Related papers: Efficient Two-Stage Group Testing Algorithms for G…
The use of group testing to locate all instances of disease in a large population of blood samples was first considered seventy years ago. Since then, several methods have been used to approximate the minimum expected number of tests. 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…
Union-free codes and disjunctive codes are two combinatorial structures, which are used in nonadaptive group testing to find a set of $d$ defective elements among $n$ samples by carrying out the minimal number of tests $t$. It is known that…
We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…
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…
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…
Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to…
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…
The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible…
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 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…
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…
In this note, we present a new adaptive algorithm for generalized group testing, which is asymptotically optimal if $d=o(\log_2|E|)$, $E$ is a set of potentially contaminated sets, $d$ is a maximal size of elements of $E$. Also, we design a…
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…
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…
A family of variable stage size multistage tests of simple hypotheses is described, based on efficient multistage sampling procedures. Using a loss function that is a linear combination of sampling costs and error probabilities, these tests…
Multi-cancer early detection (MCED) tests offer to screen for multiple types of cancer with a single blood sample. Despite their promising diagnostic performance, evidence regarding their population benefit is not yet available. Expecting…
When fitting statistical models, some predictors are often found to be correlated with each other, and functioning together. Many group variable selection methods are developed to select the groups of predictors that are closely related to…
In confirmatory clinical trials, it has been proposed to use a simple iterative graphical approach to construct and perform intersection hypotheses tests with a weighted Bonferroni-type procedure to control type I errors in the strong…
Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the…