Pooling or Sampling: Collective Dynamics for Electrical Flow Estimation
Abstract
The computation of electrical flows is a crucial primitive for many recently proposed optimization algorithms on weighted networks. While typically implemented as a centralized subroutine, the ability to perform this task in a fully decentralized way is implicit in a number of biological systems. Thus, a natural question is whether this task can provably be accomplished in an efficient way by a network of agents executing a simple protocol. We provide a positive answer, proposing two distributed approaches to electrical flow computation on a weighted network: a deterministic process mimicking Jacobi's iterative method for solving linear systems, and a randomized token diffusion process, based on revisiting a classical random walk process on a graph with an absorbing node. We show that both processes converge to a solution of Kirchhoff's node potential equations, derive bounds on their convergence rates in terms of the weights of the network, and analyze their time and message complexity.
Cite
@article{arxiv.1804.06127,
title = {Pooling or Sampling: Collective Dynamics for Electrical Flow Estimation},
author = {Luca Becchetti and Vincenzo Bonifaci and Emanuele Natale},
journal= {arXiv preprint arXiv:1804.06127},
year = {2019}
}