A tight lower bound on non-adaptive group testing estimation

09/19/2023

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by   Tsun-Ming Cheung, et al.

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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 fixed 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 a similar lower bound in the threshold query model.