3 research outputs found
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