James E. Borrett

Adaptive Constraint Satisfaction: The Quickest First Principle

The choice of a particular algorithm for solving a given class of constraint satisfaction problems is often confused by exceptional behaviour of algorithms. One method of reducing the impact of this exceptional behaviour is to adopt an adaptive philosophy to constraint satisfaction problem solving. In this report we describe one such adaptive algorithm, based on the principle of chaining. It is designed to avoid the phenomenon of exceptionally hard problem instances. Our algorithm shows how the speed of more naive algorithms can be utilised safe in the knowledge that the exceptional behaviour can be bounded. Our work clearly demonstrates the potential benefits of the adaptive approach and opens a new front of research for the constraint satisfaction community.

A Context for Constraint Satisfaction Problem Formulation Selection

Much research effort has been applied to finding effective ways for solving constraint satisfaction problems. However, the most fundamental aspect of constraint satisfaction problem solving, problem formulation, has received much less attention. This is important because the selection of an appropriate formulation can have dramatic effects on the efficiency of any constraint satisfaction problem solving algorithm.In this paper, we address the issue of problem formulation. We identify the heuristic nature of generating a good formulation and we propose a context for this process. Our work presents the research community with a focus for the many elements which affect problem formulation and this is illustrated with the example adding redundant constraints. It also provides a significant step towards the goal of automatic selection of problem formulations.

Predicting Phase Transitions of Binary Constraint Satisfaction Problems with Constraint Graph Information

Constraint satisfaction is at the core of many applications, such as scheduling. The study of phase transition has benefited algorithm selection and algorithm development in constraint satisfaction. Recent research provides evidence that constraint graph topology affects where phase transitions occur in constraint satisfaction problems. In this article, a new phase transition predictor which takes constraint graph information into consideration is proposed. The new predictor allows variation in the tightness of individual constraints and node degree variation in constraint graph. Experiments were conducted to study the usefulness of the new predictor on random binary constraint satisfaction problems. Results show that the new predictor is able to produce predictions as good as the state-of-the-art predictor in general, but do considerably better in sparsely constrained problems, particularly when the node degree variation in their constraint graphs is high.