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Constraint Satisfaction Problems: Algorithms and Complexity

Final Report Summary - CSP-COMPLEXITY (Constraint Satisfaction Problems: Algorithms and Complexity)

Constraint Satisfaction Problems are computational problems that appear in many areas of computer science, for example in optimization, scheduling, database theory, and knowledge representation. The project CSP-Complexity explored the computational complexity of constraint satisfaction problems: in particular the question which CSPs are polynomial-time tractable. It was already known that classifying the complexity of CSPs is closely related to central questions in universal algebra. One of the outcomes of the project is that universal algebra can also be used when the constraint satisfaction problems are over infinite domains, using concepts and results from model theory and Ramsey theory. This led to several powerful classification results for CSPs over infinite domains, but also to new research directions in the mathematical fields mentioned above.