15,666 research outputs found
Simple Dynamics for Plurality Consensus
We study a \emph{Plurality-Consensus} process in which each of anonymous
agents of a communication network initially supports an opinion (a color chosen
from a finite set ). 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 \emph{bias} 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 additional nodes. The goal is having the
process to converge to the \emph{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 \emph{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 with high probability, provided that .
We then prove that our upper bound above is tight as long as . This fact implies an exponential time-gap between the
plurality-consensus process and the \emph{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.Comment: Preprint of journal versio
Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems
In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons
Stabilizing Consensus with Many Opinions
We consider the following distributed consensus problem: Each node in a
complete communication network of size initially holds an \emph{opinion},
which is chosen arbitrarily from a finite set . The system must
converge toward a consensus state in which all, or almost all nodes, hold the
same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be
one among those initially present in the system. This condition should be met
even in the presence of an adaptive, malicious adversary who can modify the
opinions of a bounded number of nodes in every round.
We consider the \emph{3-majority dynamics}: At every round, every node pulls
the opinion from three random neighbors and sets his new opinion to the
majority one (ties are broken arbitrarily). Let be the number of valid
opinions. We show that, if , where is a
suitable positive constant, the 3-majority dynamics converges in time
polynomial in and with high probability even in the presence of an
adversary who can affect up to nodes at each round.
Previously, the convergence of the 3-majority protocol was known for
only, with an argument that is robust to adversarial errors. On
the other hand, no anonymous, uniform-gossip protocol that is robust to
adversarial errors was known for
- …