The Complexity of Constraint Languages

@inproceedings{Cohen2006TheCO,
  title={The Complexity of Constraint Languages},
  author={David A. Cohen and Peter Jeavons},
  booktitle={Handbook of Constraint Programming},
  year={2006}
}
Publisher Summary This chapter discusses one of the most fundamental challenges in constraint programming: to understand the computational complexity of problems involving constraints. One way in which this occurs is that there is some special structure in the way that the constraints overlap and intersect each other. The natural theory for discussing the structure of such interaction between constraints is the mathematical theory of hypergraphs. Another way in which constraint problems are… Expand
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References

SHOWING 1-10 OF 114 REFERENCES
Classifying the Complexity of Constraints Using Finite Algebras
TLDR
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
The complexity of maximal constraint languages
TLDR
This paper systematically study the complexity of all maximal constraint languages, that is, languages whose expressive power is just weaker than that of the language of all constraints. Expand
Implementing a Test for Tractability
TLDR
An automated analysis includes the derivation of more than 450 000 new NP-completeness results, and precisely identifies the small set of individual relations which cannot be classified as either tractable or NP-complete using the algebraic conditions presented in previous papers. Expand
How to Determine the Expressive Power of Constraints
TLDR
It is shown that indicator problems provide a simple method to test for tractability and the expressive power of a given set of constraint types is determined by certain algebraic properties of the underlying relations. Expand
A dichotomy theorem for constraints on a three-element set
  • A. Bulatov
  • Mathematics, Computer Science
  • The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.
  • 2002
TLDR
Every subclass of the CSP defined by a set of allowed constraints is either tractable or NP-complete, and the criterion separating them is that conjectured by Bulatov et al. (2001). Expand
Tractable conservative constraint satisfaction problems
  • A. Bulatov
  • Mathematics, Computer Science
  • 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
TLDR
This work completely characterize conservative constraint languages that give rise to CSP classes solvable in polynomial time, and obtains a complete description of those (directed) graphs H for which the List H-Coloring problem is poynomial time solvable. Expand
An Algebraic Approach to Multi-sorted Constraints
TLDR
A new algebraic framework is described which allows us to deal more precisely with problems where different variables may have different domains, and is able to identify new tractable classes of constraints by combining algorithms devised for the simplified, single domain, problem. Expand
Closure properties of constraints
TLDR
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
Towards a dichotomy theorem for the counting constraint satisfaction problem
TLDR
It is proved that if a subclass of the #CSP is tractable, then constraints allowed by the class satisfy some very restrictive condition: it has to have a Mal'tsev polymorphism, that is a ternary operation m(x, y, z) such that x = x. Expand
Constructing Constraints
TLDR
It is shown that for languages over a finite domain the concept of an 'indicator problem' gives a universal construction for any constraint within the expressive power of a language. Expand
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