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The cable-communications systems, -center, and minimum spanning-tree problems are contained within a general graph optimization-synthesis problem. In the minimum spanningtree problem, a decomposition technique is used in constructing minimal-length trees. This problem is related to the -center problem where the total number of vertices is estimated from the length of the spanning tree. Both results, vertex estimate and decomposition, are utilized in the cable-communications systems problem. A procedure and example are provided for estimating the dollar cost of a cable-communications system.