In sahasrabuddhe2000multicast's Cost Optimization section, it states that when the link weight is asymmetric, the problem of finding a minimum-cost group-shared multicast tree can be reduced to the Steiner tree problem by constructing an undirected graph G' that has the same set of vertices as the directed graph G, but with undirected links that have costs equal to the sum of the costs of the corresponding directed links in G. It says:
Now, it is easy to verify that T is a minimum-cost group-shared multicast tree in G if and only if T′ is a Steiner tree in G′.
But I can easily find counterexamples: a counter example(ignore other edges of the steiner tree) where the group-shared tree do not use the same link for both direction. What did I miss?
