On the intercluster distance of a tree metric
For two vertex clusters of a tree metric, we show that the sum of the average intracluster distances is always less than or equal to twice of the average intercluster distance. We show the feature in a more general form of weighted distance. This feature provides a 2-approximation algorithm for the minimum average intercluster distance spanning tree problem, which is a generalization of the minimum routing cost spanning tree or minimum average distance spanning tree problem. The results in this paper can be further generalized to more than two clusters. (c) 2006 Elsevier B.V. All rights reserved.
tree metric graph optimization problem approximation algorithm