Fully Decentralized Design of Initialization-free Distributed Network Size Estimation

TL;DR

A distributed scheme for estimating the network size, which refers to the total number of agents in a network, is proposed, based on an assumption that each agent has a unique identifier, and an estimation algorithm for obtaining the largest identifier value.

Abstract

In this paper, we propose a distributed scheme for estimating the network size, which refers to the total number of agents in a network. By leveraging a synchronization technique for multi-agent systems, we devise an agent dynamics that ensures convergence to an equilibrium point located near the network size regardless of its initial condition. Our approach is based on an assumption that each agent has a unique identifier, and an estimation algorithm for obtaining the largest identifier value. By adopting this approach, we successfully implement the agent dynamics in a fully decentralized manner, ensuring accurate network size estimation even when some agents join or leave the network.

Figures (3)

• Figure 1: The network is initially represented by the graph (a) and remains for $t\in[0,200)$. When edge $(1,6)$ is added at $t=200$, the network is given by the graph (b). Subsequently, upon the removal of edge $(1,6)$ and the addition of new edge $(6,16)$, the network changes to the graph (c).
• Figure 2: States $z_i(t)$ for largest identifier estimation are represented as dashed lines. They are color-coded: red if $i\in\{1,\cdots,5\}$, green if $i\in\{6,\cdots,15\}$, and blue otherwise.
• Figure 3: States $x_i(t)$ for network size estimation are illustrated as dashed lines. They are color-coded: red if $i\in\{1,\cdots,5\}$, green if $i\in\{6,\cdots,15\}$, and blue otherwise.

Theorems & Definitions (2)

• proof
• proof