Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Paper:

TR23-141 | 19th September 2023 21:54

A Tight Lower Bound of $\Omega(\log n)$ for the Estimation of the Number of Defective Items

RSS-Feed




TR23-141
Authors: Nader Bshouty, Gergely Harcos
Publication: 20th September 2023 09:15
Downloads: 247
Keywords: 


Abstract:

Let $X$ be a set of items of size $n$ , which may contain some defective items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive) if $Q$ contains at least one defective item, i.e., $Q\cap I \neq \emptyset$, and $0$ (negative) otherwise.

We give a novel approach to obtaining tight lower bounds in non-adaptive randomized group testing. Employing this new method, we can prove the following result.

Any non-adaptive randomized algorithm that, for any set of defective items $I$, with probability at least $2/3$, returns an estimate of the number of defective items $|I|$ to within a constant factor requires at least
$\Omega({\log n})$ tests.

Our result matches the upper bound of $O(\log n)$ and solves the open problem posed by Damaschke and Sheikh Muhammad.



ISSN 1433-8092 | Imprint