Finding a minimum spanning tree on a directed graph

Question

What algorithm can I use to find a minimum spanning tree on a directed graph? I tried using a modification of Prim's algorithm, but wasn't able to make it work.

Solution

The equivalent of a minimum spanning tree in a directed graph is called an optimum branching or a minimum-cost arborescence. The classical algorithm for solving this problem is the Chu-Liu/Edmonds algorithm. There have been several optimized implementations of this algorithm over the years using better data structures; the best one that I know of uses a Fibonacci heap and runs in time O(m + n log n) and is due to Galil et al.

Hope this helps!

Comments

[Ian R. O'Brien]

What steps do you need to take to calculate this value?

[Alejandro]

Does Kruskal's count as a modified Prim's?

[user3347255]

I was able to solve it. thank you!

[Nikunj Banka]

MST for a directed graph is a different problem. It is the Minimum Cost Arborescence Problem.

[Jordan]

anyone happen to know of an implementation of this? I've found limited implementations of the Chu-Liu/Edmonds algorithm, but nothing for the algorithm by Galil et al.