相关论文: Group testing with Random Pools: Phase Transitions…
Let $X$ be a set of items of size $n$ that contains some defective items, denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The outcome of a test is $1$ if $Q$ contains at least…
This paper considers the problem of Quantitative Group Testing (QGT) where there are some defective items among a large population of $N$ items. We consider the scenario in which each item is defective with probability $K/N$, independently…
Group testing is an efficient method for testing a large population to detect infected individuals. In this paper, we consider an efficient adaptive two stage group testing scheme. Using a straightforward analysis, we characterize the…
We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
Assessing risk of cascading failure in an electrical grid requires identifying many small "defective" subsets of the N elements in a power system, such that the simultaneous failure of all elements in a defective set triggers a large…
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…
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…
We study the group test for DNA library screening based on probabilistic approach. Group test is a method of detecting a few positive items from among a large number of items, and has wide range of applications. In DNA library screening,…
Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can…
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 the problem usually referred to as group testing in the context of COVID-19. Given $n$ samples taken from patients, how should we select mixtures of samples to be tested, so as to maximize information and minimize the number of…
In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $n$ items among which $k$ are defective, the…
Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…
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…
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…
The group testing problem asks for efficient pooling schemes and algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected samples while conducting the least…
Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and…
In this paper, we study the problem of non-adaptive group testing, in which one seeks to identify which items are defective given a set of suitably-designed tests whose outcomes indicate whether or not at least one defective item was…
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…