English
Related papers

Related papers: On Detecting Some Defective Items in Group Testing

200 papers

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 task of non-adaptive group testing is to identify up to $d$ defective items from $N$ items, where a test is positive if it contains at least one defective item, and negative otherwise. If there are $t$ tests, they can be represented as…

Information Theory · Computer Science 2020-01-07 Thach V. Bui , Minoru Kuribayashi , Tetsuya Kojima , Roghayyeh Haghvirdinezhad , Isao Echizen

In this paper, we introduce a variation of the group testing problem where each test is specified by an ordered subset of items and returns the first defective item in the specified order or returns null if there are no defectives. We refer…

Information Theory · Computer Science 2024-09-30 Waqar Mirza , Nikhil Karamchandani , Niranjan Balachandran

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

Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the…

Information Theory · Computer Science 2013-07-11 Sheng Cai , Mohammad Jahangoshahi , Mayank Bakshi , Sidharth Jaggi

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 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 this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…

Information Theory · Computer Science 2024-05-10 Thach V. Bui , 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 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

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

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

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 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

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

Information Theory · Computer Science 2023-09-19 Jonathan Scarlett , Oliver Johnson

\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

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

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

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