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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

In a group testing scheme, a set of tests is designed to identify a small number $t$ of defective items that are present among a large number $N$ of items. Each test takes as input a group of items and produces a binary output indicating…

Information Theory · Computer Science 2016-11-17 Arya Mazumdar

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

Group testing was conceived during World War II to identify soldiers infected with syphilis using as few tests as possible, and it has attracted renewed interest during the COVID-19 pandemic. A long-standing assumption in the probabilistic…

Social and Information Networks · Computer Science 2022-11-18 Surin Ahn , Wei-Ning Chen , Ayfer Ozgur

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 group testing, the task is to determine the distinguished members of a set of objects L by asking subset queries of the form ``does the subset Q of L contain a distinguished object?'' The primary biological application of group testing…

Combinatorics · Mathematics 2008-02-03 Emanuel Knill , S. Muthukrishnan

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

An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…

Combinatorics · Mathematics 2016-09-06 Emanuel Knill

We consider a version of the classical group testing problem motivated by PCR testing for COVID-19. In the so-called tropical group testing model, the outcome of a test is the lowest cycle threshold (Ct) level of the individuals pooled…

Information Theory · Computer Science 2024-10-15 Vivekanand Paligadu , Oliver Johnson , Matthew Aldridge

The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications…

Information Theory · Computer Science 2025-01-23 Venkata Gandikota , Nikita Polyanskii , Haodong Yang

In the context of fault-detection problems, the objective is to identify all defective items among a set of $n$ binary-state items using the minimum number of tests. The {group testing} paradigm, which allows testing a subset of items in a…

Combinatorics · Mathematics 2025-11-18 Jun Wu , Yongxi Cheng , Zhen Yang , Feng Chu , Junkai He

We study a class of hypothesis testing problems in which, upon observing the realization of an $n$-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal distribution or, alternatively, whether…

Statistics Theory · Mathematics 2010-11-22 Louigi Addario-Berry , Nicolas Broutin , Luc Devroye , Gábor Lugosi

In one-stage or non-adaptive group testing, instead of testing every sample unit individually, they are split, bundled in pools, and simultaneously tested. The results are then decoded to infer the states of the individual items. This…

Applications · Statistics 2020-12-04 Christoph Schumacher , Matthias Täufer

We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…

Data Structures and Algorithms · Computer Science 2019-04-09 Pascal Schweitzer , Daniel Wiebking

Detection of defective members of large populations has been widely studied in the statistics community under the name "group testing", a problem which dates back to World War II when it was suggested for syphilis screening. There the main…

Information Theory · Computer Science 2009-09-28 Mahdi Cheraghchi , Ali Hormati , Amin Karbasi , Martin Vetterli

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

Union-free codes and disjunctive codes are two combinatorial structures, which are used in nonadaptive group testing to find a set of $d$ defective elements among $n$ samples by carrying out the minimal number of tests $t$. It is known that…

Information Theory · Computer Science 2022-01-13 Ilya Vorobyev

We study the problem of learning a hidden hypergraph $G=(V,E)$ by making a single batch of queries (non-adaptively). We consider the hyperedge detection model, in which every query must be of the form: ``Does this set $S\subseteq V$ contain…

Information Theory · Computer Science 2025-01-23 Bethany Austhof , Lev Reyzin , Erasmo Tani

Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…

Probability · Mathematics 2026-01-14 Remco van der Hofstad , Julia Komjathy , Viktoria Vadon

The goal of combinatorial group testing is to efficiently identify up to $d$ defective items in a large population of $n$ items, where $d \ll n$. Defective items satisfy certain properties while the remaining items in the population do not.…

Information Theory · Computer Science 2019-04-02 Thach V. Bui , Minoru Kuribayashi , Mahdi Cheraghchi , Isao Echizen