1. A method implemented by a networking device functioning as a computing node, the method to resolve sub-trees of a loosely specified multicast distribution tree (MDT), the method to utilize global identifiers for sub-trees to enable differentiation of traffic of different sub-trees at shared replication nodes, the method implemented at each of the nodes of the network that are part of the MDT, the method comprising: checking whether any leaves of sub-trees are roots that have failed; merging the sub-trees with leaves that are the roots that failed with the sub-trees with the failed root; selecting a sub-tree in the set of sub-trees in the MDT rooted at a current node; computing a selected sub-tree from root to leaves; and generating a translation of sub-tree identifiers between the sub-tree identifiers of the selected sub-tree and a sub-tree identifier of an upstream sub-tree, in response to the computing node being the sub-tree root of the selected sub-tree.