Related papers: Random and quasi-random designs in group testing
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
In group testing, simple binary-output tests are designed to identify a small number $t$ of defective items that are present in a large population of $N$ items. Each test takes as input a group of items and produces a binary output…
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…
Group testing is the process of pooling arbitrary subsets from a set of $n$ items so as to identify, with a minimal number of tests, a "small" subset of $d$ defective items. In "classical" non-adaptive group testing, it is known that when…
In a \emph{group testing} scheme, a set of tests is designed to identify a small number $t$ of defective items among a large set (of size $N$) of items. In the non-adaptive scenario the set of tests has to be designed in one-shot. In this…
Group testing techniques are widely used in resource-constrained settings, such as infectious-disease screening, blood safety, DNA library screening, and industrial inspection, where the efficient use of limited testing resources depends…
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…
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 construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2…
We consider the problem of identifying the defectives from a population of items via a non-adaptive group testing framework with a random pooling-matrix design. We analyze the sufficient number of tests needed for approximate set…
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…
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 is a long studied problem in combinatorics: A small set of $r$ ill people should be identified out of the whole ($n$ people) by using only queries (tests) of the form "Does set X contain an ill human?". In this paper we…
We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is…
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…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
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 identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…