存在删除情况下的组合分组测试
Combinatorial Group Testing in Presence of Deletions
AI总结：
本文首次研究抗删除噪声的非自适应组合分组测试，刻画了对抗性删除下成功识别缺陷物品的充要条件，并给出测试矩阵构造与高效恢复算法。
摘要：
分组测试研究旨在利用少量合并测试，从大规模群体中识别出一小组有缺陷物品的策略。既定技术已在从信道通信到高效识别COVID-19感染者的广泛应用中发挥巨大作用。尽管自20世纪40年代以来，对分组测试及其变体已有大量研究，但尚未研究对删除噪声具有鲁棒性的测试策略。许多实际系统会出现删除错误，例如无线通信和数据存储系统。此类测试结果的删除会导致测试之间出现异步，而当前的分组测试策略无法处理。在本工作中，我们率先开展对删除噪声具有鲁棒性的非自适应分组测试策略的研究。我们刻画了即使在特定测试输出被对抗性删除后仍能成功识别有缺陷物品的必要条件和充分条件。我们还提供了测试矩阵的构造以及一种高效的恢复算法。
英文摘要：
The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications ranging from channel communication to identifying COVID-19-infected individuals efficiently. Despite significant research on group testing and its variants since the 1940s, testing strategies robust to deletion noise have yet to be studied. Many practical systems exhibit deletion errors, for instance, in wireless communication and data storage systems. Such deletions of test outcomes lead to asynchrony between the tests, which the current group testing strategies cannot handle. In this work, we initiate the study of non-adaptive group testing strategies resilient to deletion noise. We characterize the necessary and sufficient conditions to successfully identify the defective items even after the adversarial deletion of certain test outputs. We also provide constructions of testing matrices along with an efficient recovery algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
