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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

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Statistics Theory · Mathematics 2022-02-17 Jack Noonan , Anatoly Zhigljavsky

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

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 2018-10-05 Jonathan Scarlett

Group testing concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary…

Information Theory · Computer Science 2026-05-13 Daniel McMorrow , Nikhil Karamchandani , Sidharth Jaggi

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

We study the problem of estimating the number of defective items in adaptive Group testing by using a minimum number of queries. We improve the existing algorithm and prove a lower bound that show that, for constant estimation, the number…

Data Structures and Algorithms · Computer Science 2023-12-22 Nader H. Bshouty , Vivian E. Bshouty-Hurani , George Haddad , Thomas Hashem , Fadi Khoury , Omar Sharafy

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 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

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

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

Information Theory · Computer Science 2020-01-27 Steffen Bondorf , Binbin Chen , Jonathan Scarlett , Haifeng Yu , Yuda Zhao

Group testing is a long studied problem in combinatorics: A small set of $r$ ill people should be identified out of the whole ($n$ people) by using only queries (tests) of the form "Does set X contain an ill human?". In this paper we…

Data Structures and Algorithms · Computer Science 2008-04-29 Ely Porat , Amir Rothschild

Given $n$ items with at most $d$ of which being positive, instead of testing these items individually, the theory of combinatorial group testing aims to identify all positive items using as few tests as possible. This paper is devoted to a…

Information Theory · Computer Science 2016-10-26 Chong Shangguan , Gennian Ge

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

We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…

Data Structures and Algorithms · Computer Science 2007-11-14 Marc Mezard , Cristina Toninelli

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

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 has numerous practical applications. One of the defining features of group testing is…

Information Theory · Computer Science 2021-11-12 Bernard Teo , Jonathan Scarlett

We study the group testing problem with non-adaptive randomized algorithms. Several models have been discussed in the literature to determine how to randomly choose the tests. For a model ${\cal M}$, let $m_{\cal M}(n,d)$ be the minimum…

Machine Learning · Computer Science 2019-11-06 Nader H. Bshouty , George Haddad , Catherine A. Haddad-Zaknoon

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

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