Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
Decomposing constraint satisfaction problems using database techniques
Artificial Intelligence
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
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 Approximability of Three-valued MAX CSP
SIAM Journal on Computing
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
The expressive power of valued constraints: Hierarchies and collapses
Theoretical Computer Science
Complexity of Constraints
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
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
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Min CSP on four elements: moving beyond submodularity
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Meditations on quantified constraint satisfaction
Logic and Program Semantics
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On galois connections and soft computing
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advences in computational intelligence - Volume Part II
The complexity of three-element min-sol and conservative min-cost-hom
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The complexity of any optimisation problem depends critically on the form of the objective function. Valued constraint satisfaction problems are discrete optimisation problems where the function to be minimised is given as a sum of cost functions defined on specified subsets of variables. These cost functions are chosen from some fixed set of available cost functions, known as a valued constraint language. We show in this paper that when the costs are non-negative rational numbers or infinite, then the complexity of a valued constraint problem is determined by certain algebraic properties of this valued constraint language, which we call weighted polymorphisms. We define a Galois connection between valued constraint languages and sets of weighted polymorphisms and show how the closed sets of this Galois connection can be characterised. These results provide a new approach in the search for tractable valued constraint languages.