Distributed Estimation and Control of Algebraic Connectivity over Random Graphs

TL;DR

This paper introduces a distributed stochastic power iteration algorithm enabling ad-hoc network nodes to estimate and control algebraic connectivity in random topologies, ensuring robust network performance.

Contribution

It presents a novel stochastic power iteration method for distributed estimation and control of algebraic connectivity in random graphs, with proven convergence and robustness.

Findings

Algorithm converges almost surely to true connectivity

Method effectively adapts node transmission power to optimize connectivity

Numerical results confirm robustness to link failures

Abstract

In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph. Using results from stochastic approximation theory, we prove that the proposed method converges almost surely (a.s.) to the desired value of connectivity even in the presence of imperfect communication scenarios. The estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network, in order to maximize the network connectivity in the presence of realistic Medium Access Control (MAC) protocols or simply to drive the connectivity toward a desired target value. Numerical results corroborate our theoretical findings, thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.