Graph Homomorphisms and Universal Algebra
For theoretical computer scientists, this provides a pedagogical introduction to a powerful algebraic framework for classifying CSP complexity, though it is a survey/tutorial rather than new research.
This course introduces the universal-algebraic approach to study the computational complexity of finite-domain constraint satisfaction problems (CSPs), focusing on the tractability vs. NP-hardness border. It covers cyclic terms and bounded width theorems, starting with directed graph homomorphism problems.
Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between polynomial-time tractability and NP-hardness. In this course we introduce the universal-algebraic approach to study the computational complexity of finite-domain CSPs. The course covers in particular the cyclic terms and bounded width theorems. To keep the presentation accessible, we start the course in the tangible setting of directed graphs and graph homomorphism problems.