Abstract
We consider the problem of nonadaptive noiseless group testing of$N$ items of which$K$ are defective. We describe four detection algorithms, the${\tt COMP}$ algorithm of Chan et al. , two new algorithms,${\tt DD}$ and${\tt SCOMP}$, which require stronger evidence to declare an item defective, and an essentially optimal but computationally difficult algorithm called${\tt SSS}$. We consider an important class of designs for the group testing problem, namely those in which the test structure is given via a Bernoulli random process. In this class of Bernoulli designs, by considering the asymptotic rate of these algorithms, we show that${\tt DD}$ outperforms${\tt COMP}$, that${\tt DD}$ is essentially optimal in regimes where$K\geq\sqrt N$, and that no algorithm can perform as well as the best nonrandom adaptive algorithms when$K>N^{0.35}$. In simulations, we see that${\tt DD}$ and${\tt SCOMP}$ far outperform${\tt COMP}$, with${\tt SCOMP}$ very close to the optimal${\tt SSS}$, especially in cases with larger$K$.