With the development of connected filters in the last decade, many algorithms have been proposed to compute the max-tree. Max-tree allows computation of the most advanced connected operators in a simple way. However, no exhaustive comparison of these algorithms has been proposed so far and the choice of an algorithm over another depends on many parameters. Since the need for fast algorithms is obvious for production code, we present an in depth comparison of five algorithms and some variations of them in a unique framework. Finally, a decision tree will be proposed to help the user choose the most appropriate algorithm according to their requirements.