# Approximating k-Hop Minimum-Spanning Trees

#### Ernst Althaus, Stefan Funke, Sariel Har-Peled, Jochen Konemann, Edgar A. Ramos, and Martin Skutella

Given a complete graph on~n nodes with metric edge costs, the minimum-cost \$k\$-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(log n) times that of a minimum-cost \$k\$-hop spanning-tree.