Related papers: Small-Error Cascaded Group Testing
The motivation for this paper comes from the ongoing SARS-CoV-2 Pandemic. Its goal is to present a previously neglected approach to non-adaptive group testing and describes it in terms of residuated pairs on partially ordered sets. Our…
In group testing, the task is to determine the distinguished members of a set of objects L by asking subset queries of the form ``does the subset Q of L contain a distinguished object?'' The primary biological application of group testing…
Group testing enables to identify infected individuals in a population using a smaller number of tests than individual testing. To achieve this, group testing algorithms commonly assume knowledge of the number of infected individuals;…
Non-adaptive group testing refers to the problem of inferring a sparse set of defectives from a larger population using the minimum number of simultaneous pooled tests. Recent positive results for noiseless group testing have motivated the…
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…
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.…
In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…
Group testing is a well-known search problem that consists in detecting of $s$ defective members of a set of $t$ samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all…
Group testing enables the identification of a small subset of defective items within a larger population by performing tests on pools of items rather than on each item individually. Over the years, it has not only attracted attention from…
The 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 $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our…
The goal of group testing is to identify a small number of defective items within a large population. In the non-adaptive setting, tests are designed in advance and represented by a measurement matrix $\mM$, where rows correspond to tests…
We consider the problem of non-adaptive group testing of $N$ items out of which $K$ or less items are known to be defective. We propose a testing scheme based on left-and-right-regular sparse-graph codes and a simple iterative decoder. We…
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…
In industrial engineering and manufacturing, quality control is an essential part of the production process of a product. To ensure proper functionality of a manufactured good, rigorous testing has to be performed to identify defective…
In combinatorial group testing problems Questioner needs to find a defective element $x\in [n]$ by testing subsets of $[n]$. In [18] the authors introduced a new model, where each element knows the answer for those queries that contain it…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and…
We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We…
Group testing is a well known search problem that consists in detecting up to $s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on properly chosen subsets of $[t]$. In classical group testing the goal is to find…
Group testing is a well known search problem that consists in detecting up to $s$ defective elements of the set $[t]=\{1,\ldots,t\}$ by carrying out tests on properly chosen subsets of $[t]$. In classical group testing the goal is to find…
We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…