Minimum spanning tree with hop restrictions

Let U = (u(ij))(n)(i,j=l) be a symmetric requirement matrix. Let d = (d(ij))(n)(i,j=l) 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) is an element of {1, 2, infinity}. We present a polynomial algorithm for the problem when the graph induced by the edges with u(ij) < infinity is 2-vertex-connected. We also present a polynomial algorithm with bounded performance guarantee for the general case. (C) 2003 Elsevier Inc. All rights reserved.