Group testing enables the identification of a small subset of defective items within a larger population by performing tests on pools of items rather than on each item individually. Over the years, it has not only attracted attention from the academic community, but has also demonstrated its potential in addressing real-world problems such as infectious disease screening, drug discovery and manufacturing quality control. With the emergence of the COVID-19 pandemic, interest in group testing has grown further, particularly in non-adaptive testing, due to its time efficiency compared to adaptive approaches. This highlights the importance of improving the performance currently achievable in such a scheme. This article focuses on advancing the field of noiseless non-adaptive group testing. The main objective of this work is to study and maximize the probability of successfully identifying the subset of defective items while performing as few tests as possible. To this end, we first note current well-known decoding algorithms, as well as established test design strategies for assigning items to pools. From this review, we identify key opportunities for improvement that inform the development of new decoding algorithms. Specifically, we propose a novel method, Weighted Sequential Combinatorial Orthogonal Matching Pursuit (W-SCOMP), to enhance the efficiency of existing detection procedures. Theoretical results demonstrate that W-SCOMP outperforms other algorithms in noiseless non-adaptive group testing. Furthermore, we develop a simulation framework to model the group testing process and conduct comparative evaluations between the proposed and existing algorithms. The empirical results are consistent with the theoretical findings. Overall, our work expands the range of available decoding algorithms and contributes to the broader understanding of noiseless non-adaptive group testing.

翻译：群组检测通过对项目池而非单个项目进行测试，实现在大规模群体中识别少量缺陷项目的子集。多年来，它不仅吸引了学术界的关注，还在解决传染病筛查、药物发现和制造质量控制等实际问题中展现出潜力。随着COVID-19大流行的出现，群组检测因其相较于自适应方法的时间效率优势而受到进一步关注，特别是在非自适应检测领域。这突显了提升此类方案当前可达到性能的重要性。本文致力于推进无噪声非自适应群组检测领域的发展。本工作的主要目标是研究并最大化成功识别缺陷项目子集的概率，同时尽可能减少测试次数。为此，我们首先梳理了当前知名的解码算法，以及用于将项目分配至测试池的成熟测试设计策略。通过此综述，我们识别出关键改进方向，为开发新型解码算法提供依据。具体而言，我们提出了一种新方法——加权顺序组合正交匹配追踪（W-SCOMP），以提升现有检测流程的效率。理论结果表明，在无噪声非自适应群组检测中，W-SCOMP优于其他算法。此外，我们开发了一个模拟框架来建模群组检测过程，并对所提算法与现有算法进行了比较评估。实证结果与理论发现一致。总体而言，我们的工作拓展了可用解码算法的范围，并促进了对无噪声非自适应群组检测的更广泛理解。