is developed. In this algorithm, all variables are given tentative ....

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Haralick, R., and Elliot, G. L. 1980. Increasing tree search efficiency for constraint satisfaction problems.

....all variable values are determined simultaneously, and all constraints are checked concurrently.Multiple variable values can be changed simultaneously when some constraints are not satisfied. In order to prune the search space, this algorithm introduces a technique similar to forwardchecking [8]. Simulation results show that the order of the search tree size in this algorithm is approximately the same as that in the Davis Putnam procedure [5] which is widely used as a complete search algorithm for solving SAT problems. Then, we show how the parallel checking algorithm can be ....

....digit in C 2 is x 3 , while the second lowest digit in C 3 is x 2 . Therefore, we can conclude that at least x 3 s digit must be changed to satisfy all clauses; changing digits lower than x 3 is useless. This procedure is similar to the backtracking algorithm that introduces forwardchecking [8], where backtracking is performed immediately after some variable has no consistent value with the variables that have already assigned their values. Introducing Forward Checking (ii) Another procedure that greatly contributes to the efficiency of forward checking is to assign the variable value ....

Haralick, R. and Elliot, G. L.: Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence,Vol. 14, (1980) 263--313

....and free means the frequency is available at the cell. Weshow the outline of the basic algorithm in Figure 3. In the initial state, all vector elements of a cell are free, and stack is empty. This algorithm is basically a depth first branch and bound algorithm that incorporates forward checking [9]. Therefore, as long as the cell ordering heuristic and the frequencyordering heuristic are exhaustive, this algorithm can eventually find an optimal solution. The worst case time complexityisO(M S init ) where M init is the initial upper bound of frequencies, and S = P N i=1 d i . B. ....

Haralick, R. and Elliot, G. L.: Increasing Tree Search Efficiency for Constraint Satisfaction Problems, Artificial Intelligence,Vol. 14, (1980) 263--313

....next variable, 7 variables that maximally constrain the rest of the search space are usually preferred, and therefore, the most highly constrained variable is selected. For value selection, instead, the least constraining value is preferred, in order to maximize future options for instantiations [6]. A well known look ahead method is forward checking, which performs a limited form of arc consistency at each step, ruling out some values that would lead to a dead end. Currently, a popular form of look ahead scheme, called MAC (for Maintaining Arc Consistency) performs arc consistency at each ....

M. Haralick and G. L. Elliot. Increasing tree-search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....such that only values (queen locations) that do not attack each other are accepted. For instance, if variable 1 is assigned the value B, then the constraint between variable 1 and 2 would allow only values D, E, and F to be assigned to variable 2. One type of propagation is forward checking [10]. At each point in the search the forward checking propagator examines constraints in which only one variable in the constraint s scheme has not been instantiated. All of this variable s domain values 34 E F A C B D Q Q Q Q Q Q 3 5 4 2 1 6 Figure 4.1: 6 queens solution 3 Q Q Q 1 ....

R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....and Morgan Kaufmann Publishers. All rights reserved. Debruyne Bessi ere Search algorithms differ in the kind of local consistency they achieve after each choice of a value for a variable. Most of them enforce partial arc consistency, going from forward checking (FC,Golomb Baumert, 1965; Haralick Elliott, 1980), which only removes the values directly arc inconsistent with the last assignment, to really full look ahead (RFL, Gaschnig, 1974) which achieves full arc consistency. Arc consistency (AC) and partial forms of arc consistency are widely used for two reasons. First, they have low space and time ....

Haralick, R., & Elliott, G. (1980). Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14, 263--313.

....hundreds of random problems were created, each with 20 to 70 variables, with 10, 20 or 30 values each. Each problem was created to be close to the phase transition region for its problem size. We compared the pAC heuristic to several well studied variable ordering heuristics Brelaz, FF, FFdeg, [1, 4] as well as a random selection criterion. The constructive search procedure was a highly optimized forwardchecking back jumping search algorithm [11] and each of the heuristics was employed using this search procedure. We observed that the pAC heuristic required one to three orders of magnitude ....

Richard M. Haralick and Gordon L. Elliot. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14(3):263--313, 1980.

