On Finding a Subset of Healthy Individuals from a Large Population

In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of “healthy” items from a large population containing a small number of “defective” items. We show that an impressive reduction in the number of tests is achievable compared to the approach of first identifying all the defective items and then picking the required number of healthy items from the complement set. For example, in the asymptotic regime with the population size N → ∞, to identify L healthy items out of a population containing K defective items, when the tests are reliable, our results show that O (