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Given a set of nodes Nᵢ (i = 1, 2, , n) which may represent cities and a set of requirements r₈₉ which may represent the number of telephone calls between Nᵢ and Nⱼ, the problem is to build a spanning tree connecting these n nodes such that the total cost of communication of the spanning tree is a minimum among all spanning trees. The cost of communication for a pair of nodes is r₈₉ multiplied by the sum of the distances of arcs which form the unique path connecting Nᵢ and Nⱼ in the spanning tree. Summing over all pmatrix n \\ 2 \ pmatrix pairs of nodes, we have the total cost of communication of the spanning tree. Note that the problem is different from the minimum spanning tree problem solved by Kruskal and Prim.
T. C. Hu (Sun,) studied this question.