Group testing enables to identify infected individuals in a population using a smaller number of tests than individual testing. To achieve this, group testing algorithms commonly assume knowledge of the number of infected individuals; nonadaptive and several adaptive algorithms fall in this category. Some adaptive algorithms, like binary splitting, operate without this assumption, but require a number of stages that may scale linearly with the size of the population. In this paper we contribute a new algorithm that enables a balance between the number of tests and the number of stages used, and which we term diagonal group testing. Diagonal group testing, like binary splitting, does not require knowledge of the number of infected individuals, yet unlike binary splitting, is order-optimal w.r.t. the expected number of tests it requires and is guaranteed to succeed in a small number of stages that scales at most logarithmically with the size of the population. Numerical evaluations, for diagonal group testing and a hybrid approach we propose, support our theoretical findings.

翻译：群体检测能够通过比个体检测更少的检测次数来识别群体中的感染者。为实现这一目标，群体检测算法通常需要假设感染者的数量；非自适应算法及多种自适应算法均属于此类。部分自适应算法（如二分分裂算法）可在无此假设条件下运行，但其所需的检测阶段数可能随群体规模线性增长。本文提出一种新型算法，可在检测次数与使用阶段数之间实现平衡，我们将其命名为对角群体检测。与二分分裂算法类似，对角群体检测无需知晓感染者数量，但与二分分裂算法不同的是，该方法在所需检测次数的期望值上具有阶数最优性，且能在至多随群体规模对数增长的少量阶段内保证成功。针对所提出的对角群体检测及其混合方法的数值评估结果支持了我们的理论发现。