Abstract
In Classical group testing, one is given a population of n items N which contains some defective d items inside. A group test (pool) is a test on a subset of N. Under the circumstance of no errors, a test is negative if the testing pool contains no defective items and the test is positive if the testing pool contains at least one defective item but we don’t know which one. The goal is to find all defectives by using as less tests as possible, mainly to minimize the number of tests (in the worst case situation). Let M(d, n) denote the minimum number of tests in the worst case situation where \(|N|=n\) and d is the number of defectives. In this paper, we focus on estimating M(d, n) and obtain a better result than known ones in various cases of d and n.
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Acknowledgements
The authors are grateful to the reviewers for carefully reading the manuscripts and making helpful comments. Also, we appreciate the suggestions of Kuo-Ching Hwang and Wu-Hsiung Lin in writing this article
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Lu, J., Fu, HL. Quaternary splitting algorithm in group testing. J Comb Optim 41, 73–79 (2021). https://doi.org/10.1007/s10878-020-00661-6
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DOI: https://doi.org/10.1007/s10878-020-00661-6