We study the problem of identifying a small set $k\sim n^\theta$, $0<\theta<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is to minimise the total number of tests required. In this paper we make the (realistic) assumption that tests are noisy, i.e.\ that a group that contains an infected individual may return a negative test result or one that does not contain an infected individual may return a positive test results with a certain probability. The noise need not be symmetric. We develop an algorithm called SPARC that correctly identifies the set of infected individuals up to $o(k)$ errors with high probability with the asymptotically minimum number of tests. Additionally, we develop an algorithm called SPEX that exactly identifies the set of infected individuals w.h.p. with a number of tests that matches the information-theoretic lower bound for the constant column design, a powerful and well-studied test design.

翻译：我们研究在包含n个个体的庞大群体中，通过同时检测多个个体组成的混合样本，识别规模k∼n^θ（0<θ<1）的小规模感染者集合的问题。所有检测同时进行。目标是最小化所需的总检测次数。本文基于现实假设：检测存在噪声，即包含感染者的样本可能以一定概率返回阴性结果，而不含感染者的样本也可能以一定概率返回阳性结果。噪声不必对称。我们提出名为SPARC的算法，该算法能以最少检测次数（渐近最优）高概率识别感染者集合，错误数仅为o(k)。此外，我们提出名为SPEX的算法，能在恒定列设计（一种高效且广泛研究的检测设计）中，以与信息论下界匹配的检测次数高精度识别感染者集合。