Pooled testing to isolate infected individuals

The usual problem for group testing is this: For a given number of individuals and a given prevalence, how many tests T* are required to find every infected individual? In real life, however, the problem is usually different: For a given number of individuals, a given prevalence, and a limited number of tests T much smaller than T*, how can these tests best be used? In this conference paper, we outline some recent results on this problem for two models. First, the "practical" model, which is relevant for screening for COVID-19 and has tests that are highly specific but imperfectly sensitive, shows that simple algorithms can be outperformed at low prevalence and high sensitivity. Second, the "theoretical" model of very low prevalence with perfect tests gives interesting new mathematical results.