2023/09/19 by Tsun-Ming Cheung, Bshouty, Nader H., Cheung, Tsun-Ming +5
Medicine · Biochemistry, Genetics and Molecular Biology · Computer Science · #SARS-CoV-2 detection and testing #Advanced biosensing and bioanalysis techniques #Privacy-Preserving Technologies in Data
paper · pdf · doi:10.48550/arxiv.2309.10286
Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The group testing estimation problem concerns estimating the number of defective elements d in a collection of n total within a given factor. We primarily consider the classical query model, in which a query reveals whether the selected group of elements contains a defective one. We show that any non-adaptive randomized algorithm that estimates the value of d within a constant factor requires Ω(log n) queries. This confirms that a known O(log n) upper bound by Bshouty (2019) is tight and resolves a conjecture by Damaschke and Sheikh Muhammad (2010). Additionally, we prove similar matching upper and lower bounds in the threshold query model.