In the group testing problem the aim is to identify a small set of k ⁓ nθ infected individuals out of a population size n, 0 < θ < 1. We avail ourselves of a test procedure capable of testing groups of individuals, with the test returning a positive result if and only if at least one individual in the group is infected. The aim is to devise a test design with as few tests as possible so that the set of infected individuals can be identified correctly with high probability. We establish an explicit sharp information-theoretic/algorithmic phase transition minf for non-adaptive group testing, where all tests are conducted in parallel. Thus with more than minf tests the infected individuals can be identified in polynomial time with high probability, while learning the set of infected individuals is information-theoretically impossible with fewer tests. In addition, we develop an optimal adaptive scheme where the tests are conducted in two stages.

中文翻译：

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最佳组测试

在小组测试问题中，目标是确定一小组ķ⁓nθ受感染的个体超出人口规模n, 0 <θ< 1. 我们利用能够对个体群体进行检测的检测程序，当且仅当群体中至少有一个个体被感染时，检测才会返回阳性结果。目的是设计一种测试设计尽可能少的测试，以便能够以高概率正确识别受感染个体的集合。我们建立了明确的信息理论/算法相变米信息对于非自适应组测试，所有测试都是并行进行的。因此与超过米信息测试 感染者可以在多项式时间内以很高的概率被识别出来，而学习感染者的集合是信息化的——理论上不可能用更少的测试。此外，我们开发了一个最佳自适应方案，其中测试分两个阶段进行。