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In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $n$ items among which $k$ are defective, the…

Information Theory · Computer Science 2021-07-30 Wei Heng Bay , Eric Price , Jonathan Scarlett

In group testing, simple binary-output tests are designed to identify a small number $t$ of defective items that are present in a large population of $N$ items. Each test takes as input a group of items and produces a binary output…

Information Theory · Computer Science 2017-04-11 Alexander Barg , Arya Mazumdar

Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find…

Data Structures and Algorithms · Computer Science 2016-06-13 Annalisa De Bonis

The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…

Information Theory · Computer Science 2021-11-08 Thach V. Bui , Mahdi Cheraghchi , An T. H. Nguyen , Thuc D. Nguyen

In the group testing problem, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical…

Information Theory · Computer Science 2022-09-28 Nelvin Tan , Way Tan , Jonathan Scarlett

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 $Q$…

Data Structures and Algorithms · Computer Science 2023-09-19 Nader H. Bshouty , Gergely Harcos

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

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

We consider adaptive group testing in the linear regime, where the number of defective items scales linearly with the number of items. We analyse an algorithm based on generalized binary splitting. Provided fewer than half the items are…

Information Theory · Computer Science 2020-04-07 Matthew Aldridge

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

In this paper, we study the problem of non-adaptive group testing, in which one seeks to identify which items are defective given a set of suitably-designed tests whose outcomes indicate whether or not at least one defective item was…

Information Theory · Computer Science 2025-09-26 Lan V. Truong , Matthew Aldridge , Jonathan Scarlett

In probabilistic nonadaptive group testing (PGT), we aim to characterize the number of pooled tests necessary to identify a random $k$-sparse vector of defectives with high probability. Recent work has shown that $n$ tests are necessary…

Information Theory · Computer Science 2021-06-15 Larkin Flodin , Arya Mazumdar

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…

Data Structures and Algorithms · Computer Science 2023-12-08 Nader H. Bshouty , Tsun-Ming Cheung , Gergely Harcos , Hamed Hatami , Anthony Ostuni

Group testing is concerned with identifying $t$ defective items in a set of $m$ items, where each test reports whether a specific subset of items contains at least one defective. In non-adaptive group testing, the subsets to be tested are…

Computational Geometry · Computer Science 2020-12-03 Benjamin Aram Berendsohn , László Kozma

In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of $n$ items and $k$ defectives, we provide an algorithm attaining…

Information Theory · Computer Science 2020-06-19 Eric Price , Jonathan Scarlett

Group testing has recently attracted significant attention from the research community due to its applications in diagnostic virology. An instance of the group testing problem includes a ground set of individuals which includes a small…

Information Theory · Computer Science 2022-02-25 Esmaeil Karimi , Anoosheh Heidarzadeh , Krishna R. Narayanan , Alex Sprintson

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

The conventional model of disjunctive group testing assumes that there are several defective elements (or defectives) among a large population, and a group test yields the positive response if and only if the testing group contains at least…

Information Theory · Computer Science 2019-08-20 A. G. D'yachkov , N. A. Polyanskii , V. Yu. Shchukin , I. V. Vorobyev

In the group testing problem the aim is to identify a small set of $k\sim n^\theta$ infected individuals out of a population size $n$, $0<\theta<1$. We avail ourselves of a test procedure capable of testing groups of individuals, with the…

Discrete Mathematics · Computer Science 2021-05-14 Amin Coja-Oghlan , Oliver Gebhard , Max Hahn-Klimroth , Philipp Loick

The goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our…

Information Theory · Computer Science 2019-01-09 Thach V. Bui , Minoru Kuribayashi , Mahdi Cheraghchi , Isao Echizen