Peter Jeavons

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Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. Here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite(More)
Many combinatorial search problems can be expressed as “constraint satisfaction problems” and this class of problems is known to be NP-complete in general. In this paper, we investigate the subclasses that arise from restricting the possible constraint types. We first show that any set of constraints that does not give rise to an NP-complete(More)
We describe a general algebraic formulation for a wide range of combinato-rial problems including Satisfiability, Graph Colorability and Graph Iso-morphism. In this formulation each problem instance is represented by a pair of relational structures, and the solutions to a given instance are homomorphisms between these relational structures. The(More)
Over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types. One very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations, known as polymorphisms. In(More)
There is a very close relationship between constraint satisfaction problems and the satisfaction of join-dependencies in a relational database which is due to a common underlying structure, namely a hypergraph. By making that relationship explicit we are able to adapt techniques previously developed for the study of relational databases to obtain new(More)
One of the most fundamental challenges in constraint programming is to understand the computational complexity of problems involving constraints. It has been shown that the class of all constraint satisfaction problem instances is NP-hard [71], so it is unlikely that efficient general-purpose algorithms exist for solving all forms of constraint problem.(More)
We review the many different definitions of symmetry for constraint satisfaction problems (CSPs) that have appeared in the literature, and show that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as an operation preserving the constraints. We refer to these as solution(More)