Related papers: Optimal Multistage Group Testing Algorithm for 3 D…
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…
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 consider the problem of non-adaptive group testing of $N$ items out of which $K$ or less items are known to be defective. We propose a testing scheme based on left-and-right-regular sparse-graph codes and a simple iterative decoder. We…
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and…
Non-adaptive group testing involves grouping arbitrary subsets of $n$ items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to…
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…
We describe group sequential tests which efficiently incorporate information from multiple endpoints allowing for early stopping at pre-planned interim analyses. We formulate a testing procedure where several outcomes are examined, and…
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…
We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies…
Decision making needs to take an uncertain environment into account. Over the last decades, robust optimization has emerged as a preeminent method to produce solutions that are immunized against uncertainty. The main focus in robust…
Inspired by applications in testing for Covid-19, we consider a variant of two-stage group testing called "conservative" (or "trivial") two-stage testing, where every item declared to be defective must be definitively confirmed by being…
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…
Given $p$ samples, each of which may or may not be defective, group testing (GT) aims to determine their defect status by performing tests on $n < p$ `groups', where a group is formed by mixing a subset of the $p$ samples. Assuming that the…
In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…
When the infection prevalence of a disease is low, Dorfman showed 80 years ago that testing groups of people can prove more efficient than testing people individually. Our goal in this paper is to propose new group testing algorithms that…
Inspired by recent results from collusion-resistant traitor tracing, we provide a framework for constructing efficient probabilistic group testing schemes. In the traditional group testing model, our scheme asymptotically requires T ~ 2 K…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
The graph based approach to multiple testing is an intuitive method that enables a study team to represent clearly, through a directed graph, its priorities for hierarchical testing of multiple hypotheses, and for propagating the available…
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…
This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of…