Best-of-Three Voting on Dense Graphs
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Authors
Kang, Nan
Rivera, Nicolás
Publication Date
2019-06-17Journal Title
The 31st ACM Symposium on Parallelism in Algorithms and Architectures
Conference Name
SPAA '19: 31st ACM Symposium on Parallelism in Algorithms and Architectures
ISBN
9781450361842
Type
Conference Object
This Version
AM
Metadata
Show full item recordCitation
Kang, N., & Rivera, N. (2019). Best-of-Three Voting on Dense Graphs. The 31st ACM Symposium on Parallelism in Algorithms and Architectures https://doi.org/10.1145/3323165.3323207
Abstract
Given a graph $G$ of $n$ vertices, where each vertex is initially attached an
opinion of either red or blue, we investigate a random process known as the
Best-of-three voting. In this process, at each time step, every vertex chooses
three neighbours at random and adopts the majority colour. We study this
process for a class of graphs with minimum degree $d = n^{\alpha}$\,, where
$\alpha = \Omega\left( (\log \log n)^{-1} \right)$. We prove that if initially
each vertex is red with probability greater than $1/2+\delta$, and blue
otherwise, where $\delta \geq (\log d)^{-C}$ for some $C>0$, then with high
probability this dynamic reaches a final state where all vertices are red
within $O\left( \log \log n\right) + O\left( \log \left( \delta^{-1} \right)
\right)$ steps.
Sponsorship
European Research Council
Funder references
ECH2020 EUROPEAN RESEARCH COUNCIL (ERC) (679660)
Identifiers
External DOI: https://doi.org/10.1145/3323165.3323207
This record's URL: https://www.repository.cam.ac.uk/handle/1810/294471
Rights
All rights reserved