Related papers: A Diagonal Splitting Algorithm for Adaptive Group …
The group testing problem is concerned with identifying a small set of infected individuals in a large population. At our disposal is a testing procedure that allows us to test several individuals together. In an idealized setting, a test…
We study the problem usually referred to as group testing in the context of COVID-19. Given n samples collected from patients, how should we select and test mixtures of samples to maximize information and minimize the number of tests? Group…
The conventional model of disjunctive group testing assumes that there are several defective elements (or defectives) among a large population, and a group test yields the positive response if and only if the testing group contains at least…
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 the context of fault-detection problems, the objective is to identify all defective items among a set of $n$ binary-state items using the minimum number of tests. The {group testing} paradigm, which allows testing a subset of items in a…
Efficient two-stage group testing algorithms that are particularly suited for rapid and less-expensive DNA library screening and other large scale biological group testing efforts are investigated in this paper. The main focus is on novel…
The group testing problem consists of determining a sparse subset of defective items from within a larger set of items via a series of tests, where each test outcome indicates whether at least one defective item is included in the test. We…
Group testing can help maintain a widespread testing program using fewer resources amid a pandemic. In group testing, we are given $n$ samples, one per individual. These samples are arranged into $m < n$ pooled samples, where each pool is…
Detection of defective members of large populations has been widely studied in the statistics community under the name "group testing", a problem which dates back to World War II when it was suggested for syphilis screening. There the main…
Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease…
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…
Group testing is a useful method that has broad applications in medicine, engineering, and even in airport security control. Consider a finite population of $N$ items, where item $i$ has a probability $p_i$ to be defective. The goal is to…
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…
The group testing problem is concerned with identifying a small set of $k$ infected individuals in a large population of $n$ people. At our disposal is a testing scheme that can test groups of individuals. A test comes back positive if and…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern…
The principal goal of Group Testing (GT) is to identify a small subset of "defective" items from a large population, by grouping items into as few test pools as possible. The test outcome of a pool is positive if it contains at least one…
We formulate and analyze a stochastic threshold group testing problem motivated by biological applications. Here a set of $n$ items contains a subset of $d \ll n$ defective items. Subsets (pools) of the $n$ items are tested -- the test…
In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…
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…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…