Lectures on Proof Verification and Approximation Algorithms

During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability.

This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms.

The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers.

These lectures are particularly useful for advanced courses or reading groups on the topic.