Minimum spanning tree with hop restrictions

Let U = (u_ij)_{i, j=1}ⁿ be a symmetric requirement matrix. Let d = (d_ij)_{i, j=1}ⁿ be a cost metric. A spanning tree T = (V, E_T) V = {1, 2, ..., n} is feasible if for every pair of vertices v, w the v-w path in T contains at most u_vw edges. We explore the problem of finding a minimum cost feasible spanning tree, when u_ij ∈ {1, 2, ∞}. We present a polynomial algorithm for the problem when the graph induced by the edges with u_ij < ∞ is 2-vertex-connected. We also present a polynomial algorithm with bounded performance guarantee for the general case.