تقرير
A tight lower bound on non-adaptive group testing estimation
| العنوان: | A tight lower bound on non-adaptive group testing estimation |
|---|---|
| المؤلفون: | Bshouty, Nader H., Cheung, Tsun-Ming, Harcos, Gergely, Hatami, Hamed, Ostuni, Anthony |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Data Structures and Algorithms, F.2.2 |
| الوصف: | 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. Comment: This work is a merger of arXiv:2309.09613 and arXiv:2309.10286 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.10286 |
| رقم الأكسشن: | edsarx.2309.10286 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |