How to Discreetly Spread a Rumor in a Crowd

TL;DR

This paper analyzes rumor spreading algorithms in a mobile telephone model with limited connections, topology changes, and small advertisements, showing how minimal communication improves spreading efficiency despite network dynamics.

Contribution

It introduces a new mobile telephone model with topology changes and advertisement constraints, and demonstrates how small advertisements enable efficient rumor spreading.

Findings

PUSH-PULL algorithms perform poorly without advertisements in dynamic networks.

Allowing a single-bit advertisement significantly improves spreading time.

Performance degrades gracefully as topology changes increase.

Abstract

In this paper, we study PUSH-PULL style rumor spreading algorithms in the mobile telephone model, a variant of the classical telephone model in which each node can participate in at most one connection per round; i.e., you can no longer have multiple nodes pull information from the same source in a single round. Our model also includes two new parameterized generalizations: (1) the network topology can undergo a bounded rate of change (for a parameterized rate that spans from no changes to changes in every round); and (2) in each round, each node can advertise a bounded amount of information to all of its neighbors before connection decisions are made (for a parameterized number of bits that spans from no advertisement to large advertisements). We prove that in the mobile telephone model with no advertisements and no topology changes, PUSH-PULL style algorithms perform poorly with respect to a graph's vertex expansion and graph conductance as compared to the known tight results in the classical telephone model. We then prove, however, that if nodes are allowed to advertise a single bit in each round, a natural variation of PUSH-PULL terminates in time that matches (within logarithmic factors) this strategy's performance in the classical telephone model---even in the presence of frequent topology changes. We also analyze how the performance of this algorithm degrades as the rate of change increases toward the maximum possible amount. We argue that our model matches well the properties of emerging peer-to-peer communication standards for mobile devices, and that our efficient PUSH-PULL variation that leverages small advertisements and adapts well to topology changes is a good choice for rumor spreading in this increasingly important setting.