Related papers: Optimal Multistage Group Testing Algorithm for 3 D…
We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give…
We study group-testing algorithms for resolving broadcast conflicts on a multiple access channel (MAC) and for identifying the dead sensors in a mobile ad hoc wireless network. In group-testing algorithms, we are asked to identify all the…
In the problem of classical group testing one aims to identify a small subset (of size $d$) diseased individuals/defective items in a large population (of size $n$). This process is based on a minimal number of suitably-designed group tests…
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…
We consider some computationally efficient and provably correct algorithms with near-optimal sample-complexity for the problem of noisy non-adaptive group testing. Group testing involves grouping arbitrary subsets of items into pools. Each…
The basic goal in combinatorial group testing is to identify a set of up to $d$ defective items within a large population of size $n \gg d$ using a pooling strategy. Namely, the items can be grouped together in pools, and a single…
The goal of combinatorial group testing is to efficiently identify up to $d$ defective items in a large population of $n$ items, where $d \ll n$. Defective items satisfy certain properties while the remaining items in the population do not.…
Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of…
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 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…
When $k$ factors each taking one of $v$ levels may affect the correctness or performance of a complex system, a test is selected by setting each factor to one of its levels and determining whether the system functions as expected (passes…
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 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…
The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications…
Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1-p. The goal is to identify N good items as quickly as possible. The following…
\emph{Group Testing} (GT) addresses the problem of identifying a small subset of defective items from a large population, by grouping items into as few test pools as possible. In \emph{Adaptive GT} (AGT), outcomes of previous tests can…
In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff…
The task of non-adaptive group testing is to identify up to $d$ defective items from $N$ items, where a test is positive if it contains at least one defective item, and negative otherwise. If there are $t$ tests, they can be represented as…
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…
Given $d$ defective items in a population of $n$ items with $d \ll n$, in threshold group testing without gap, the outcome of a test on a subset of items is positive if the subset has at least $u$ defective items and negative otherwise,…