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Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the…

Computation · Statistics 2024-05-16 Hiroyasu Matsushima , Yusuke Tajima , Xiao-Nan Lu , Masakazu Jimbo

We study the problem of identifying defective units in a finite population of \( n \) units, where each unit \( i \) is independently defective with known probability \( p_i \). This setting is referred to as the \emph{Generalized Group…

Statistics Theory · Mathematics 2025-06-23 Yaakov Malinovsky , Viktor Skorniakov

We study the problem of determining exactly the number of defective items in an adaptive Group testing by using a minimum number of tests. We improve the existing algorithm and prove a lower bound that shows that the number of tests in our…

Information Theory · Computer Science 2020-01-03 Nader H. Bshouty , Catherine A. Haddad-Zaknoon , Raghd Boulos , Foad Moalem , Jalal Nada , Elias Noufi , Yara Zaknoon

We consider non-adaptive threshold group testing for identification of up to $d$ defective items in a set of $n$ items, where a test is positive if it contains at least $2 \leq u \leq d$ defective items, and negative otherwise. The…

Information Theory · Computer Science 2018-09-25 Thach V. Bui , Minoru Kuribayashi , Mahdi Cheraghchi , Isao Echizen

In this paper, we derive mutual information based upper and lower bounds on the number of nonadaptive group tests required to identify a given number of "non defective" items from a large population containing a small number of "defective"…

Information Theory · Computer Science 2016-03-01 Abhay Sharma , Chandra R. Murthy

Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…

Information Theory · Computer Science 2021-07-16 Gabriel Arpino , Nicolò Grometto , Afonso S. Bandeira

\emph{Group Testing} (GT) addresses the problem of identifying a small subset of defective items from a large population, by grouping items into as few test pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can…

Information Theory · Computer Science 2020-08-17 Alejandro Cohen , Asaf Cohen , Omer Gurewitz

Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based…

Information Theory · Computer Science 2016-11-18 Mahdi Cheraghchi , Ali Hormati , Amin Karbasi , Martin Vetterli

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…

Data Structures and Algorithms · Computer Science 2021-12-24 Oliver Gebhard , Max Hahn-Klimroth , Olaf Parczyk , Manuel Penschuck , Maurice Rolvien , Jonathan Scarlett , Nelvin Tan

The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify…

Applications · Statistics 2021-06-10 Emilien Joly , Bastien Mallein

Non-adaptive group testing involves grouping arbitrary subsets of $n$ items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to…

Discrete Mathematics · Computer Science 2011-07-26 Mahdi Cheraghchi , Amin Karbasi , Soheil Mohajer , Venkatesh Saligrama

In the problem of classical group testing one aims to identify a small subset (of size $d$) diseased individuals/defective items in a large population (of size $n$). This process is based on a minimal number of suitably-designed group tests…

Information Theory · Computer Science 2022-09-26 Xiwei Cheng , Sidharth Jaggi , Qiaoqiao Zhou

We study the problem of estimating the number of defective items in adaptive Group testing by using a minimum number of queries. We improve the existing algorithm and prove a lower bound that show that, for constant estimation, the number…

Data Structures and Algorithms · Computer Science 2023-12-22 Nader H. Bshouty , Vivian E. Bshouty-Hurani , George Haddad , Thomas Hashem , Fadi Khoury , Omar Sharafy

We consider a new group testing model wherein each item is a binary random variable defined by an a priori probability of being defective. We assume that each probability is small and that items are independent, but not necessarily…

Information Theory · Computer Science 2018-07-24 Tongxin Li , Chun Lam Chan , Wenhao Huang , Tarik Kaced , Sidharth Jaggi

Let $X$ be a set of items of size $n$ that contains 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 outcome of a test is $1$ if $Q$ contains at least…

Data Structures and Algorithms · Computer Science 2023-08-16 Nader H. Bshouty

We consider the problem of non-adaptive group testing of $N$ items out of which $K$ or less items are known to be defective. We propose a testing scheme based on left-and-right-regular sparse-graph codes and a simple iterative decoder. We…

Information Theory · Computer Science 2017-01-27 Avinash Vem , Nagaraj T. Janakiraman , Krishna R. Narayanan

The group testing problem consists of determining a sparse subset of defective items from within a larger set of items via a series of tests, where each test outcome indicates whether at least one defective item is included in the test. We…

Information Theory · Computer Science 2026-04-24 Daniel McMorrow , Jonathan Scarlett

In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the…

Combinatorics · Mathematics 2012-04-09 Dániel Gerbner , Balázs Keszegh , Dömötör Pálvölgyi , Gábor Wiener

The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no…

Information Theory · Computer Science 2026-05-15 Matthew Aldridge , Oliver Johnson , Jonathan Scarlett

The basic goal in combinatorial group testing is to identify a set of up to $d$ defective items within a large population of size $n \gg d$ using a pooling strategy. Namely, the items can be grouped together in pools, and a single…

Discrete Mathematics · Computer Science 2013-01-21 Mahdi Cheraghchi