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The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible…

Statistical Mechanics · Physics 2009-11-13 M. Mézard , M. Tarzia , C. Toninelli

We consider nonadaptive probabilistic group testing in the linear regime, where each of n items is defective independently with probability p in (0,1), and p is a constant independent of n. We show that testing each item individually is…

Information Theory · Computer Science 2025-09-26 Matthew Aldridge

The goal of the group testing problem is to identify a set of defective items within a larger set of items, using suitably-designed tests whose outcomes indicate whether any defective item is present. In this paper, we study how the number…

Information Theory · Computer Science 2023-01-18 Ivan Lau , Jonathan Scarlett , Yang Sun

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and…

Information Theory · Computer Science 2019-01-30 Jonathan Scarlett , Volkan Cevher

Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, $d$ defectives, $r$ inhibitors and $n-d-r$ normal items in a population of $n$ items. The presence of any inhibitor in…

Information Theory · Computer Science 2014-12-16 Abhinav Ganesan , Javad Ebrahimi , Sidharth Jaggi , Venkatesh Saligrama

We consider the probabilistic group testing problem where $d$ random defective items in a large population of $N$ items are identified with high probability by applying binary tests. It is known that $\Theta(d \log N)$ tests are necessary…

Information Theory · Computer Science 2019-02-27 Huseyin A. Inan , Peter Kairouz , Mary Wootters , Ayfer Ozgur

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 consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the…

Information Theory · Computer Science 2017-10-24 Chao Wang , Qing Zhao , Chen-Nee Chuah

We study the problem of group testing with a non-adaptive randomized algorithm in the random incidence design (RID) model where each entry in the test is chosen randomly independently from $\{0,1\}$ with a fixed probability $p$. The…

Machine Learning · Computer Science 2017-08-10 Nader H. Bshouty , Nuha Diab , Shada R. Kawar , Robert J. Shahla

The goal of group testing is to identify a small number of defective items within a large population. In the non-adaptive setting, tests are designed in advance and represented by a measurement matrix $\mM$, where rows correspond to tests…

Information Theory · Computer Science 2025-09-10 Trung-Khang Tran , Thach V. Bui

In the group-testing literature, efficient algorithms have been developed to minimize the number of tests required to identify all minimal "defective" sub-groups embedded within a larger group, using deterministic group splitting with a…

Discrete Mathematics · Computer Science 2020-10-20 Laurence A. Clarfeld , Margaret J. Eppstein

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

In the classical combinatorial (adaptive) group testing problem, one is given two integers \(d\) and \(n\), where \(0\le d\le n\), and a population of \(n\) items, exactly \(d\) of which are known to be defective. The question is to devise…

Combinatorics · Mathematics 2014-07-24 David Cariolaro , Zhaiming Shen , Yi Zhang

In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…

Combinatorics · Mathematics 2021-10-15 Bingchen Qian , Xin Wang , Gennian Ge

We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give…

Information Theory · Computer Science 2015-02-04 Tom Kealy , Oliver Johnson , Robert Piechocki

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

We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We…

Information Theory · Computer Science 2021-08-30 Mustafa Doger , Sennur Ulukus

In industrial engineering and manufacturing, quality control is an essential part of the production process of a product. To ensure proper functionality of a manufactured good, rigorous testing has to be performed to identify defective…

Methodology · Statistics 2025-04-02 Michael Balzer

We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies…

Information Theory · Computer Science 2021-02-11 Gianluigi Liva , Enrico Paolini , Marco Chiani

Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the…

Information Theory · Computer Science 2016-01-26 A. G. D'yachkov , I. V. Vorobyev , N. A. Polyanskii , V. Yu. Shchukin