In computer science, the minimum routing cost spanning tree of a weighted graph is a spanning tree minimizing the sum of pairwise distances between vertices in the tree. It is also called the optimum distance spanning tree, shortest total path length spanning tree, minimum total distance spanning tree, or minimum average distance spanning tree. In an unweighted graph, this is the spanning tree of minimum Wiener index. Hu (1974) writes that the problem of constructing these trees was proposed by Francesco Maffioli.
The minimum routing cost spanning tree of an unweighted interval graph can be constructed in linear time. A polynomial time algorithm is also known for distance-hereditary graphs, weighted so that the weighted distances are hereditary.