29,470 research outputs found
Self-Stabilizing Repeated Balls-into-Bins
We study the following synchronous process that we call "repeated
balls-into-bins". The process is started by assigning balls to bins in
an arbitrary way. In every subsequent round, from each non-empty bin one ball
is chosen according to some fixed strategy (random, FIFO, etc), and re-assigned
to one of the bins uniformly at random.
We define a configuration "legitimate" if its maximum load is
. We prove that, starting from any configuration, the
process will converge to a legitimate configuration in linear time and then it
will only take on legitimate configurations over a period of length bounded by
any polynomial in , with high probability (w.h.p.). This implies that the
process is self-stabilizing and that every ball traverses all bins in
rounds, w.h.p
Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree
We present algorithms for distributed verification and silent-stabilization
of a DFS(Depth First Search) spanning tree of a connected network. Computing
and maintaining such a DFS tree is an important task, e.g., for constructing
efficient routing schemes. Our algorithm improves upon previous work in various
ways. Comparable previous work has space and time complexities of bits per node and respectively, where is the highest
degree of a node, is the number of nodes and is the diameter of the
network. In contrast, our algorithm has a space complexity of bits
per node, which is optimal for silent-stabilizing spanning trees and runs in
time. In addition, our solution is modular since it utilizes the
distributed verification algorithm as an independent subtask of the overall
solution. It is possible to use the verification algorithm as a stand alone
task or as a subtask in another algorithm. To demonstrate the simplicity of
constructing efficient DFS algorithms using the modular approach, We also
present a (non-sielnt) self-stabilizing DFS token circulation algorithm for
general networks based on our silent-stabilizing DFS tree. The complexities of
this token circulation algorithm are comparable to the known ones
Self-stabilizing Numerical Iterative Computation
Many challenging tasks in sensor networks, including sensor calibration,
ranking of nodes, monitoring, event region detection, collaborative filtering,
collaborative signal processing, {\em etc.}, can be formulated as a problem of
solving a linear system of equations. Several recent works propose different
distributed algorithms for solving these problems, usually by using linear
iterative numerical methods.
In this work, we extend the settings of the above approaches, by adding
another dimension to the problem. Specifically, we are interested in {\em
self-stabilizing} algorithms, that continuously run and converge to a solution
from any initial state. This aspect of the problem is highly important due to
the dynamic nature of the network and the frequent changes in the measured
environment.
In this paper, we link together algorithms from two different domains. On the
one hand, we use the rich linear algebra literature of linear iterative methods
for solving systems of linear equations, which are naturally distributed with
rapid convergence properties. On the other hand, we are interested in
self-stabilizing algorithms, where the input to the computation is constantly
changing, and we would like the algorithms to converge from any initial state.
We propose a simple novel method called \syncAlg as a self-stabilizing variant
of the linear iterative methods. We prove that under mild conditions the
self-stabilizing algorithm converges to a desired result. We further extend
these results to handle the asynchronous case.
As a case study, we discuss the sensor calibration problem and provide
simulation results to support the applicability of our approach
Universality and Sharpness in Absorbing-State Phase Transitions
We consider the Activated Random Walk model in any dimension with any sleep
rate and jump distribution and ergodic initial state. We show that the
stabilization properties depend only on the average density of particles,
regardless of how they are initially located on the lattice
Persistence based analysis of consensus protocols for dynamic graph networks
This article deals with the consensus problem involving agents with
time-varying singularities in the dynamics or communication in undirected graph
networks. Existing results provide control laws which guarantee asymptotic
consensus. These results are based on the analysis of a system switching
between piecewise constant and time-invariant dynamics. This work introduces a
new analysis technique relying upon classical notions of persistence of
excitation to study the convergence properties of the time-varying multi-agent
dynamics. Since the individual edge weights pass through singularities and vary
with time, the closed-loop dynamics consists of a non-autonomous linear system.
Instead of simplifying to a piecewise continuous switched system as in
literature, smooth variations in edge weights are allowed, albeit assuming an
underlying persistence condition which characterizes sufficient inter-agent
communication to reach consensus. The consensus task is converted to
edge-agreement in order to study a stabilization problem to which classical
persistence based results apply. The new technique allows precise computation
of the rate of convergence to the consensus value.Comment: This article contains 7 pages and includes 4 figures. it is accepted
in 13th European Control Conferenc
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