Steiner minimal trees

Chu CCN, Wong Y-C (2008) FLUTE fast lookup table based rectilinear Steiner minimal tree algorithm for VLSI design. IEEE Trans CAD 27(l) 70-83... 

For a given set H of revoked receivers, let ui,... be the leaves corresponding to the elements in IZ. The method to partition M TZ into disjoint subsets is as follows. Consider the (directed) Steiner Tree ST TZ) defined by the set 71 of vertices and the root, i.e. the minimal subtree of the full binary tree that connects all the leaves in TZ. ST 7Z) is unique. Let Si, ..., Si be all the subtrees of the original tree that hang off ST 7Z), that is, all subtrees whose roots ui,..., are adjacent to nodes of outdegree 1 in ST 7Z), but they are not in ST 7Z). The next claim follows immediately and shows that this construction is indeed a cover, as required. 

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