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arXiv · 2309.10286

A tight lower bound on non-adaptive group testing estimation

Nader H. Bshouty·Tsun-Ming Cheung·Gergely Harcos·Hamed Hatami·Anthony Ostuni
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Abstract

Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{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 $\Omega(\log n)$ 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.

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Nader H. Bshouty, Tsun-Ming Cheung, Gergely Harcos, Hamed Hatami, Anthony Ostuni. 2023-09-19. A tight lower bound on non-adaptive group testing estimation. https://arxiv.org/abs/2309.10286

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