Section: New Results
Keywords : minimum spanning tree.
Approximating k-hop minimum spanning trees (ATIPE)
Participant : Ernst Althaus.
In  , we consider the problem of computing minimum-cost spanning trees with depth restrictions. Specifically, we are given an n-node complete graph G, a metric cost-function con its edges, and an integer k1 . The goal in the minimum-cost k-hop spanning tree ( ) is to compute a spanning tree Tin Gof minimum total cost such that the longest root-leaf-path in the tree has at most kedges.
Our main result is an algorithm that computes a tree of depth at most kand total expected cost O(log n) times that of a minimum-cost k-hop spanning-tree. The result is based upon earlier work on metric space approximation due to Fakcharoenphol et al, and Bartal. In particular, we show that the problem can be solved exactly in polynomial time when the cost metric cis induced by a so called hierarchically well-separated tree .