Fast distributed consensu algorithms based on advection-diffusion processes

Distributed consensus algorithms have recently gained a 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. The goal of this work is to show that modeling a consensus algorithm as the homogenization process of a fluid through an advection-diffusion process provides a fundamental clue to design innovative consensus algorithms whose convergence rate can be increased by acting on the (equivalent) advection mechanism, without increasing the coverage radius of any sensor. In particular, we show the increase of convergence rate resulting from a proper interplay between advection and diffusion mechanisms.