On the Longest Spanning Tree with Neighborhoods

12/08/2017

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by   Ke Chen, et al.

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We study a maximization problem for geometric network design. Given a set of n compact neighborhoods in R^d, select a point in each neighborhood, so that the longest spanning tree on these points (as vertices) has maximum length. Here we give an approximation algorithm with ratio 0.511, which represents the first, albeit small, improvement beyond 1/2. While we suspect that the problem is NP-hard already in the plane, this issue remains open.