文章基本信息

标题：Information-Theoretic and Algorithmic Thresholds for Group Testing
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作者：Amin Coja-Oghlan ; Oliver Gebhard ; Max Hahn-Klimroth 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：132
页码：1-14
DOI：10.4230/LIPIcs.ICALP.2019.43
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one individual in the group is infected. With all tests conducted in parallel, what is the least number of tests required to identify the status of all individuals? In a recent test design [Aldridge et al. 2016] the individuals are assigned to test groups randomly, with every individual joining an equal number of groups. We pinpoint the sharp threshold for the number of tests required in this randomised design so that it is information-theoretically possible to infer the infection status of every individual. Moreover, we analyse two efficient inference algorithms. These results settle conjectures from [Aldridge et al. 2014, Johnson et al. 2019].
关键词：Group testing problem; phase transitions; information theory; efficient algorithms; sharp threshold; Bayesian inference