We consider the problem of computing a minimum cycle
basis of a directed graph with m arcs and n nodes.
We adapt the greedy approach proposed by Horton
and hereby obtain a very simple exact algorithm of
complexity O(m4 n), being as fast
as the first algorithm proposed for this problem.
Moreover, the speed-up of Golynski and Horton
applies to this problem, providing an exact algorithm
of complexity O(m^ω n), in particular O(m3.376 n).
Finally, we prove that these greedy approaches fail for more specialized
subclasses of directed cycle bases.
