Rumor source detection with multiple observations under adaptive diffusions

TL;DR

This paper investigates how multiple independent observations affect the ability to identify rumor sources in adaptive diffusion processes on infinite regular trees, revealing that source obfuscation diminishes with more snapshots.

Contribution

It demonstrates that source obfuscation is limited with three or more observations and characterizes the tradeoff between spreading and anonymity in adaptive diffusion protocols.

Findings

Two snapshots still allow weak source obfuscation.

Three snapshots enable source detection with constant probability.

Tradeoff between spreading speed and obfuscation in adaptive protocols.

Abstract

Recent work, motivated by anonymous messaging platforms, has introduced adaptive diffusion protocols which can obfuscate the source of a rumor: a "snapshot adversary" with access to the subgraph of "infected" nodes can do no better than randomly guessing the entity of the source node. What happens if the adversary has access to multiple independent snapshots? We study this question when the underlying graph is the infinite $d$-regular tree. We show that (1) a weak form of source obfuscation is still possible in the case of two independent snapshots, but (2) already with three observations there is a simple algorithm that finds the rumor source with constant probability, regardless of the adaptive diffusion protocol. We also characterize the tradeoff between local spreading and source obfuscation for adaptive diffusion protocols (under a single snapshot). These results raise questions about the robustness of anonymity guarantees when spreading information in social networks.