论文标题
线性方案中的保守两阶段组测试
Conservative two-stage group testing in the linear regime
论文作者
论文摘要
受到COVID-19的应用程序的启发，我们考虑了一个两阶段组测试的变体，称为“保守”（或“琐事”）两阶段测试，其中每个声明为有缺陷的项目都必须通过在第二阶段进行确定确定。我们在线性方向上研究了这一点，在线性方面，在项目数量较大时固定了。我们研究了第一阶段的各种非适应性测试设计，并为所需的测试总数提供了新的下限。我们发现，Broder和Kumar（Arxiv：2004.01684）所研究的第一阶段设计，每项恒定测试和每次测试的恒定项目对于所有患病率都非常接近最佳，并且由于患病率趋于零，因此在极限上是最佳的。模拟备份理论结果。
Inspired by applications in testing for Covid-19, we consider a variant of two-stage group testing called "conservative" (or "trivial") two-stage testing, where every item declared to be defective must be definitively confirmed by being tested by itself in the second stage. We study this in the linear regime where the prevalence is fixed while the number of items is large. We study various nonadaptive test designs for the first stage, and derive a new lower bound for the total number of tests required. We find that a first-stage design as studied by Broder and Kumar (arXiv:2004.01684) with constant tests per item and constant items per test is extremely close to optimal for all prevalences, and is optimal in the limit as the prevalence tends to zero. Simulations back up the theoretical results.
