Cse525: Randomized Algorithms and Probabilistic Analysis Lecture 4

One useful application of random algorithms is to approximate NP-hard problems: although there is no known polynomial time algorithm for finding the optimal solution these problems, it is often possible to find a randomized algorithm that can find an approximately optimal solution. One common method for doing this is called Randomized Rounding of Linear Programs(LPs). The basic idea is to take an NP-hard problem, relax the constraints such that it becomes a linear program, which we know how to solve efficiently, and then somehow convert that solution back to an approximate solution to the original problem. The basic recipe is as follows: