Recognition of d-dimensional Monge arrays
Discrete Applied Mathematics
Permuting matrices to avoid forbidden submatrices
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
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)
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
On bounded occurrence constraint satisfaction
Information Processing Letters - Special issue analytical theory of fuzzy control with applications
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
Complexity classifications of boolean constraint satisfaction problems
Some APX-completeness results for cubic graphs
Theoretical Computer Science
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Some optimal inapproximability results
Journal of the ACM (JACM)
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
A combinatorial algorithm for MAX CSP
Information Processing Letters
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
Incomplete Directed Perfect Phylogeny
SIAM Journal on Computing
The Nonapproximability of Non-Boolean Predicates
SIAM Journal on Discrete Mathematics
Every 2-CSP allows nontrivial approximation
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
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
A new algorithm for optimal 2-constraint satisfaction and its implications
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
Towards a dichotomy theorem for the counting constraint satisfaction problem
Information and Computation
Maximum H-colourable subdigraphs and constraint optimization with arbitrary weights
Journal of Computer and System Sciences
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
On the complexity of global constraint satisfaction
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
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
Submodularity on a tree: unifying L-convex and bisubmodular functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Min CSP on four elements: moving beyond submodularity
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the complexity of submodular function minimisation on diamonds
Discrete Optimization
Towards minimizing k-submodular functions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
A characterisation of the complexity of forbidding subproblems in binary Max-CSP
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of finite-valued CSPs
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 the maximum constraint satisfaction problem (MAX CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maximize the number (or the total weight, for the weighted case) of satisfied constraints. This problem is NP-hard in general, and, therefore, it is natural to study how restricting the allowed types of constraints affects the approximability of the problem. In this article, we show that any MAX CSP problem with a finite set of allowed constraint types, which includes all fixed-value constraints (i.e., constraints of the form x = a), is either solvable exactly in polynomial time or else is APX-complete, even if the number of occurrences of variables in instances is bounded. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description relies on the well-known algebraic combinatorial property of supermodularity.