Related papers: Construction of Almost Disjunct Matrices for Group…
The goal of the group testing problem is to identify a set of defective items within a larger set of items, using suitably-designed tests whose outcomes indicate whether any defective item is present. In this paper, we study how the number…
We consider an efficiently decodable non-adaptive group testing (NAGT) problem that meets theoretical bounds. The problem is to find a few specific items (at most $d$) satisfying certain characteristics in a colossal number of $N$ items as…
Identification of up to $d$ defective items and up to $h$ inhibitors in a set of $n$ items is the main task of non-adaptive group testing with inhibitors. To efficiently reduce the cost of this Herculean task, a subset of the $n$ items is…
Group testing is concerned with identifying $t$ defective items in a set of $m$ items, where each test reports whether a specific subset of items contains at least one defective. In non-adaptive group testing, the subsets to be tested are…
The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This…
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…
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…
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…
Combinatorial group testing (CGT) is used to identify defective items from a set of items by grouping them together and performing a small number of tests on the groups. Recently, group testing has been used to design efficient COVID-19…
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.…
We study the problem of identifying defective units in a finite population of \( n \) units, where each unit \( i \) is independently defective with known probability \( p_i \). This setting is referred to as the \emph{Generalized Group…
This paper proposes a novel generalization of group testing, called multi-group testing, which relaxes the notion of "testing subset" in group testing to "testing multi-set". The generalization aims to learn more information of each item to…
We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…
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…
We propose a novel group testing method, termed semi-quantitative group testing, motivated by a class of problems arising in genome screening experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary pooling scheme that…
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…
We develop a new notion called $(1-\epsilon)$-tester for a set $M$ of functions $f:A\to C$. A $(1-\epsilon)$-tester for $M$ maps each element $a\in A$ to a finite number of elements $B_a=\{b_1,\ldots,b_t\}\subset B$ in a smaller sub-domain…
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…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
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…