Percolation of Lipschitz surface and tight bounds on the spread of information among mobile agents

TL;DR

This paper analyzes how quickly information spreads among mobile agents performing random walks on a torus, establishing tight bounds on flooding time and introducing a new analytical technique.

Contribution

It provides the first tight upper bounds on flooding time for mobile agents on a torus and introduces a novel method for analyzing such spreading processes.

Findings

Tight upper bounds on flooding time were established.

A new analytical technique for mobile agent processes was introduced.

Results are applicable to various spreading processes involving mobile agents.

Abstract

We consider the problem of spread of information among mobile agents on the torus. The agents are initially distributed as a Poisson point process on the torus, and move as independent simple random walks. Two agents can share information whenever they are at the same vertex of the torus. We study the so-called flooding time: the amount of time it takes for information to be known by all agents. We establish a tight upper bound on the flooding time, and introduce a technique which we believe can be applicable to analyze other processes involving mobile agents.