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.STACS.2017.44
URN: urn:nbn:de:0030-drops-69897
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/6989/
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Ivaskovic, Andrej ; Kosowski, Adrian ; Pajak, Dominik ; Sauerwald, Thomas

Multiple Random Walks on Paths and Grids

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LIPIcs-STACS-2017-44.pdf (0.5 MB)

Abstract

We derive several new results on multiple random walks on "low dimensional" graphs.

First, inspired by an example of a weighted random walk on a path of three vertices given by Efremenko and Reingold, we prove the following dichotomy: as the path length n tends to infinity, we have a super-linear speed-up w.r.t. the cover time if and only if the number of walks k is equal to 2. An important ingredient of our proofs is the use of a continuous-time analogue of multiple random walks, which might be of independent interest. Finally, we also present the first tight bounds on the speed-up of the cover time for any d-dimensional grid with d >= 2 being an arbitrary constant, and reveal a sharp transition between linear and logarithmic speed-up.

BibTeX - Entry

@InProceedings{ivaskovic_et_al:LIPIcs:2017:6989,
  author =	{Andrej Ivaskovic and Adrian Kosowski and Dominik Pajak and Thomas Sauerwald},
  title =	{{Multiple Random Walks on Paths and Grids}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte ValleĢe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6989},
  URN =		{urn:nbn:de:0030-drops-69897},
  doi =		{10.4230/LIPIcs.STACS.2017.44},
  annote =	{Keywords: random walks, randomized algorithms, parallel computing}
}

Keywords: random walks, randomized algorithms, parallel computing
Collection: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue Date: 2017
Date of publication: 06.03.2017

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