Constraint satisfaction has always played a central role in computational

complexity theory; appropriate versions of CSPs are classical complete

problems for most standard complexity classes. CSPs constitute a very rich and

yet sufficiently manageable class of problems to give a good perspective on

general computational phenomena. For instance, they help to understand which

mathematical properties make a computational problem tractable (in a wide

sense, e.g., polynomial-time solvable, non-trivially approximable,

fixed-parameter tractable, or definable in a weak logic). In the last decade,

research activity in this area has significantly intensified and hugely

impressive progress was made.

The Dagstuhl Seminar 18231 "The Constraint Satisfaction Problem: Complexity and

Approximability" was aimed at bringing together researchers using all the

different techniques in the study of the CSP so that they can share their

insights obtained during the past three years. This report documents the

material presented during the course of the seminar.