Related papers: Information-theoretic and algorithmic thresholds f…
In the group-testing literature, efficient algorithms have been developed to minimize the number of tests required to identify all minimal "defective" sub-groups embedded within a larger group, using deterministic group splitting with a…
Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1-p. The goal is to identify N good items as quickly as possible. The following…
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…
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…
We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the…
We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…
We study the group testing problem with non-adaptive randomized algorithms. Several models have been discussed in the literature to determine how to randomly choose the tests. For a model ${\cal M}$, let $m_{\cal M}(n,d)$ be the minimum…
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…
Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the…
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 pandemics or epidemics, public health authorities need to rapidly test a large number of individuals, both to determine the line of treatment as well as to know the spread of infection to plan containment, mitigation and future…
This paper is based on the observation that, during Covid-19 epidemic, the choice of which individuals should be tested has an important impact on the effectiveness of selective confinement measures. This decision problem is closely related…
Testing symptomatic individuals for a disease can deliver treatment resources, if tests' results turn positive, which speeds up their treatment and might also decrease individuals' contacts to other ones. An imperfect test, however, might…
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…
Testing individuals for pathogens can affect the spread of epidemics. Understanding how individual-level processes of sampling and reporting test results can affect community- or population-level spread is a dynamical modeling question. The…
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…
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…
Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to identify all items by means of group testing. This is the generalized group testing problem (hereafter GGTP). In the case of…
Recent papers initiated the study of a generalization of group testing where the potentially contaminated sets are the members of a given hypergraph F=(V,E). This generalization finds application in contexts where contaminations can be…
In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…