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DOI: 10.4230/LIPIcs.ICALP.2016.147
URN: urn:nbn:de:0030-drops-62918
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6291/
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Koch, Christoph ; Lengler, Johannes

Bootstrap Percolation on Geometric Inhomogeneous Random Graphs

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LIPIcs-ICALP-2016-147.pdf (0.5 MB)


Abstract

Geometric inhomogeneous random graphs (GIRGs) are a model for scale-free networks with underlying geometry. We study bootstrap percolation on these graphs, which is a process modelling the spread of an infection of vertices starting within a (small) local region. We show that the process exhibits a phase transition in terms of the initial infection rate in this region. We determine the speed of the process in the supercritical case, up to lower order terms, and show that its evolution is fundamentally influenced by the underlying geometry. For vertices with given position and expected degree, we determine the infection time up to lower order terms. Finally, we show how this knowledge can be used to contain the infection locally by removing relatively few edges from the graph. This is the first time that the role of geometry on bootstrap percolation is analysed mathematically for geometric scale-free networks.

BibTeX - Entry

@InProceedings{koch_et_al:LIPIcs:2016:6291,
  author =	{Christoph Koch and Johannes Lengler},
  title =	{{Bootstrap Percolation on Geometric Inhomogeneous Random Graphs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{147:1--147:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6291},
  URN =		{urn:nbn:de:0030-drops-62918},
  doi =		{10.4230/LIPIcs.ICALP.2016.147},
  annote =	{Keywords: Geometric inhomogeneous random graphs, scale-free network, bootstrap percolation, localised infection process, metastability threshold}
}

Keywords: Geometric inhomogeneous random graphs, scale-free network, bootstrap percolation, localised infection process, metastability threshold
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 17.08.2016


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