....value to give to the current variable, and reduce the search space by maintaining a certain level of local consistency during the search (e.g. Bacchus van Run, 1995; Bessi ere R egin, 1996; c fl2001 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved. Chen van Beek Haralick Elliott, 1980; McGregor, 1979; Nadel, 1989; Sabin Freuder, 1994) Lookback schemes are invoked whenever the algorithm encounters a dead end and prepares for the backtracking step. Look back schemes include the functions that decide how far to backtrack by analyzing the reasons for the dead end (backjumping) ....

.... and to the development of algorithms for achieving these levels of consistency by removing inconsistencies (e.g. Mackworth, 1977a; Montanari, 1974) and to effective backtracking algorithms for finding solutions to CSPs that maintain a level of consistency during the search (e.g. Gaschnig, 1978; Haralick Elliott, 1980; McGregor, 1979; Sabin Freuder, 1994) Mackworth (1977a) defines three properties of binary CSPs that characterize local consistencies: node, arc, and path consistency. Mackworth (1977b) generalizes arc consistency to non binary CSPs. Definition 4 (arc consistency) Given a constraint C and a ....

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Haralick, R. M., & Elliott, G. L. (1980). Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14, 263--313.

....in constraint satisfaction problems. This information can be used as a heuristic to guide constructive search algorithms: for a given variable, choose the value which appears in the most solutions. Similar proposals for counting solutions or estimating solution probabilities have been made [6, 14, 4, 11, 16, 15]. Solution probabilities are orthogonal to preference over solutions (e.g. 3, 1] or probabilistic constraints (e.g. 1] in which there is uncertainty regarding whether a constraint applies. The main purpose of this paper is to document a connection between constraint reasoning and ....

....approximate solution probabilities computed by pAC when used as a dynamic variable and value ordering heuristic, i.e. after each assignment, the solution probabilities were recomputed. We found that the reduction in search costs is dramatic, up to two orders of magnitude smaller than First Fail [6] or Least Constrained [2] The price for this success is the cost of computing the heuristic values: even for relatively large ffl, say ffl = 0:1, and few iterations, e.g. MaxIter= 50, the cost of performing all the floating point operations is such that search requires almost an order of ....

Richard M. Haralick and Gordon L. Elliot. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14(3):263--313, 1980.

....influence the efficiency of the constraint solving when only one solution to the problem is required. It has little effect when the search is for all solutions. In this study, we considered two labelings, the naive labeling and the first fail labeling. The first fail labeling uses a principle [11] which says that to succeed, try first where you are the most likely to fail. This principle recommends the choice of the most constrained variable which (for the finite domain) means choosing a variable with the smallest domain. Further refinements commonly used in first fail labeling consist of ....

HARALICK r. and ELLIOT G. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263-313, 1980.

....and special characteristics. 2.5.1 Forward Checking Since RestartRepair LbM progressively extends a consistent partial labelling, viz. VarsDone, it is possible to incorporate look ahead techniques into the algorithm. One of the simplest and most successful of these is forward checking [Haralick Elliott, 1980; Nadel, 1989; Tsang, 1993] This has been widely used in backtrack search, and has also been implemented more recently in restart search [Yokoo, 1994] We follow this trend and enhance RestartRepair LbM with forward checking. The implementation is slightly ## more complicated than that required ....

R. Haralick and G. Elliott, Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence, 1980

....problem. Any scheduling problem with finite domains, and in fact any satisficing NPcomplete problem over finite domains, can be stated as a CSP. The value of the CSP framework is that heuristics and consistency methods have been studied thoroughly and can be leveraged for the scheduling problem (Haralick Elliott 1980; Prosser 1993; Kondrak van Beek 1997; Bacchus van Run 1997) 3.4 Demand Profiles Demand profiles rapidly identify the hard part of a scheduling problem. Define the demand function of an operation on a machine D o m (t) as the probability that operation o uses machine m at time t. Demand ....

....will have hard parts, or bottlenecks. 7.1 Heuristics for Start Time Assignments Sadeh Fox start from the realization that once a schedule length is imposed, finding any valid assignment of start times to operations is a CSP. They leverage generic CSP consistency methods like forward checking (Haralick Elliott 1980) that are well understood and extremely helpful in basic backtracking search. They try generic domain independent heuristics, but find them lacking. So they develop new heuristics tailored to scheduling to choose a good refinement. There are two decision points in global search for start time ....

Haralick, R. M., and Elliott, G. L. 1980. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14:263--313.

