Approximating k-hop minimum-spanning trees

Given a complete graph on~n nodes with metric edge costs, the minimum-costk-hop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest root-leaf-path in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(logn) times that of a minimum-cost k-hop spanning-tree.