文章基本信息

标题：A Fast Binary Splitting Approach to Non-Adaptive Group Testing
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作者：Eric Price ; Jonathan Scarlett
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：176
页码：13:1-13:20
DOI：10.4230/LIPIcs.APPROX/RANDOM.2020.13
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of n items and k defectives, we provide an algorithm attaining high-probability recovery with O(k log n) scaling in both the number of tests and runtime, improving on the best known O(kÂ² log k â<. log n) runtime previously available for any algorithm that only uses O(k log n) tests. Our algorithm bears resemblance to Hwangâs adaptive generalized binary splitting algorithm (Hwang, 1972); we recursively work with groups of items of geometrically vanishing sizes, while maintaining a list of "possibly defective" groups and circumventing the need for adaptivity. While the most basic form of our algorithm requires Î©(n) storage, we also provide a low-storage variant based on hashing, with similar recovery guarantees.
关键词：Group testing; sparsity; sublinear-time decoding; binary splitting