Abstract
Given a metric graph G=(V,E,w), a specific vertex c∈V, and an integer p, let T be a depth-2 spanning tree of G rooted at c such that c is adjacent to p vertices called hubs and each of the remaining vertices is adjacent to a hub. The Starp-Hub Routing Cost Problem is to find a spanning tree T of G satisfying the conditions stated above such that the sum of distances between all pairs of vertices in T is minimized. In this paper, we prove that the Starp-Hub Routing Cost Problem is NP-hard. A 3-approximation algorithm running in time O(n2) is given for solving the same problem where n is the number of vertices in the input graph. Moreover, we give an example to show that the analysis of the approximation ratio cannot be better than 2−ϵ for any ϵ>0.
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