Non-adaptive group testing with inhibitors

Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, d defectives, r inhibitors and n-d-r normal items in a population of n items. The presence of any inhibitor in a test can prevent the expression of a defective. For this model, we propose a probabilistic non-adaptive pooling design with a low complexity decoding algorithm. We show that the sample complexity of the number of tests required for guaranteed recovery with vanishing error probability using the proposed algorithm scales as T = O(d log n) and equation in the regimes r = O(d) and d = o(r) respectively. In the former regime, the number of tests meets the lower bound order while in the latter regime, the number of tests is shown to exceed the lower bound order by a log r over d multiplicative factor. The decoding complexity of the proposed decoding algorithm scales as O(nT).