descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint , Other literature type 01 Jan 2018Embargo end date: 01 Jan 2017 English Publisher:Springer International PublishingJournal:Discrete Mathematics, Algorithms and Applications, volume 12, page 2,050,067 (issn: 1793-8309, eissn: 1793-8317,

Authors: Ke Chen; Adrian Dumitrescu;

doi: 10.1007/978-3-319-78455-7_2 , 10.1142/s1793830920500676 , 10.48550/arxiv.1712.03297

arXiv: http://arxiv.org/abs/1712.03297

On the Longest Spanning Tree with Neighborhoods

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Abstract

We study a maximization problem for geometric network design. Given a set of [Formula: see text] compact neighborhoods in [Formula: see text], 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 [Formula: see text], which represents the first, albeit small, improvement beyond [Formula: see text]. While we suspect that the problem is NP-hard already in the plane, this issue remains open.

Related Organizations

University of Wisconsin System
United States
University of Wisconsin–Milwaukee
United States

Keywords

Computational Geometry (cs.CG), FOS: Computer and information sciences, Mathematics - Metric Geometry, FOS: Mathematics, Computer Science - Computational Geometry, Metric Geometry (math.MG)

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