On the Longest Spanning Tree with Neighborhoods
Ke Chen, Adrian Dumitrescu

TL;DR
This paper introduces an approximation algorithm for a geometric network design problem involving selecting points in neighborhoods to maximize the longest spanning tree length, achieving a ratio of 0.511, slightly better than 1/2.
Contribution
The paper presents the first approximation algorithm with a ratio above 0.5 for the problem of maximizing the longest spanning tree in neighborhoods.
Findings
Approximation ratio achieved is 0.511.
The problem is likely NP-hard even in the plane.
Open question remains on NP-hardness proof.
Abstract
We study a maximization problem for geometric network design. Given a set of compact neighborhoods in , 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 , which represents the first, albeit small, improvement beyond . While we suspect that the problem is NP-hard already in the plane, this issue remains open.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Complexity and Algorithms in Graphs · Advanced Graph Theory Research
