2.1 Simple Approximation Algorithm

In this note, the cut C is referred as the cut-set and the size of the cut |C| as the size of the cut-set. For a graph, a maximum cut is a cut whose size is at least the size of any other cut. The problem of finding a maximum cut in a graph is known as the maximum cut problem. The problem is NP-hard. Simple 0.5approximation algorithms existed long time ago, but no improvement was made till 1990s by Goemans and Williamson [GW95] using semidefinite programming and randomized rounding that achieves an approximation ratio 0.878. We describe one 0.5-approximation algorithm in Section 2.1 and then Goemans and Williamson’s method in Section 2.2.