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On Sharp Thresholds in Random Geometric Graphs

Authors: Milan Bradonjic and Will Perkins

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)


Abstract
We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for satisfiability.

Cite as

Milan Bradonjic and Will Perkins. On Sharp Thresholds in Random Geometric Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 500-514, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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@InProceedings{bradonjic_et_al:LIPIcs.APPROX-RANDOM.2014.500,
  author =	{Bradonjic, Milan and Perkins, Will},
  title =	{{On Sharp Thresholds in Random Geometric Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{500--514},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  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.2014.500},
  URN =		{urn:nbn:de:0030-drops-47195},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.500},
  annote =	{Keywords: Sharp thresholds, random geometric graphs, k-SAT}
}
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