On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Exact and approximate reasoning about temporal relations
Computational Intelligence
The complexity of infinite H-colouring
Journal of Combinatorial Theory Series B
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
A shorter model theory
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
Building tractable disjunctive constraints
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning
Theoretical Computer Science
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra
Journal of the ACM (JACM)
Acyclic Homomorphisms and Circular Colorings of Digraphs
SIAM Journal on Discrete Mathematics
Point algebras for temporal reasoning: algorithms and complexity
Artificial Intelligence
A Graph of a Relational Structure and Constraint Satisfaction Problems
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Relation Algebras and their Application in Temporal and Spatial Reasoning
Artificial Intelligence Review
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
Determining the consistency of partial tree descriptions
Artificial Intelligence
Dichotomies in the Complexity of Solving Systems of Equations over Finite Semigroups
Theory of Computing Systems
Tractability and learnability arising from algebras with few subpowers
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
A complete classification of tractability in RCC-5
Journal of Artificial Intelligence Research
The complexity of equality constraint languages
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Qualitative temporal and spatial reasoning revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Maximal infinite-valued constraint languages
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
Semilinear Program Feasibility
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
The complexity of rooted phylogeny problems
Proceedings of the 13th International Conference on Database Theory
On the containment of forbidden patterns problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Proceedings of the forty-third annual ACM symposium on Theory of computing
An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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Allowing templates with infinite domains greatly expands therange of problems that can be formulated as a non-uniformconstraint satisfaction problem. It turns out that many CSPs overinfinite templates can be formulated with templates that areω-categorical. We survey examples of such problems intemporal and spatial reasoning, infinite-dimensional algebra,acyclic colorings in graph theory, artificial intelligence,phylogenetic reconstruction in computational biology, and treedescriptions in computational linguistics. We then give an introduction to the universal-algebraic approachto infinite-domain constraint satisfaction, and discuss how cores,polymorphism clones, and pseudo-varieties can be used to study thecomputational complexity of CSPs with ω-categoricaltemplates. The theoretical results will be illustrated by examplesfrom the mentioned application areas. We close with a series ofopen problems and promising directions of future research.