I am planning to teach approximation algorithms for problems such as job scheduling and number partitioning. I would like to teach proofs, but the proofs I found in the original papers (e.g. this one) are quite hard to understand - they use complicated weighting schcemes, and there is no explanation of how these particular weights were derived.
I am looking for a textbook (or an article) that explains these proofs in a more 'didactic' way, that is, the proof is developed step by step, such that the reader can understand how the proof was derived, and use this understanding to develop similar proofs.
What is a good textbook for this topic?