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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

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

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

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

We consider the problem of identifying the defectives from a population of items via a non-adaptive group testing framework with a random pooling-matrix design. We analyze the sufficient number of tests needed for approximate set…

Information Theory · Computer Science 2024-12-03 Sameera Bharadwaja H. , Chandra R. Murthy

In group testing, 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 testing, data…

Information Theory · Computer Science 2020-11-11 Nelvin Tan , Jonathan Scarlett

We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that…

Data Structures and Algorithms · Computer Science 2011-11-09 David Eppstein , Michael T. Goodrich , Daniel S. Hirschberg

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

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…

Information Theory · Computer Science 2023-07-19 Amin Emad , Olgica Milenkovic

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

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

Given $d$ defective items in a population of $n$ items with $d \ll n$, in threshold group testing without gap, the outcome of a test on a subset of items is positive if the subset has at least $u$ defective items and negative otherwise,…

Information Theory · Computer Science 2024-05-10 Thach V. Bui , Yeow Meng Chee , Van Khu Vu

In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m \ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used…

Information Theory · Computer Science 2020-09-28 Mahdi Cheraghchi , Vasileios Nakos

Group testing tackles the problem of identifying a population of $K$ defective items from a set of $n$ items by pooling groups of items efficiently in order to cut down the number of tests needed. The result of a test for a group of items…

Information Theory · Computer Science 2015-08-20 Kangwook Lee , Ramtin Pedarsani , Kannan Ramchandran

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

The group testing problem is concerned with identifying a small number $k \sim n^\theta$ for $\theta \in (0,1)$ of infected individuals in a large population of size $n$. At our disposal is a testing procedure that allows us to test groups…

Discrete Mathematics · Computer Science 2019-11-19 Max Hahn-Klimroth , Philipp Loick

Group testing is the combinatorial problem of identifying the defective items in a population by grouping items into test pools. Recently, nonadaptive group testing - where all the test pools must be decided on at the start - has been…

Information Theory · Computer Science 2013-01-31 Matthew Aldridge

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

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

The goal of non-adaptive group testing is to identify at most $d$ defective items from $N$ items, in which a test of a subset of $N$ items is positive if it contains at least one defective item, and negative otherwise. However, in many…

Information Theory · Computer Science 2018-03-19 Thach V. Bui , Tetsuya Kojima , Minoru Kuribayashi , Isao Echizen