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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.45
Traveling in Randomly Embedded Random Graphs

Authors: Alan Frieze and Wesley Pegden

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

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.
Cite as

Alan Frieze and Wesley Pegden. Traveling in Randomly Embedded Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 45:1-45:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{frieze_et_al:LIPIcs.APPROX-RANDOM.2017.45,
  author =	{Frieze, Alan and Pegden, Wesley},
  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 =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.45},
  URN =		{urn:nbn:de:0030-drops-75949},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.45},
  annote =	{Keywords: Traveling Salesman, Euclidean, Shortest Path}
}
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