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DOI: 10.4230/LIPIcs.ICALP.2016.136
URN: urn:nbn:de:0030-drops-62711
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6271/
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Berenbrink, Petra ; Friedetzky, Tom ; Giakkoupis, George ; Kling, Peter

Efficient Plurality Consensus, Or: the Benefits of Cleaning up from Time to Time

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Abstract

Plurality consensus considers a network of n nodes, each having one of k opinions. Nodes execute a (randomized) distributed protocol with the goal that all nodes adopt the plurality (the opinion initially supported by the most nodes). Communication is realized via the Gossip (or random phone call) model. A major open question has been whether there is a protocol for the complete graph that converges (w.h.p.) in polylogarithmic time and uses only polylogarithmic memory per node (local memory). We answer this question affirmatively. We propose two protocols that need only mild assumptions on the bias in favor of the plurality. As an example of our results, consider the complete graph and an arbitrarily small constant multiplicative bias in favor of the plurality. Our first protocol achieves plurality consensus in O(log(k)*log(log(n))) rounds using log(k) + Theta(log(log(k))) bits of local memory. Our second protocol achieves plurality consensus in O(log(n)*log(log(n))) rounds using only log(k) + 4 bits of local memory. This disproves a conjecture by Becchetti et al. (SODA'15) implying that any protocol with local memory log(k)+O(1) has worst-case runtime Omega(k). We provide similar bounds for much weaker bias assumptions. At the heart of our protocols lies an undecided state, an idea introduced by Angluin et al. (Distributed Computing'08).

BibTeX - Entry

@InProceedings{berenbrink_et_al:LIPIcs:2016:6271,
  author =	{Petra Berenbrink and Tom Friedetzky and George Giakkoupis and Peter Kling},
  title =	{{Efficient Plurality Consensus, Or: the Benefits of Cleaning up from Time to Time}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{136:1--136:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6271},
  URN =		{urn:nbn:de:0030-drops-62711},
  doi =		{10.4230/LIPIcs.ICALP.2016.136},
  annote =	{Keywords: plurality consensus, voting, majority, distributed, gossip}
}

Keywords: plurality consensus, voting, majority, distributed, gossip
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 17.08.2016


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