License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.1
URN: urn:nbn:de:0030-drops-128670
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12867/
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Abu-Affash, A. Karim ; Bhore, Sujoy ; Carmi, Paz ; Mitchell, Joseph S. B.

Planar Bichromatic Bottleneck Spanning Trees

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LIPIcs-ESA-2020-1.pdf (0.9 MB)

Abstract

Given a set P of n red and blue points in the plane, a planar bichromatic spanning tree of P is a geometric spanning tree of P, such that each edge connects between a red and a blue point, and no two edges intersect. In the bottleneck planar bichromatic spanning tree problem, the goal is to find a planar bichromatic spanning tree T, such that the length of the longest edge in T is minimized. In this paper, we show that this problem is NP-hard for points in general position. Our main contribution is a polynomial-time (8√2)-approximation algorithm, by showing that any bichromatic spanning tree of bottleneck λ can be converted to a planar bichromatic spanning tree of bottleneck at most 8√2 λ.

BibTeX - Entry

@InProceedings{abuaffash_et_al:LIPIcs:2020:12867,
  author =	{A. Karim Abu-Affash and Sujoy Bhore and Paz Carmi and Joseph S. B. Mitchell},
  title =	{{Planar Bichromatic Bottleneck Spanning Trees}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{1:1--1:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12867},
  URN =		{urn:nbn:de:0030-drops-128670},
  doi =		{10.4230/LIPIcs.ESA.2020.1},
  annote =	{Keywords: Approximation Algorithms, Bottleneck Spanning Tree, NP-Hardness}
}

Keywords: Approximation Algorithms, Bottleneck Spanning Tree, NP-Hardness
Collection: 28th Annual European Symposium on Algorithms (ESA 2020)
Issue Date: 2020
Date of publication: 26.08.2020

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