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.2018.45
URN: urn:nbn:de:0030-drops-94494
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9449/
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Johansson, Tony

The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree

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Abstract

We consider a random walk process, introduced by Orenshtein and Shinkar [Tal Orenshtein and Igor Shinkar, 2014], which prefers to visit previously unvisited edges, on the random r-regular graph G_r for any odd r >= 3. We show that this random walk process has asymptotic vertex and edge cover times 1/(r-2)n log n and r/(2(r-2))n log n, respectively, generalizing the result from [Cooper et al., to appear] from r = 3 to any larger odd r. This completes the study of the vertex cover time for fixed r >= 3, with [Petra Berenbrink et al., 2015] having previously shown that G_r has vertex cover time asymptotic to rn/2 when r >= 4 is even.

BibTeX - Entry

@InProceedings{johansson:LIPIcs:2018:9449,
  author =	{Tony Johansson},
  title =	{{The Cover Time of a Biased Random Walk on a Random Regular Graph of Odd Degree}},
  booktitle =	{Approximation, Randomization, and Combinatorial  Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{45:1--45:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Eric Blais and Klaus Jansen and Jos{\'e} D. P. Rolim and David Steurer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9449},
  URN =		{urn:nbn:de:0030-drops-94494},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.45},
  annote =	{Keywords: Random walk, random regular graph, cover time}
}

Keywords: Random walk, random regular graph, cover time
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)
Issue Date: 2018
Date of publication: 13.08.2018

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