Optimum Communication Spanning Trees in Series-Parallel Networks
Ehab S. Elmallah, Charles J. Colbourn · SIAM Journal on Computing · 1985
The optimum communication spanning tree problem is to locate a spanning tree which minimizes the sum of the lengths of the shortest routes between all pairs of vertices in a graph, weighted by traffic requirements. Although NP-complete in general, this problem has an efficient solution for series-parallel graphs when all requirements are equal. This problem was introduced by Hu, who gave an efficient solution for the restricted case when the network is complete and the distances are equal.