English
Related papers

Related papers: Threshold Decoding for Disjunctive Group Testing

200 papers

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

The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new…

Information Theory · Computer Science 2015-03-13 George Kamal Atia , Venkatesh Saligrama

A binary code is said to be a disjunctive list-decoding $s_L$-code (LD $s_L$-code), $s \ge 2$, $L \ge 1$, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any $s$ sets…

Information Theory · Computer Science 2015-03-31 Arkadii D'yachkov , Ilya Vorobyev , Nikita Polyanskii , Vladislav Shchukin

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 Group Testing, the objective is to identify $K$ defective items out of $N$, $K\ll N$, by testing pools of items together and using the least amount of tests possible. Recently, a fast decoding method based on binary splitting (Price and…

Information Theory · Computer Science 2025-01-23 Xiaxin Li , Arya Mazumdar

In the problem of classical group testing one aims to identify a small subset (of size $d$) diseased individuals/defective items in a large population (of size $n$). This process is based on a minimal number of suitably-designed group tests…

Information Theory · Computer Science 2022-09-26 Xiwei Cheng , Sidharth Jaggi , Qiaoqiao Zhou

The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify…

Applications · Statistics 2021-06-10 Emilien Joly , Bastien Mallein

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

We consider the nonadaptive group testing with N items, of which $K = \Theta(N^\theta)$ are defective. We study a test design in which each item appears in nearly the same number of tests. For each item, we independently pick L tests…

Information Theory · Computer Science 2018-09-26 Oliver Johnson , Matthew Aldridge , Jonathan Scarlett

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

We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…

Information Theory · Computer Science 2020-09-08 Nader H. Bshouty , Catherine A. Haddad-Zaknoon

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 principal goal of Group Testing (GT) is to identify a small subset of "defective" items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one…

Information Theory · Computer Science 2020-08-13 Alejandro Cohen , Asaf Cohen , Omer Gurewitz

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main…

Information Theory · Computer Science 2016-03-01 Abhay Sharma , Chandra R. Murthy

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 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 at least one defective item is present. This problem is relevant in areas such as medical…

Information Theory · Computer Science 2022-10-24 Eric Price , 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

The disjointness of a stabilizer code is a quantity used to constrain the level of the logical Clifford hierarchy attainable by transversal gates and constant-depth quantum circuits. We show that for any positive integer constant $c$, the…

Quantum Physics · Physics 2025-09-30 John Bostanci , Aleksander Kubica

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

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