一种易处理的非自适应非二值测量分组检验方法
A tractable non-adaptative group testing method for non-binary measurements
摘要：
分组测试的原始问题在于通过对项目组进行测试来识别集合中的缺陷项目，该测试检测该组中至少一个缺陷项目的存在。这样做的目的是通过尽可能少的测试来识别集合中的所有缺陷项目。这个问题与多个领域有关，其中包括生物学和计算机科学。在本文中，我们考虑应用于项目组的测试返回一个\emph{load}，测量该组中最有缺陷的项目的缺陷程度。在这种情况下，我们提出了一个简单的非自适应算法，允许检测的集合中的所有有缺陷的项目。该方法改进了经典的群测试算法，只使用测试的二进制响应。最近，群体检测作为解决COVID-19检测试剂盒（特别是RT-qPCR）短缺的潜在工具受到了关注。这些测试返回样本的病毒载量，病毒载量在个体之间差异很大。因此，我们的模型提出了这个问题的一些关键特征。我们的目标是使用额外的信息，代表病毒载量构建一个一阶段池测试算法在这个理想化的版本。我们表明，在正确的条件下，检测污染样品所需的测试总数可以大大减少。
英文摘要：
The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify all defective items of the collection with as few tests as possible. This problem is relevant in several fields, among which biology and computer sciences. In the present article we consider that the tests applied to groups of items returns a \emph{load}, measuring how defective the most defective item of the group is. In this setting, we propose a simple non-adaptative algorithm allowing the detection of all defective items of the collection. This method improves on classical group testing algorithms using only the binary response of the test. Group testing recently gained attraction as a potential tool to solve a shortage of COVID-19 test kits, in particular for RT-qPCR. These tests return the viral load of the sample and the viral load varies greatly among individuals. Therefore our model presents some of the key features of this problem. We aim at using the extra piece of information that represents the viral load to construct a one-stage pool testing algorithm on this idealized version. We show that under the right conditions, the total number of tests needed to detect contaminated samples can be drastically diminished.
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