The Quest towards Optimal Approximability of CSPs

Constraint Satisfaction Problems (CSPs) have long been a central topic in theoretical computer science, offering a rich and historically significant field of study, particularly from the perspectives of checking satisfiability in polynomial time and designing approximation algorithms. This survey explores past and recent advances in understanding the approximability of CSPs, highlighting key breakthroughs and challenges that have emerged along the way. We discuss the connections approximability of CSPs share with other areas of mathematics, such as combinatorics, analysis, and algebra. Finally, this article provides open questions and future directions in the area of approximation of CSPs and closely related problems.