Online Maximum Directed Cut

We investigate a natural online version of the well-known MAXIMUM DIRECTED CUT problem on DAGs. We propose a deterministic algorithm and show that it achieves a competitive ratio of 3 root 3/2 approximate to 2.5981. We then give a lower bound argument to show that no deterministic algorithm can achieve a ratio of 3 root 3/2 - epsilon for any epsilon > 0 thus showing that our algorithm is essentially optimal. Then, we extend our technique to improve upon the analysis of an old result: we show that greedily derandomizing the trivial randomized algorithm for MAXDICUT in general graphs improves the competitive ratio from 4 to 3, and also provide a tight example.