1. Start with the problem (e.g. MAX-SAT) you want to design an algorithm for.
2. Formulate the problem as an IntegerLinearProgram IP (for example).
4. Design an algorithm taking the following form:
5. Use the ProbabilisticMethod? to show that the integer solution X' approximately meets the constraints of the IP with positive probability. Use the fact that the cost of the optimal fractional solution X* gives you a bound on OPT.
6. [Optional] Convert the randomized algorithm into a deterministic algorithm using the MethodOfConditionalProbabilities? .