I've found a problem that boils down to this: I need to find the non-rooted MST of a directed weighted graph. In other words, I need to find the minimal set of edges such that from any one node in the graph you can get to all others.
This is similar to the rooted MST digraph problem, which the chu-liu algorithm solves quite nicely. My intuition is to calculate the rooted MST for all nodes using chu-liu and then merge each, removing redundancies along the way. However, I don't believe that that would be optimal.
Has anybody been working on this? Can you point me towards some papers that I should read?