Analyzing the MAX 2-SAT and MAX DI-CUT approximation algorithms of Feige and Goemans

We present a complete analysis of the MAX 2-SAT and MAX DI-CUT approximation algorithms of Feige and Goemans using various analytical and computational tools. By ne-tuning the rotation functions used we obtain minutely improved performance ratios for these problems. The rotation functions used for getting these improvements are essentially optimal as the performance ratios obtained using them almost completely match upper bounds that we obtain on the performance ratios that can be achieved using any rotation function. We also discuss possibilities of getting improved approximation algorithms for these problems.