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12
ArcConsistency and ArcConsistency Again
 Artificial Intelligence
, 1994
"... Constraint networks are known as a useful way to formulate problems such as design, scene labeling, temporal reasoning, and more recently natural language parsing. The problem of the existence of solutions in a constraint network is NPcomplete. Hence, consistency techniques have been widely studied ..."
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Cited by 136 (11 self)
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Constraint networks are known as a useful way to formulate problems such as design, scene labeling, temporal reasoning, and more recently natural language parsing. The problem of the existence of solutions in a constraint network is NPcomplete. Hence, consistency techniques have been widely studied to simplify constraint networks before or during the search of solutions. Arcconsistency is the most used of them. Mohr and Henderson [Moh&Hen86] have proposed AC4, an algorithm having an optimal worstcase time complexity. But it has two drawbacks: its space complexity and its average time complexity. In problems with many solutions, where the size of the constraints is large, these drawbacks become so important that users often replace AC4 by AC3 [Mac&Fre85], a nonoptimal algorithm. In this paper, we propose a new algorithm, AC6, which keeps the optimal worstcase time complexity of AC4 while working out the drawback of space complexity. More, the average time complexity of AC6 is optimal for constraint networks where nothing is known about the semantic of the constraints. At the end of the paper, experimental results show how much AC6 outperforms AC3 and AC4. 1.
Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 51 (3 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems
 In Proceedings of the Second International Conference on Principles and Practice of Constraint Programming
, 1996
"... . In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often le ..."
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Cited by 40 (3 self)
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. In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often led us to consider FC or FCCBJ associated with a "minimum domain" variable ordering heuristic as the best techniques to solve a wide variety of constraint networks. In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks. 1 Introducti...
Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems
 CONSTRAINTS
, 2002
"... There are two main solving schemas for constraint satisfaction and optimization problems: i) search, whose basic step is branching over the values of a variables, and ii) dynamic programming, whose basic step is variable elimination. Variable elimination is time and space exponential in a graph para ..."
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Cited by 22 (6 self)
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There are two main solving schemas for constraint satisfaction and optimization problems: i) search, whose basic step is branching over the values of a variables, and ii) dynamic programming, whose basic step is variable elimination. Variable elimination is time and space exponential in a graph parameter called induced width, which renders the approach infeasible for many problem classes. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be e#ectively combined with search, because the elimination of variables may reduce drastically the search tree size. In this
Boosting Search with Variable Elimination
, 2000
"... Variable elimination is the basic step of Adaptive Consistency [4]. It transforms the problem into an equivalent one, having one less variable. Unfortunately, there are many classes of problems for which it is infeasible, due to its exponential space and time complexity. However, by restricting ..."
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Cited by 16 (1 self)
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Variable elimination is the basic step of Adaptive Consistency [4]. It transforms the problem into an equivalent one, having one less variable. Unfortunately, there are many classes of problems for which it is infeasible, due to its exponential space and time complexity. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables, reduces the search tree size. In this paper
Blocksolve: a BottomUp Approach for Solving Quantified CSPs
 In Proceedings of CP2006
, 2006
"... Abstract. Thanks to its extended expressiveness, the quantified constraint satisfaction problem (QCSP) can be used to model problems that are difficult to express in the standard CSP formalism. This is only recently that the constraint community got interested in QCSP and proposed algorithms to solv ..."
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Cited by 8 (0 self)
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Abstract. Thanks to its extended expressiveness, the quantified constraint satisfaction problem (QCSP) can be used to model problems that are difficult to express in the standard CSP formalism. This is only recently that the constraint community got interested in QCSP and proposed algorithms to solve it. In this paper we propose BlockSolve, an algorithm for solving QCSPs that factorizes computations made in branches of the search tree. Instead of following the order of the variables in the quantification sequence, our technique searches for combinations of values for existential variables at the bottom of the tree that will work for (several) values of universal variables earlier in the sequence. An experimental study shows the good performance of BlockSolve compared to a state of the art QCSP solver. 1
Measuring Search Trees
 Proceedings ECAI’04 Workshop on Modelling and Solving Problems with Constraints
, 2004
"... The SAT and CSP communities make a great use of search effort comparisons to assess the validity of an algorithm or a heuristic. There exist different ways... ..."
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Cited by 6 (0 self)
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The SAT and CSP communities make a great use of search effort comparisons to assess the validity of an algorithm or a heuristic. There exist different ways...
A Simple Way to Improve Path Consistency Processing in Interval Algebra Networks
, 1996
"... Reasoning about qualitative temporal information is essential in many artificial intelligence problems. In particular, many tasks can be solved using the intervalbased temporal algebra introduced by Allen (All83). In this framework, one of the main tasks is to compute the transitive closure of a ne ..."
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Cited by 4 (0 self)
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Reasoning about qualitative temporal information is essential in many artificial intelligence problems. In particular, many tasks can be solved using the intervalbased temporal algebra introduced by Allen (All83). In this framework, one of the main tasks is to compute the transitive closure of a network of relations between intervals (also called path consistency in a CSPlike terminology). Almost all previous path consistency algorithms proposed in the temporal reasoning literature were based on the constraint reasoning algorithms PC1 and PC2 (Mac77). In this paper, we first show that the most efficient of these algorithms is the one which stays the closest to PC2. Afterwards, we propose a new algorithm, using the idea "one support is sufficient" (as AC3 (Mac77) does for arc consistency in constraint networks). Actually, to apply this idea, we simply changed the way compositionintersection of relations was achieved during the path consistency process in previous algorithms. Intr...
Dynamic Combination of Search and Variable Elimination in CSP and MaxCSP
"... Variable elimination is the basic step of Adaptive Consistency [8]. It transforms the problem into an equivalent one, having one less variable. Unfortunately, there are many classes of problems for which it is infeasible, due to its exponential space and time complexity. However, by restricting va ..."
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Cited by 1 (1 self)
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Variable elimination is the basic step of Adaptive Consistency [8]. It transforms the problem into an equivalent one, having one less variable. Unfortunately, there are many classes of problems for which it is infeasible, due to its exponential space and time complexity. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables, reduces the search tree size. In this paper we introduce VarElimSearch(S;k), a hybrid metaalgorithm that combines search and variable elimination. The parameter S names the particular search procedure and k controls the tradeoff between the two strategies. The algorithm is space exponential in k. Regarding time, we show that its complexity is bounded by k and a structural parameter from the constraint graph. We also provide experimental evidence that the hybrid algorithm can outperform stateoftheart algorithms in binary sparse problems. Experiments cover the tasks of finding one solution
Using the Symmetry of Relations to Establish ArcConsistency in Constraint Networks
"... In [1, 2], Bessière and Cordier said that the AC6 arcconsistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are symmetric. None of the previous algorithms achievin ..."
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In [1, 2], Bessière and Cordier said that the AC6 arcconsistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are symmetric. None of the previous algorithms achieving arcconsistency (AC3 [5, 6], AC4 [7], AC6) use this property. We propose here an improved version of AC6 (the best algorithm for arcconsistency) which uses this property. Then, we claim that our new algorithm is optimal in the number of constraint checks performed. 1. Introduction In the last five years, the number of applications using constraint networks 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 reallife applications using constraint networks are limited to a forwardchecking search procedure [4], or use an arcconsistency filtering a...