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Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(∗,m)C, which is equivalent to m-wise consistency proposed in relational databases. We also define wR(∗,m)C, a weaker variant of this property. We propose an algorithm for enforcing… (More)

Freuder and Elfe (1996) introduced Neighborhood Inverse Consistency (NIC) as a strong local consistency property for binary CSPs. While enforcing NIC can significantly filter the variables domains, the proposed algorithm is too costly to be used on dense graphs or for lookahead during search. In this paper, we introduce and characterize Relational… (More)

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research… (More)

The tractability of a Constraint Satisfaction Problem (CSP) is guaranteed by a direct relationship between its consistency level and a structural parameter of its constraint network such as the treewidth. This result is not widely exploited in practice because enforcing higher-level consistencies can be costly and can change the structure of the constraint… (More)

Computing the minimal network of a Constraint Satisfaction Problem (CSP) is a useful and difficult task. Two algorithms, PerTuple and AllSol, were proposed to this end. The performances of these algorithms vary with the problem instance. We use Machine Learning techniques to build a classifier that predicts which of the two algorithms is likely to be more… (More)

Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems (CSPs). As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational… (More)

One fundamental research result in the area of Constraint Processing (CP) is a condition that guarantees problem tractability by relating the consistency level of a Constraint Satisfaction Problem (CSP) to the structure of the problem. In our research, we propose to build effective problem-solving strategies that exploit the above-mentioned result in… (More)

The minimal constraint network of a constraint satisfaction problem (CSP) is a compiled version of the problem where every tuple in a constraint’s relation appears in at least one solution to the CSP. Recently, Gottlob argued that, when a CSP has this property, a number of NP-hard queries can be answered in polynomial time, but he also showed that deciding… (More)

Determining the appropriate level of local consistency to enforce on a given instance of a Constraint Satisfaction Problem (CSP) is not an easy task. However, selecting the right level may determine our ability to solve the problem. Adaptive parameterized consistency was recently proposed for binary CSPs as a strategy to dynamically select one of two local… (More)

Relational consistency algorithms are instrumental for solving difficult instances of Constraint Satisfaction Problems (CSPs), often allowing backtrack-free search. In this paper, we improve an algorithm for enforcing relational consistency by exploiting the property that the constraints of the dual encoding of a CSP are piecewise functional. This property… (More)