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Related papers: Sparse Combinatorial Group Testing

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This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of $N$ items, where item $i$ has the probability $p$ ($p_i$ in the generalized group testing)…

Methodology · Statistics 2021-02-19 Yaakov Malinovsky , Paul S. Albert

In this paper, we study bounds on the minimum length of $(k,n,d)$-superimposed codes introduced by Agarwal et al. [1], in the context of Non-Adaptive Group Testing algorithms with runlength constraints. A $(k,n,d)$-superimposed code of…

Information Theory · Computer Science 2022-08-31 Stefano Della Fiore , Marco Dalai , Ugo Vaccaro

Let $G$ be a finite group. In order to determine the smallest cardinality $d(G)$ of a generating set of $G$ and a generating set with this cardinality, one should repeat many times the test whether a subset of $G$ of small cardinality…

Group Theory · Mathematics 2023-06-14 Andrea Lucchini , Dhara Thakkar

Group testing (GT) is the art of identifying binary signals and the marketplace for exchanging new ideas for related fields such as unique-element counting, compressed sensing, traitor tracing, and geno-typing. A GT scheme can be…

Information Theory · Computer Science 2024-05-28 Hsin-Po Wang , Venkatesan Guruswami

In multistage group testing, the tests within the same stage are considered nonadaptive, while those conducted across different stages are adaptive. Specifically, when the pools within the same stage are disjoint, meaning that the entire…

Information Theory · Computer Science 2025-07-10 Guojiang Shao

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

We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…

Machine Learning · Statistics 2022-06-16 Amin Coja-Oghlan , Oliver Gebhard , Max Hahn-Klimroth , Alexander S. Wein , Ilias Zadik

We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…

Information Theory · Computer Science 2012-02-13 Mahdi Cheraghchi

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

We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…

Information Theory · Computer Science 2022-11-08 Anand Jerry George , Clément L. Canonne

Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…

Group Theory · Mathematics 2024-07-01 Michael Chapman , Irit Dinur , Alexander Lubotzky

The minimax sample complexity of group distributionally robust optimization (GDRO) has been determined up to a $\log(K)$ factor, where $K$ is the number of groups. In this work, we venture beyond the minimax perspective via a novel notion…

Machine Learning · Computer Science 2025-02-03 Quan Nguyen , Nishant A. Mehta , Cristóbal Guzmán

Up to date, only lower and upper bounds for the optimal configuration of a Square Array (A2) Group Testing (GT) algorithm are known. We establish exact analytical formulae and provide a couple of applications of our result. First, we…

Statistics Theory · Mathematics 2023-04-18 Ugnė Čižikovienė , Viktor Skorniakov

Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the…

Computation · Statistics 2024-05-16 Hiroyasu Matsushima , Yusuke Tajima , Xiao-Nan Lu , Masakazu Jimbo

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

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…

Machine Learning · Computer Science 2024-06-26 Rares-Darius Buhai , Jingqiu Ding , Stefan Tiegel

The problem of distributed matrix-vector product is considered, where the server distributes the task of the computation among $n$ worker nodes, out of which $L$ are compromised (but non-colluding) and may return incorrect results.…

Information Theory · Computer Science 2023-05-12 Sarthak Jain , Martina Cardone , Soheil Mohajer

Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease…

Quantitative Methods · Quantitative Biology 2023-08-03 Ananthan Nambiar , Chao Pan , Vishal Rana , Mahdi Cheraghchi , João Ribeiro , Sergei Maslov , Olgica Milenkovic

Among the challenges that the COVID-19 pandemic outbreak revealed is the problem to reduce the number of tests required for identifying the virus carriers in order to contain the viral spread while preserving the tests reliability. To cope…

Information Theory · Computer Science 2021-12-24 Catherine A. Haddad-Zaaknoon

In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff…

Discrete Mathematics · Computer Science 2021-05-14 Amin Coja-Oghlan , Oliver Gebhard , Max Hahn-Klimroth , Philipp Loick