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Classifying the Complexity of Constraints Using Finite Algebras
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored. Expand
Closure properties of constraints
This paper investigates the subclasses that arise from restricting the possible constraint types, and shows that any set of constraints that does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition. Expand
On the Algebraic Structure of Combinatorial Problems
  • P. Jeavons
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 28 June 1998
A general algebraic formulation for a wide range of combinatorial problems including Satisfiability, Graph Colorability and Graph Isomorphism is described, and it is demonstrated that the complexity of solving this decision problem is determined in many cases by simple algebraic properties of the relational structures involved. Expand
Constraints, Consistency and Closure
A simple algebraic property is described which characterises all possible constraint types for which strong k-consistency is sufficient to ensure global consistency, for each k > 2. Expand
The complexity of soft constraint satisfaction
It is shown that many tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms and the notion of multimorphism is used to give a complete classification of complexity for the Boolean case which extends several earlier classification results for particular special cases. Expand
Tractable Constraints on Ordered Domains
A restricted set of contraints is identified which gives rise to a class of tractable problems which generalizes the notion of a Horn formula in propositional logic to larger domain sizes, and it is proved that the class of problems generated by any larger set of constraints is NP-complete. Expand
Constraint Satisfaction Problems and Finite Algebras
It is shown that any restricted set of constraint types can be associated with a finite universal algebra and the result is a dichotomy theorem which significantly generalises Schaefer's dichotomy for the Generalised Satisfiability problem. Expand
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
The broken-triangle property is introduced, which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure and can be detected in polynomial time. Expand
Quantified Constraints: Algorithms and Complexity
This paper considers a more general framework for constraint satisfaction problems which allows arbitrary quantifiers over constrained variables, rather than just existential quantifiers, and shows that the complexity of such extended problems is determined by the surjective polymorphisms of the constraint predicates. Expand
Algebraic structures in combinatorial problems