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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)

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)

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)

a r t i c l e i n f o a b s t r a c t The Constraint Satisfaction Problem (CSP) is a central generic problem in artificial intelligence. Considerable progress has been made in identifying properties which ensure tractability in such problems, such as the property of being tree-structured. In this paper we introduce the broken-triangle property, which allows… (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)

Although the constraint satisfaction problem is NP-complete in general, a number of constraint classes have been identiied for which some xed level of local consistency is suucient 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 suucient… (More)

Finding solutions to a constraint satisfaction problem is known to be an NP-complete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. In this paper we identify a restricted set of contraints which gives rise to a class of tractable problems. This class generalizes the notion… (More)