Many random walks are faster than one

Noga Alon, Gady Kozma, Chen Avin, Zvi Lotker, Michal Koucky, Mark R. Tuttle

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time-the expected time required to visit every node in a graph at least once-and we show that for a large collection of interesting graphs, running many random walks in parallel jdelds a speed-up in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speed-up is sometimes possible, but that some natural graphs allow only a logarithmic speed-up. A problem related to ours (in which the walks start from some probabilistic distribution on vertices) was previously studied in the context of space efficient algorithms for undirected fit-connectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds.

Original languageEnglish
Title of host publicationSPAA'08 - Proceedings of the 20th Annual Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages119-128
Number of pages10
ISBN (Print)9781595939739
DOIs
StatePublished - 2008
Event20th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'08 - Munich, Germany
Duration: 14 Jun 200816 Jun 2008

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference20th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'08
Country/TerritoryGermany
CityMunich
Period14/06/0816/06/08

Keywords

  • Cover time
  • Distributed algorithms
  • Graph search
  • Random walks
  • Speed-up

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