On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Characterising tractable constraints
Artificial Intelligence
Algorithmic complexity of list colorings
Discrete Applied Mathematics
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
On the algebraic structure of combinatorial problems
Theoretical Computer Science
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
Hypertree decompositions and tractable queries
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The complexity of H-colouring of bounded degree graphs
Discrete Mathematics
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
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
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
Constraints and universal algebra
Annals of Mathematics and Artificial Intelligence
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Constraint Satisfaction Problems in Non-deterministic Logarithmic Space
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A Game-Theoretic Approach to Constraint Satisfaction
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Functions of multiple-valued logic and the complexity of constraint satisfaction: A short survey
ISMVL '03 Proceedings of the 33rd International Symposium on Multiple-Valued Logic
Constraint Processing
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)
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Near-Unanimity Functions and Varieties of Reflexive Graphs
SIAM Journal on Discrete Mathematics
Constraint satisfaction, databases, and logic
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Constraints, consistency and closure
Artificial Intelligence
Dichotomy for tree-structured trigraph list homomorphism problems
Discrete Applied Mathematics
Interval graphs, adjusted interval digraphs, and reflexive list homomorphisms
Discrete Applied Mathematics
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
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
Qualitative constraint satisfaction problems: An extended framework with landmarks
Artificial Intelligence
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
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In a constraint satisfaction problem (CSP), the aim is to find an assignment of values to a given set of variables, subject to specified constraints. The CSP is known to be NP-complete in general. However, certain restrictions on the form of the allowed constraints can lead to problems solvable in polynomial time. Such restrictions are usually imposed by specifying a constraint language, that is, a set of relations that are allowed to be used as constraints. A principal research direction aims to distinguish those constraint languages that give rise to tractable CSPs from those that do not. We achieve this goal for the important version of the CSP, in which the set of values for each individual variable can be restricted arbitrarily. Restrictions of this type can be studied by considering those constraint languages which contain all possible unary constraints; we call such languages conservative. We completely characterize conservative constraint languages that give rise to polynomial time solvable CSP classes. In particular, this result allows us to obtain a complete description of those (directed) graphs H for which the List H-Coloring problem is solvable in polynomial time. The result, the solving algorithm, and the proofs heavily use the algebraic approach to CSP developed in Jeavons et al. [1997], Jeavons [1998], Bulatov et al. [2005], and Bulatov and Jeavons [2001b, 2003].