Adaptive Group Testing on Networks with Community Structure: The Stochastic Block Model

TL;DR

This paper explores how leveraging community structure in networks can improve group testing efficiency for infectious diseases, especially COVID-19, by introducing a new infection model and community-aware algorithms that outperform traditional methods under certain conditions.

Contribution

It introduces a network-based infection model over the stochastic block model and develops community-aware algorithms that outperform baseline methods in specific regimes.

Findings

Community-aware algorithms outperform baseline in strong community regimes.

The proposed algorithms are order-optimal in certain parameter settings.

Results extend to noisy testing scenarios.

Abstract

Group testing was conceived during World War II to identify soldiers infected with syphilis using as few tests as possible, and it has attracted renewed interest during the COVID-19 pandemic. A long-standing assumption in the probabilistic variant of the group testing problem is that individuals are infected by the disease independently. However, this assumption rarely holds in practice, as diseases often spread through interactions between individuals and therefore cause infections to be correlated. Inspired by characteristics of COVID-19 and other infectious diseases, we introduce an infection model over networks which generalizes the traditional i.i.d. model from probabilistic group testing. Under this model, we ask whether knowledge of the network structure can be leveraged to perform group testing more efficiently, focusing specifically on community-structured graphs drawn from the stochastic block model. We prove that a simple community-aware algorithm outperforms the baseline binary splitting algorithm when the model parameters are conducive to "strong community structure." Moreover, our novel lower bounds imply that the community-aware algorithm is order-optimal in certain parameter regimes. We extend our bounds to the noisy setting and support our results with numerical experiments.