A generalized linear time algorithm for an optimal k-distance dominating set of a weighted tree

The new algorithm finds an optimal k-distance dominating set D in a weighted trees T=(V,E) with link-weights w(x,y)>0 in time O(|V|). It generalizes a previous linear time algorithm for an optimal k-hop dominating set for an unweighted tree. This significantly increases the applications of dominating sets in trees.