License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.13
URN: urn:nbn:de:0030-drops-158232
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15823/
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Biniaz, Ahmad ; Daliri, Majid ; Moradpour, Amir Hossein

A 10-Approximation of the π/2-MST

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LIPIcs-STACS-2022-13.pdf (1 MB)

Abstract

Bounded-angle spanning trees of points in the plane have received considerable attention in the context of wireless networks with directional antennas. For a point set P in the plane and an angle α, an α-spanning tree (α-ST) is a spanning tree of the complete Euclidean graph on P with the property that all edges incident to each point p ∈ P lie in a wedge of angle α centered at p. The α-minimum spanning tree (α-MST) problem asks for an α-ST of minimum total edge length. The seminal work of Anscher and Katz (ICALP 2014) shows the NP-hardness of the α-MST problem for α = 2π/3, π and presents approximation algorithms for α = π/2, 2π/3, π.
In this paper we study the α-MST problem for α = π/2 which is also known to be NP-hard. We present a 10-approximation algorithm for this problem. This improves the previous best known approximation ratio of 16.

BibTeX - Entry

@InProceedings{biniaz_et_al:LIPIcs.STACS.2022.13,
  author =	{Biniaz, Ahmad and Daliri, Majid and Moradpour, Amir Hossein},
  title =	{{A 10-Approximation of the \pi/2-MST}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15823},
  URN =		{urn:nbn:de:0030-drops-158232},
  doi =		{10.4230/LIPIcs.STACS.2022.13},
  annote =	{Keywords: Euclidean spanning trees, approximation algorithms, bounded-angle visibility}
}

Keywords: Euclidean spanning trees, approximation algorithms, bounded-angle visibility
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022

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