On the complexity of H-coloring
Journal of Combinatorial Theory Series B
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)
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
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
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
Constraint Satisfaction Problems in Non-deterministic Logarithmic Space
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Learnability of quantified formulas
Theoretical Computer Science
The complexity of counting homomorphisms seen from the other side
Theoretical Computer Science
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
The complexity of soft constraint satisfaction
Artificial Intelligence
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Journal of Computer and System Sciences
Ruling out polynomial-time approximation schemes for hard constraint satisfaction problems
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of positive-weight constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so that the total weight of satisfied constraints is maximized. We consider this problem and its variant Max AW CSP where the weights are allowed to be both positive and negative, and study how the complexity of the problems depends on the allowed constraint types. We prove that Max AW CSP over an arbitrary finite domain exhibits a dichotomy: it is either polynomial-time solvable or NP-hard. Our proof builds on two results that may be of independent interest: one is that the problem of finding a maximum H-colourable subdigraph in a given digraph is either NP-hard or trivial depending on H, and the other a dichotomy result for Max CSP with a single allowed constraint type.