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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)

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)

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)

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)

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)

In this report we discuss constraint satisfaction problems. These are problems in which values must be assigned to a collection of variables , subject to speciied constraints. We focus speciically on problems in which the domain of possible values for each variable is nite. The report surveys the various conditions that have been shown to be suucient to… (More)

Many combinatorial search problems can be expressed as “constraint satisfaction problems” using an appropriate “constraint language”, that is, a set of relations over some fixed finite set of values. It is well-known that there is a trade-off between the expressive power of a constraint language and the complexity of the problems it… (More)