....nodes are also counted as consistency checks. Hierarchical Systematic Search We first compare hierarchical and flat versions of systematic search through the whole solution space. In the following experiments we use forward checking (FC) with the fail first dynamic variable ordering heuristic (Haralick and Elliott 1980), because of its efficiency and relatively simple implementation. For the first experiment, a series of problem ensembles was generated. An ensemble contains 50 random problems with complete constraint graphs (cliques) i.e. p 1 =1, and the same average constraint tightness. The number of ....

Haralick, R., Elliott, G. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14(3): 263-313, 1980.

....a significant amount of time to find them. The above datasets cover a wide range of cardinality values, data densities and distributions; thus they provide a good estimation for the performance of the algorithms on other domains. As a benchmark for systematic search we used forward checking (FC) [18], because it is considered one of the most effective algorithms for general CSP problems [4] as well as for structural queries [26] 27] The current implementation of FC works in a branch and bound manner: i) in case the user inputs a target similarity to be retrieved, instantiations are ....

Haralick R.M., Elliot G.L. "Increasing Tree Search Efficiency for Constraint Satisfaction Problems". Artificial Intelligence, vol. 14, pp. 263-313, 1980.

....2 All of the improvements to backtracking the author is aware or can be view this way. Of course, we do not have enough space (and the reader probably does not have enough patience) to demonstrate this for all of these algorithms. 3 Since constraint propagating algorithms like forward checking [7] and MAC [8] maintain a certain degree of consistency all the consistencies that can be discovered must involve the full set of assignments CurAsgns: all subsets of CurAsgns are already know to be consistencies for all unpruned future values. 4 Given that the algorithm is complete, as most ....

R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

....temporarily pruned from the domains of those variables, and restored when the search backtracks and 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 is known to be inconsistent it is easy to prune it (e.g. it can be delinked from a linked list ....

....3g and the constraint A B. Further, say that along the current path of the search tree we instantiate A at level 5, that the value 3 of A has already been pruned by a prior assignment at level 1, and that no other values of A have been pruned. Hence at level 5 CurDom[A] f1; 2g, 3 2 PrunedVals[1], and 3:prlevel = 1. Say that we next make the assignment A 1, and then forward check the unassigned variables. When we forward check B we find that its values 2 and 3 are both inconsistent with A 1. Forward checking would prune both of these values to level 5. However, closer examination shows ....

R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

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Haralick, R., Elliott, G.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14 (1980) 263--313

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Robert M. Haralick and Gordon L. Elliot. Increasing Tree Search Efficiency for Constraint Satisfaction Problems. Artificial Intelligence, 14(3):263--313, 1980.

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Haralick, R.M., and Elliott, G.L., Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence , Vol14, 263-313, 1980

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Haralick, R. & Elliot, G. (1980). Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14: 263--313.

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R.M. Haralick and G.L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14(3):263--313, 1980.

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Haralick, R.M., Elliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14 (1980) 263--314

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R. M. Haralick and G. L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

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R. M. Haralick and G. L. Elliot, `Increasing tree search efficiency for constraint satisfaction problems', Artif. Intell., 14, 263--314, (1980).

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R.M. Haralick and G.L. Elliott, Increasing Tree Search Efficiency for Constraint Satisfaction Problems, Artif. Intell. 14 (1980) 263-313

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R. Haralick, G. Elliot, Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence 14 (1980) 263--313.

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Haralick, R.M. and Elliot, G.L. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263--313, 1980.

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R.M. Haralick and G.L. Elliott, Increasing Tree Search Efficiency for Constraint Satisfaction Problems, Artif. Intell. 14 (1980) 263-313.

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R.M. Haralick and G.L. Elliott. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14(3):263--313, 1980.

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R. Haralick and G. Elliot. Increasing tree search efficiency for constraint satisfaction. Journal of Artificial Intelligence, 14:263--313, 1980.

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R. Haralick and G. Elliot. Increasing tree search efficiency for constraint satisfaction. Journal of Artificial Intelligence, 14:263--313, 1980.

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R. M. Haralick and G. L. Elliot, `Increasing tree search efficiency for constraint satisfaction problems', Artificial Intelligence, 14, 263--313 (1980).

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R. M. Haralick, etc., Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, Vol.14, (1980) pp.263-313.

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R.M. Haralick and G.L. Elliott. Increasing tree search efficiency for Constraint Satisfaction Problems. Artificial Intelligence, 14:263--313, 1980.

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