A Framework for Decision-based Consistencies

International audienceConsistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (general- ized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S∆φ, E∆φ, B∆φ and D∆φ, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this gen- eral framework provides us with a better insight into decision-based con- sistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones

Four particle cluster approximation for the Maier-Saupe model of the isotropic-nematic phase transition

The cluster variation theory for the Maier-Saupe model of the isotropic-nematic phase transition is extended to the four-particle level. As in the case of the Heisenberg ferromagnet, the irregularities of the three-particle cluster approximation applied to cubic lattices, where there are no triangles of nearest neighbors, disappear. The extension from three- to four-particle clusters yields improved values of all quantities, characteristic for the phase transition

Kaon photoproduction: background contributions, form factors and missing resonances

The photoproduction p(gamma, K+)Lambda process is studied within a field-theoretic approach. It is shown that the background contributions constitute an important part of the reaction dynamics. We compare predictions obtained with three plausible techniques for dealing with these background contributions. It appears that the extracted resonance parameters drastically depend on the applied technique. We investigate the implications of the corrections to the functional form of the hadronic form factor in the contact term, recently suggested by Davidson and Workman (Phys. Rev. C 63, 025210). The role of background contributions and hadronic form factors for the identification of the quantum numbers of ``missing'' resonances is discussed.Comment: 11 pages, 7 eps figures, submitted to Phys. Rev.

Interactively solving school timetabling problems using extensions of constraint programming

Timetabling problems have been frequently studied due to their wide range of applications. However, they are often solved manually because of the lack of appropriate computer tools. Although many approaches mainly based on local search or constraint programming seem to have been quite successful in recent years, they are often highly dedicated to specific problems and encounter difficulties to take the dynamic and over-constrained nature of such problems. We were confronted with such an over-constrained and dynamic problem in our institution. This paper deals with a timetabling system based on constraint programming with the use of explanations to offer a dynamic behaviour and to allow automatic relaxations of constraints. Our tool has successfully answered the needs of the current planner by providing solutions in a few minutes instead of a week of manual design.We present in this paper the techniques used, the results obtained and a discussion on the effects of the automation of the timetabling process

Domain k-Wise Consistency Made as Simple as Generalized Arc Consistency

Abstract. In Constraint Programming (CP), Generalized Arc Consistency (GAC) is the central property used for making inferences when solving Constraint Satisfaction Problems (CSPs). Developing simple and practical filtering algorithms based on consistencies stronger than GAC is a challenge for the CP community. In this paper, we propose to combine k-Wise Consistency (kWC) with GAC, where kWC states that every tuple in a constraint can be extended to every set of k − 1 additional constraints. Our contribution is as follows. First, we derive a domain-filtering consistency, called Domain k-Wise Consistency (DkWC), from the combination of kWC and GAC. Roughly speaking, this property corresponds to the pruning of values of GAC, when enforced on a CSP previously made kWC. Second, we propose a procedure to enforce DkWC, relying on an encoding of kWC to generate a modified CSP called k-interleaved CSP. Formally, we prove that enforcing GAC on the k-interleaved CSP corresponds to enforcing DkWC on the initial CSP. Consequently, we show that the strong DkWC can be enforced very easily in constraint solvers since the k-interleaved CSP is rather immediate to generate and only existing GAC propagators are required: in a nutshell, DkWC is made as simple and practical as GAC. Our experimental results show the benefits of our approach on a variety of benchmarks.

Global Inverse Consistency for Interactive Constraint Satisfaction

International audienceSome applications require the interactive resolution of a constraint problem by a human user. In such cases, it is highly desirable that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We call this property global inverse consistency. Existing systems simulate this either by maintaining arc consistency after each assignment performed by the user or by compiling offline the problem as a multi-valued decision diagram. In this paper, we define several questions related to global inverse consistency and analyse their complexity. Despite their theoretical intractability, we propose several algorithms for enforcing global inverse consistency and we show that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. We finally extend our contribution to the inverse consistency of tuples