Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
A dichotomy theorem for maximum generalized satisfiability problems
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Closure properties of constraints
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The complexity of maximal constraint languages
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Universal Algebra and Applications in Theoretical Computer Science
Universal Algebra and Applications in Theoretical Computer Science
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A Graph of a Relational Structure and Constraint Satisfaction Problems
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
The complexity of soft constraint satisfaction
Artificial Intelligence
Constraint Satisfaction Problems of Bounded Width
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An algebraic theory of complexity for valued constraints: establishing a Galois connection
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
The Dichotomy for Conservative Constraint Satisfaction Problems Revisited
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
An algebraic theory of complexity for valued constraints: establishing a Galois connection
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The connection between the complexity of constraint languages and clone theory, discovered by Cohen and Jeavons in a series of papers, has been a fruitful line of research on the complexity of CSPs. In a recent result, Cohen et al. [14] have established a Galois connection between the complexity of valued constraint languages and so-called weighted clones. In this paper, we initiate the study of weighted clones. Firstly, we prove an analogue of Rosenberg's classification of minimal clones for weighted clones. Secondly, we show minimality of several weighted clones whose support clone is generated by a single minimal operation. Finally, we classify all Boolean weighted clones. This classification implies a complexity classification of Boolean valued constraint languages obtained by Cohen et al. [13]