Everything from exam2.
LP
* solve 2 or 3 variable LP by hand.
* given NP problem, what is the integer linear program.
* SAT, VC, coloring
* given solution to relaxed ILP, round it to give an answer to the NP problem.
New algorithms
* ILP/relax/round for VC
For your own good, you ought to review (after the final stuff)
* chinese remainder theorem. randomized algorithm for equality testing in terms of communication complexity
* ...