Fast distributed average consensus algorithms based on advection-diffusion processes

Authors:
Stefania Sardellitti;Massimiliano Giona;Sergio Barbarossa
Affiliations:
INFOCOM Department, University of Rome "La Sapienza," Rome, Italy;Chemical Engineering Department, University of Rome "La Sapienza," Rome, Italy;INFOCOM Department, University of Rome "La Sapienza," Rome, Italy
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

Distributed consensus algorithms have recently gained large interest in sensor networks as a way to achieve globally optimal decisions in a totally decentralized way, that is, without the need of sending all the data collected by the sensors to a fusion center. However, distributed algorithms are typically iterative and they suffer from convergence time and energy consumption. In this paper, we show that introducing appropriate asymmetric interaction mechanisms, with time-varying weights on each edge, it is possible to provide a substantial increase of convergence rate with respect to the symmetric time-invariant case. The basic idea underlying our approach comes from modeling the average consensus algorithm as an advection-diffusion process governing the homogenization of fluid mixtures. Exploiting such a conceptual link, we show how introducing interaction mechanisms among nearby nodes, mimicking suitable advection processes, yields a substantial increase of convergence rate. Moreover, we show that the homogenization enhancement induced by the advection term produces a qualitatively different scaling law of the convergence rate versus the network size with respect to the symmetric case.