Noisy Adaptive Group Testing for Community-Oriented Models.

We consider the group testing problem over probabilistic community-oriented infection models, which have attracted significant attention in the wake of the COVID-19 pandemic. To the best of our knowledge, existing theoretical results on the complexity of group testing in such settings are derived under the assumption that tests are noiseless. We present novel upper and lower bounds for the noisy case, focusing on adaptive group testing schemes tailored to the community structure of the population. For the achievability result, we devise an algorithm which incorporates knowledge of the community structure into a noisy binary search procedure from [1]. Our algorithm exhibits favorable performance in the context of the recently-introduced stochastic block infection model [2]. Furthermore, our lower bound applies to any adaptive algorithm, any probabilistic infection model, and any (noisy or noiseless) testing model satisfying certain natural criteria, and thus can be of independent interest.