Inria / Raweb 2004
Project-Team: MODBIO

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## Section: New Results

Keywords: minimum spanning tree.

## Approximating k-hop minimum spanning trees (ATIPE)

Participant: Ernst Althaus.

In a paper to appear in Operations Research Letters in 2005, 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 c on its edges, and an integer k1. The goal in the minimum-cost k-hop spanning tree () problem is to compute a spanning tree T in G of minimum total cost such that the longest root-leaf-path in the tree has at most k edges.

Our main result is an algorithm that computes a tree of depth at most k and total expected cost O(logn) 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. [35], and Bartal [27][28]. In particular, we show that the problem can be solved exactly in polynomial time when the cost metric c is induced by a so called hierarchically well-separated tree.