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Beschreibung:
We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5/3-ε)-approximation algorithm, for any ε > 0, unless P = NP. We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.