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.APPROX-RANDOM.2017.45
URN: urn:nbn:de:0030-drops-75949
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7594/
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Frieze, Alan ; Pegden, Wesley

Traveling in Randomly Embedded Random Graphs

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Abstract

We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a geodesic of length arbitrarily close to their Euclidean distance, and analyze the minimum length Traveling Salesperson Tour, extending the Beardwood-Halton-Hammersley theorem to this setting.

BibTeX - Entry

@InProceedings{frieze_et_al:LIPIcs:2017:7594,
  author =	{Alan Frieze and Wesley Pegden},
  title =	{{Traveling in Randomly Embedded Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{45:1--45:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7594},
  URN =		{urn:nbn:de:0030-drops-75949},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.45},
  annote =	{Keywords: Traveling Salesman, Euclidean, Shortest Path}
}

Keywords: Traveling Salesman, Euclidean, Shortest Path
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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