Related papers: Group Testing on General Set-Systems
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection…
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…
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…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
In epidemic or pandemic situations, resources for testing the infection status of individuals may be scarce. Although group testing can help to significantly increase testing capabilities, the (repeated) testing of entire populations can…
Population-wide screening is a powerful tool for controlling infectious diseases. Group testing enables such screening despite limited resources. Viral concentration of pooled samples are often positively correlated, either because…
Sample pooling consists in combining samples from multiple individuals into a single pool that is then tested using a unique test-kit. A positive test means that at least one individual within the pool is infected. Here, we propose an…
We have a large number of samples and we want to find the infected ones using as few number of tests as possible. We can use group testing which tells about a small group of people whether at least one of them is infected. Group testing is…
Group testing was conceived during World War II to identify soldiers infected with syphilis using as few tests as possible, and it has attracted renewed interest during the COVID-19 pandemic. A long-standing assumption in the probabilistic…
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…
In the {\sc Test Cover} problem we are given a hypergraph $H=(V, \mathcal{E})$ with $|V|=n, |\mathcal{E}|=m$, and we assume that $\mathcal{E}$ is a test cover, i.e. for every pair of vertices $x_i, x_j$, there exists an edge $e \in…
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…
This paper provides a short introduction to the group testing problem, and reviews various aspects of its statistical physics formulation. Two main issues are discussed: the optimal design of pools used in a two-stage testing experiment,…
We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noiseless, and the case when the measurements are…
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 identifying infected patients in a population, group testing is an effective method to reduce the number of tests and correct the test errors. In the group testing procedure, tests are performed on pools of specimens collected from…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
In this paper, an information theoretic analysis on non-adaptive group testing schemes based on sparse pooling graphs is presented. The binary status of the objects to be tested are modeled by i.i.d. Bernoulli random variables with…
In this paper, we study the problem of non-adaptive group testing, in which one seeks to identify which items are defective given a set of suitably-designed tests whose outcomes indicate whether or not at least one defective item was…
Group testing (GT) is the Boolean version of spare signal recovery and, due to its simplicity, a marketplace for ideas that can be brought to bear upon related problems, such as heavy hitters, compressed sensing, and multiple access…