License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2022.23
URN: urn:nbn:de:0030-drops-176434
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17643/
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Berenbrink, Petra ; Coja-Oghlan, Amin ; Gebhard, Oliver ; Hahn-Klimroth, Max ; Kaaser, Dominik ; Rau, Malin

On the Hierarchy of Distributed Majority Protocols

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LIPIcs-OPODIS-2022-23.pdf (0.9 MB)

Abstract

We study the consensus problem among n agents, defined as follows. Initially, each agent holds one of two possible opinions. The goal is to reach a consensus configuration in which every agent shares the same opinion. To this end, agents randomly sample other agents and update their opinion according to a simple update function depending on the sampled opinions.
We consider two communication models: the gossip model and a variant of the population model. In the gossip model, agents are activated in parallel, synchronous rounds. In the population model, one agent is activated after the other in a sequence of discrete time steps. For both models we analyze the following natural family of majority processes called j-Majority: when activated, every agent samples j other agents uniformly at random (with replacement) and adopts the majority opinion among the sample (breaking ties uniformly at random). As our main result we show a hierarchy among majority protocols: (j+1)-Majority (for j > 1) converges stochastically faster than j-Majority for any initial opinion configuration. In our analysis we use Strassen’s Theorem to prove the existence of a coupling. This gives an affirmative answer for the case of two opinions to an open question asked by Berenbrink et al. [PODC 2017].

BibTeX - Entry

@InProceedings{berenbrink_et_al:LIPIcs.OPODIS.2022.23,
  author =	{Berenbrink, Petra and Coja-Oghlan, Amin and Gebhard, Oliver and Hahn-Klimroth, Max and Kaaser, Dominik and Rau, Malin},
  title =	{{On the Hierarchy of Distributed Majority Protocols}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17643},
  URN =		{urn:nbn:de:0030-drops-176434},
  doi =		{10.4230/LIPIcs.OPODIS.2022.23},
  annote =	{Keywords: Consensus, Majority, Hierarchy, Stochastic Dominance, Population Protocols, Gossip Model, Strassen’s Theorem}
}

Keywords: Consensus, Majority, Hierarchy, Stochastic Dominance, Population Protocols, Gossip Model, Strassen’s Theorem
Collection: 26th International Conference on Principles of Distributed Systems (OPODIS 2022)
Issue Date: 2023
Date of publication: 15.02.2023

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