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.ISAAC.2019.30
URN: urn:nbn:de:0030-drops-115269
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11526/
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Ashvinkumar, Vikrant ; Gudmundsson, Joachim ; Levcopoulos, Christos ; Nilsson, Bengt J. ; van Renssen, André

Local Routing in Sparse and Lightweight Geometric Graphs

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LIPIcs-ISAAC-2019-30.pdf (0.6 MB)

Abstract

Online routing in a planar embedded graph is central to a number of fields and has been studied extensively in the literature. For most planar graphs no O(1)-competitive online routing algorithm exists. A notable exception is the Delaunay triangulation for which Bose and Morin [Bose and Morin, 2004] showed that there exists an online routing algorithm that is O(1)-competitive. However, a Delaunay triangulation can have Omega(n) vertex degree and a total weight that is a linear factor greater than the weight of a minimum spanning tree.
We show a simple construction, given a set V of n points in the Euclidean plane, of a planar geometric graph on V that has small weight (within a constant factor of the weight of a minimum spanning tree on V), constant degree, and that admits a local routing strategy that is O(1)-competitive. Moreover, the technique used to bound the weight works generally for any planar geometric graph whilst preserving the admission of an O(1)-competitive routing strategy.

BibTeX - Entry

@InProceedings{ashvinkumar_et_al:LIPIcs:2019:11526,
  author =	{Vikrant Ashvinkumar and Joachim Gudmundsson and Christos Levcopoulos and Bengt J. Nilsson and Andr{\'e} van Renssen},
  title =	{{Local Routing in Sparse and Lightweight Geometric Graphs}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{30:1--30:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11526},
  URN =		{urn:nbn:de:0030-drops-115269},
  doi =		{10.4230/LIPIcs.ISAAC.2019.30},
  annote =	{Keywords: Computational geometry, Spanners, Routing}
}

Keywords: Computational geometry, Spanners, Routing
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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