Parsimonious Flooding in Geometric Random-Walks

TL;DR

This paper analyzes the efficiency of a simplified information spreading protocol in mobile ad-hoc networks with agents performing random walks, providing bounds on the time needed for complete dissemination based on network parameters.

Contribution

It introduces a novel analysis of the Parsimonious 1-Flooding Protocol in geometric mobile networks, deriving optimal bounds on completion time with high probability.

Findings

Bounds depend on number of agents, region diameter, transmission radius, and mobility radius.

The analysis reveals the dynamic shape of the spreading process.

Results hold with high probability.

Abstract

We study the information spreading yielded by the \emph{(Parsimonious) $1$-Flooding Protocol} in geometric Mobile Ad-Hoc Networks. We consider $n$ agents on a convex plane region of diameter $D$ performing independent random walks with move radius $\rho$. At any time step, every active agent $v$ informs every non-informed agent which is within distance $R$ from $v$ ($R>0$ is the transmission radius). An agent is only active at the time step immediately after the one in which has been informed and, after that, she is removed. At the initial time step, a source agent is informed and we look at the \emph{completion time} of the protocol, i.e., the first time step (if any) in which all agents are informed. This random process is equivalent to the well-known \emph{Susceptible-Infective-Removed ($SIR$}) infection process in Mathematical Epidemiology. No analytical results are available for this random process over any explicit mobility model. The presence of removed agents makes this process much more complex than the (standard) flooding. We prove optimal bounds on the completion time depending on the parameters $n$, $D$, $R$, and $\rho$. The obtained bounds hold with high probability. We remark that our method of analysis provides a clear picture of the dynamic shape of the information spreading (or infection wave) over the time.