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URN: urn:nbn:de:0030-drops-154401
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Approximating Longest Spanning Tree with Neighborhoods

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Abstract

We study the following maximization problem in the Euclidean plane: Given a collection of neighborhoods (polygonal regions) in the plane, the goal is to select a point in each neighborhood so that the longest spanning tree on selected points has maximum length. It is not known whether or not this problem is NP-hard. We present an approximation algorithm with ratio 0.548 for this problem. This improves the previous best known ratio of 0.511.
The presented algorithm takes linear time after computing a diameter. Even though our algorithm itself is fairly simple, its analysis is rather involved. In some part we deal with a minimization problem with multiple variables. We use a sequence of geometric transformations to reduce the number of variables and simplify the analysis.

BibTeX - Entry

@InProceedings{biniaz:LIPIcs.ISAAC.2021.7,
  author =	{Biniaz, Ahmad},
  title =	{{Approximating Longest Spanning Tree with Neighborhoods}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{7:1--7:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15440},
  URN =		{urn:nbn:de:0030-drops-154401},
  doi =		{10.4230/LIPIcs.ISAAC.2021.7},
  annote =	{Keywords: Euclidean maximum spanning tree, spanning tree with neighborhoods, approximation algorithms}
}

Keywords: Euclidean maximum spanning tree, spanning tree with neighborhoods, approximation algorithms
Seminar: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue date: 2021
Date of publication: 30.11.2021


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