Integer and combinatorial optimization
Integer and combinatorial optimization
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Theoretical Computer Science
Minimization of an M-convex function
Discrete Applied Mathematics
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Boolean constraint satisfaction: complexity results for optimization problems with arbitrary weights
Theoretical Computer Science
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
Complexity classifications of boolean constraint satisfaction problems
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A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Some optimal inapproximability results
Journal of the ACM (JACM)
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The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
A combinatorial algorithm for MAX CSP
Information Processing Letters
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LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
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STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Towards a Dichotomy Theorem for the Counting Constraint Satisfaction Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The Nonapproximability of Non-Boolean Predicates
SIAM Journal on Discrete Mathematics
Is constraint satisfaction over two variables always easy?
Random Structures & Algorithms
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
Classes of Submodular Constraints Expressible by Graph Cuts
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
An algebraic characterisation of complexity for valued constraint
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Discrete Optimization
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CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
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In this paper we study the complexity of the maximum constraint satisfaction problem (MAX CSP) over an arbitrary finite domain. An instance of MAX CSP consists of a set of variables and a collection of constraints which are applied to certain specified subsets of these variables; the goal is to find values for the variables which maximize the number of simultaneously satisfied constraints. Using the theory of sub- and supermodular functions on finite lattice-ordered sets, we obtain the first examples of general families of efficiently solvable cases of MAX CSP for arbitrary finite domains. In addition, we provide the first dichotomy result for a special class of non-Boolean MAX CSP, by considering binary constraints given by supermodular functions on a totally ordered set. Finally, we show that the equality constraint over a non-Boolean domain is non-supermodular, and, when combined with some simple unary constraints, gives rise to cases of MAX CSP which are hard even to approximate.