I'm new here, so I apologize if this is not the appropriate place to ask this question.
I just started a graduate level course on approximate algorithms, and I am falling behind fast. The class is very theoretical and we are asked to prove approximation problems. We've covered traveling salesman problems, greedy algorithms, set cover, knapsack and makespan in the course of a couple weeks.
I understand the general sense of what the algorithms do, but I need help on intuition of what to do in proofs when trying to solve n-approximation problems.
What readings, topics, or skills will help my ability to solve approximation problems? After I see the solution, it makes sense, but I don't know how one would even start to think of that solution in the first place.
Thank you for any help you can offer.