After this last part the world of optimisation problem is represented in this figure. Now we have several optimization problems which are not approximable at all. Among them, I would like to stress the minimum TSP problem but also the maximum clique and the minimum graph colouring problems. Here currently we have hundreds of problems. And then we have the class APX and now we know that maximum satisfiability are in APX but are not in PTS. And also in this case hundred of problems exists in this class. And then we have the class PTAS. Also in this class hundreds of problems exist.

---