In many fault detection problems, we want to identify defective items from a set of $n$ items using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In practice, the number $d$ of defective items is often unknown in advance. In this paper, we improve the previously best algorithm for a central problem in combinatorial group testing with unknown number of defectives (Cheng et al., 2014), and prove that the number of tests used by our new algorithm is no more than $dlog\frac{n}{d}+(5-log5)d+O\left({log}^{2}d\right)$, where $log$ is of base 2.

在许多故障检测问题中，我们希望从一组 $n$使用最少测试次数的项目。组测试适用于每个测试针对项目子集的场景，并判断该子集是否包含至少一个有缺陷的项目。在实践中，数$d$有缺陷的物品通常是事先不知道的。在本文中，我们改进了先前针对缺陷数未知的组合组测试中的中心问题的最佳算法（Cheng et al., 2014），并证明我们的新算法使用的测试数量不超过$d日志\frac{n}{d}+(5-日志5)d+○\left({日志}^{2}d\right)$， 在哪里 $日志$ 是基数 2。