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Section: New Results

Keywords : minimum spanning tree.

Approximating k-hop minimum spanning trees (ATIPE)

Participant : Ernst Althaus.

In [15] , 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 k$ \ge$1 . The goal in the minimum-cost k-hop spanning tree ( Im8 ${k\mtext HMST}$ ) 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 Im8 ${k\mtext HMST}$ problem can be solved exactly in polynomial time when the cost metric cis induced by a so called hierarchically well-separated tree .


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