Total flooding time and rumor propagation on graphs

TL;DR

This paper analyzes the total flooding time in rumor propagation models on graphs, comparing the time for multiple pieces of information to the single-information case, revealing an asymptotic ratio of 3/2 for complete graphs.

Contribution

It introduces a flooding time model with multiple informations and derives the asymptotic ratio of propagation times on complete graphs, extending understanding of rumor spread dynamics.

Findings

Expected propagation time ratio approaches 3/2 for complete graphs.

Provides a comparison between multi-information and single-information flooding times.

Analyzes rumor spread dynamics in discrete-time graph models.

Abstract

We study a model of rumor propagation in discrete time where each site in the graph has initially a distinct information; we are interested in the number of "conversations" before the entire graph knows all informations. This problem can be described as a flooding time problem with multiple liquids. For the complete graph we compare the ratio between the expected propagation time for all informations and the corresponding time for a single information, obtaining the asymptotic ratio $3/2$ between them.