Clementi, Andrea ;
Ghaffari, Mohsen ;
Gualà, Luciano ;
Natale, Emanuele ;
Pasquale, Francesco ;
Scornavacca, Giacomo
A Tight Analysis of the Parallel UndecidedState Dynamics with Two Colors
Abstract
The UndecidedState Dynamics is a wellknown protocol for distributed consensus. We analyze it in the parallel PULL communication model on the complete graph with n nodes for the binary case (every node can either support one of two possible colors, or be in the undecided state).
An interesting open question is whether this dynamics is an efficient SelfStabilizing protocol, namely, starting from an arbitrary initial configuration, it reaches consensus quickly (i.e., within a polylogarithmic number of rounds). Previous work in this setting only considers initial color configurations with no undecided nodes and a large bias (i.e., Theta(n)) towards the majority color.
In this paper we present an unconditional analysis of the UndecidedState Dynamics that answers to the above question in the affirmative. We prove that, starting from any initial configuration, the process reaches a monochromatic configuration within O(log n) rounds, with high probability. This bound turns out to be tight. Our analysis also shows that, if the initial configuration has bias Omega(sqrt(n log n)), then the dynamics converges toward the initial majority color, with high probability.
BibTeX  Entry
@InProceedings{clementi_et_al:LIPIcs:2018:9610,
author = {Andrea Clementi and Mohsen Ghaffari and Luciano Gual{\`a} and Emanuele Natale and Francesco Pasquale and Giacomo Scornavacca},
title = {{A Tight Analysis of the Parallel UndecidedState Dynamics with Two Colors}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {28:128:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770866},
ISSN = {18688969},
year = {2018},
volume = {117},
editor = {Igor Potapov and Paul Spirakis and James Worrell},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9610},
URN = {urn:nbn:de:0030drops96107},
doi = {10.4230/LIPIcs.MFCS.2018.28},
annote = {Keywords: Distributed Consensus, SelfStabilization, PULL Model, Markov Chains}
}
2018
Keywords: 

Distributed Consensus, SelfStabilization, PULL Model, Markov Chains 
Seminar: 

43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Issue date: 

2018 
Date of publication: 

2018 