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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

In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…

Information Theory · Computer Science 2023-03-21 Hesam Nikpey , Jungyeol Kim , Xingran Chen , Saswati Sarkar , Shirin Saeedi Bidokhti

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

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

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention…

Information Theory · Computer Science 2016-07-05 A. G. D'yachkov , I. V. Vorobyev , N. A. Polyanskii , V. Yu. Shchukin

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

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…

Data Structures and Algorithms · Computer Science 2021-12-24 Oliver Gebhard , Max Hahn-Klimroth , Olaf Parczyk , Manuel Penschuck , Maurice Rolvien , Jonathan Scarlett , Nelvin Tan

In this paper, we propose an efficient two-stage decoding algorithm for non-adaptive Group Testing (GT) with general correlated prior statistics. The proposed solution can be applied to any correlated statistical prior represented in…

Information Theory · Computer Science 2026-03-03 Ayelet C. Portnoy , Amit Solomon , Alejandro Cohen

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

We consider the isomorphism problem for hypergraphs taking as input two hypergraphs over the same set of vertices $V$ and a permutation group $\Gamma$ over domain $V$, and asking whether there is a permutation $\gamma \in \Gamma$ that…

Data Structures and Algorithms · Computer Science 2022-10-26 Daniel Neuen

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

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

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

Let $X$ be a set of items of size $n$ that contains some defective items, denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The outcome of a test is $1$ if $Q$ contains at least…

Data Structures and Algorithms · Computer Science 2023-08-16 Nader H. Bshouty

The basic goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. The outcome of a test on a subset of items is positive if the subset has at…

Information Theory · Computer Science 2021-08-24 Thach V. Bui , Mahdi Cheraghchi , Isao Echizen

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 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 propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and…

Information Theory · Computer Science 2021-03-18 Pavlos Nikolopoulos , Sundara Rajan Srinivasavaradhan , Tao Guo , Christina Fragouli , Suhas Diggavi

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 is an efficient method for testing a large population to detect infected individuals. In this paper, we consider an efficient adaptive two stage group testing scheme. Using a straightforward analysis, we characterize the…

Methodology · Statistics 2020-08-26 Arjun Kodialam