title: Minimum spanning tree in a graph with multiple root vertices
body: <p>I would like to know if there is an algorithm which computes a minimum spanning tree (optimum branching) in a directed graph given a set of root vertices between all of these root vertices, but not only one root vertex and all other vertices in a graph.</p>
  
  <p>Given a set of root vertices [1,4,6] and a graph G like the one on the following picture:</p>
  
  <p><img src="https://i.stack.imgur.com/t4bxz.gif" alt="enter image description here"></p>
  
  <p>...the algorighm should return something like a green sub-graph on the same picture.</p>
  
  <p>I would like to get such an MST that connects all the root vertices provided to the algorithm. I tend to think that the result of the would-be algorithm is a sub-graph of the graph G which contains all root vertices and some other vertices from G.</p>
  
  <p>Notes:</p>
  
  <ol>
  <li>I know that there is no MST for a directed graph, but there is <a href="http://en.wikipedia.org/wiki/Chu%E2%80%93Liu/Edmonds_algorithm" rel="nofollow noreferrer">Chu–Liu/Edmonds algorithm</a>.</li>
  <li>I guess that a result of such an algorithm (if it is actually possible) will return an optimum branching, which includes some vertices of a graph along with all root vertices. </li>
  </ol>