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We consider non-adaptive threshold group testing for identification of up to $d$ defective items in a set of $n$ items, where a test is positive if it contains at least $2 \leq u \leq d$ defective items, and negative otherwise. The…
In a group testing scheme, a set of tests is designed to identify a small number $t$ of defective items that are present among a large number $N$ of items. Each test takes as input a group of items and produces a binary output indicating…
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…
The goal of non-adaptive group testing is to identify at most $d$ defective items from $N$ items, in which a test of a subset of $N$ items is positive if it contains at least one defective item, and negative otherwise. However, in many…
Given $d$ defective items in a population of $n$ items with $d \ll n$, in threshold group testing without gap, the outcome of a test on a subset of items is positive if the subset has at least $u$ defective items and negative otherwise,…
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…
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…
We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…
Group testing is an approach aimed at identifying up to $d$ defective items among a total of $n$ elements. This is accomplished by examining subsets to determine if at least one defective item is present. In our study, we focus on the…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
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…
In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m \ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used…
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…
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…
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…
This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive…
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…
Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find…
The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify…
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…