Pruning Trees

You have a tree (an acyclic, connected graph) with edge weights, but it is far too big. You are to prune the tree by deleting some edges so that the following property holds. For each connected component C of the pruned tree, there is some node rC such that for every node v in C, the total weight of the edges on the path between v and rC is at most some given value d. You happen to like heavy tre