An Efficient Consistency Algorithm for the Temporal Constraint Satisfaction Problem

Dechter et al. [5] proposed solving the Temporal Constraint Satisfaction Problem (TCSP) by modeling it as a meta-CSP, which is a finite CSP with a unique global constraint. The size of this global constraint is exponential in the number of time points in the original TCSP, and generalized-arc consistency is equivalent to finding the minimal network of the TCSP, which is NP-hard. We introduce _AC, an efficient consistency algorithm for filtering the meta-CSP. This algorithm significantly reduces the domains of the variables of the meta-CSP without guaranteeing arc-consistency. We use _AC as a preprocessing step to solving the meta-CSP. We show experimentally that it dramatically reduces the size of a meta-CSP and significantly enhances the performance of search for finding the minimal network of the corresponding TCS

An Efficient Consistency Algorithm for the Temporal Constraint Satisfaction Problem

Dechter et al. [5] proposed solving the Temporal Constraint Satisfaction Problem (TCSP) by modeling it as a meta-CSP, which is a finite CSP with a unique global constraint. The size of this global constraint is exponential in the number of time points in the original TCSP, and generalized-arc consistency is equivalent to finding the minimal network of the TCSP, which is NP-hard. We introduce _AC, an efficient consistency algorithm for filtering the meta-CSP. This algorithm significantly reduces the domains of the variables of the meta-CSP without guaranteeing arc-consistency. We use _AC as a preprocessing step to solving the meta-CSP. We show experimentally that it dramatically reduces the size of a meta-CSP and significantly enhances the performance of search for finding the minimal network of the corresponding TCS

Constraint Programming viewed as Rule-based Programming

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling.We consider here two types of rules. The first type, that we call equality rules, leads to a new notion of local consistency, called {\em rule consistency} that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in \cite{MS98b}). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming we show how both types of rules can be automatically generated, as {\tt CHR} rules of \cite{fruhwirth-constraint-95}. This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.Comment: 39 pages. To appear in Theory and Practice of Logic Programming Journa