Graph Homomorphisms and Universal Algebra

Abstract

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.

In version 2: Added chapter on uniform algorithms. Fixed issues in the bounded width proof. Added many exercises. Changed order of sections on Maltsev and on Universal Algebra