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- Andrei A. Bulatov, Peter Jeavons, Andrei A. Krokhin
- SIAM J. Comput.
- 2005

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)

- Peter Jeavons, David A. Cohen, Marc Gyssens
- J. ACM
- 1997

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)

- Peter Jeavons
- Theor. Comput. Sci.
- 1998

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)

- David A. Cohen, Martin C. Cooper, Peter Jeavons, Andrei A. Krokhin
- Artif. Intell.
- 2006

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)

- Marc Gyssens, Peter Jeavons, David A. Cohen
- Artif. Intell.
- 1994

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)

- Peter Jeavons, David A. Cohen, Martin C. Cooper
- Artif. Intell.
- 1998

Although the constraint satisfaction problem is NP-complete in general, a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency. In this paper we describe a simple algebraic property which characterises all possible constraint types for which strong k-consistency is… (More)

- Andrei A. Bulatov, Andrei A. Krokhin, Peter Jeavons
- ICALP
- 2000

- David A. Cohen, Peter Jeavons
- Handbook of Constraint Programming
- 2006

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)

- David A. Cohen, Peter Jeavons, Christopher Jefferson, Karen E. Petrie, Barbara M. Smith
- Constraints
- 2005

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)