Simple Dynamics for Plurality Consensus release_j7ce4p3yd5fpdlxzmcect5zng4

by Luca Becchetti, Andrea Clementi, Emanuele Natale, Francesco Pasquale, Riccardo Silvestri, Luca Trevisan

Released as a article .

2015  

Abstract

We study a Plurality-Consensus process in which each of n anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set [k]). Then, in every (synchronous) round, each agent can revise his color according to the opinions currently held by a random sample of his neighbors. It is assumed that the initial color configuration exhibits a sufficiently large bias s towards a fixed plurality color, that is, the number of nodes supporting the plurality color exceeds the number of nodes supporting any other color by s additional nodes. The goal is having the process to converge to the stable configuration in which all nodes support the initial plurality. We consider a basic model in which the network is a clique and the update rule (called here the 3-majority dynamics) of the process is the following: each agent looks at the colors of three random neighbors and then applies the majority rule (breaking ties uniformly). We prove that the process converges in time O( { k, (n/ n)^1/3} n ) with high probability, provided that s ≥ c √({ 2k, (n/ n)^1/3} n n). We then prove that our upper bound above is tight as long as k ≤ (n/ n)^1/4. This fact implies an exponential time-gap between the plurality-consensus process and the median process studied by Doerr et al. in [ACM SPAA'11]. A natural question is whether looking at more (than three) random neighbors can significantly speed up the process. We provide a negative answer to this question: In particular, we show that samples of polylogarithmic size can speed up the process by a polylogarithmic factor only.
In text/plain format

Archived Files and Locations

application/pdf  300.5 kB
file_ictg7z5psfdfzh5bcqzzg6deeu
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2015-07-27
Version   v3
Language   en ?
arXiv  1310.2858v3
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 97d2c3f0-e48f-40ec-a0b6-44cd877623a6
API URL: JSON