Related papers: Near-Optimal Noisy Group Testing via Separate Deco…
An information theoretic perspective on group testing problems has recently been proposed by Atia and Saligrama, in order to characterise the optimal number of tests. Their results hold in the noiseless case, where only false positives…
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…
Group testing enables the identification of a small subset of defective items within a larger population by performing tests on pools of items rather than on each item individually. Over the years, it has not only attracted attention from…
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…
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…
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 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…
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…
We consider the nonadaptive group testing with N items, of which $K = \Theta(N^\theta)$ are defective. We study a test design in which each item appears in nearly the same number of tests. For each item, we independently pick L tests…
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…
We study the problem of identifying a small set $k\sim n^\theta$, $0<\theta<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is…
We study the problem of determining exactly the number of defective items in an adaptive Group testing by using a minimum number of tests. We improve the existing algorithm and prove a lower bound that shows that the number of tests in our…
We consider the problem of identifying the defectives from a population of items via a non-adaptive group testing framework with a random pooling-matrix design. We analyze the sufficient number of tests needed for approximate set…
In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main…
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…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
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…
The 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 $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our…
In the group testing problem, the goal is to identify a subset of defective items within a larger set of items based on tests whose outcomes indicate whether any defective item is present. This problem is relevant in areas such as medical…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…