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：群体检测能够以比个体检测更少的测试次数识别出群体中的受感染个体。为实现这一目标，群体检测算法通常需要预知受感染个体的数量；非自适应和多种自适应算法均属于此类。某些自适应算法（如二分分割）无需此假设即可运行，但其所需阶段数可能随群体规模线性增长。本文提出一种新算法，可在测试次数与使用阶段数之间实现平衡，并将其命名为对角群体检测。与二分分割类似，对角群体检测无需预知受感染个体数量；然而不同于二分分割，该算法在期望测试次数方面达到阶数最优，且能保证在最多与群体规模呈对数增长的少量阶段内成功完成。针对所提出的对角群体检测及混合方法的数值评估结果支持了我们的理论发现。