Related papers: Noisy Linear Group Testing: Exact Thresholds and E…
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…
Group-testing refers to the problem of identifying (with high probability) a (small) subset of $D$ defectives from a (large) set of $N$ items via a "small" number of "pooled" tests. For ease of presentation in this work we focus on the…
In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the…
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…
We study the problem of estimating the number of defective items in adaptive Group testing by using a minimum number of queries. We improve the existing algorithm and prove a lower bound that show that, for constant estimation, the number…
In group testing, 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 testing, data…
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…
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…
In this paper, we introduce a variation of the group testing problem capturing the idea that a positive test requires a combination of multiple ``types'' of item. Specifically, we assume that there are multiple disjoint \emph{semi-defective…
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…
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…
In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…
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…
In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…
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 concerns itself with the accurate recovery of a set of "defective" items from a larger population via a series of tests. While most works in this area have considered the classical group testing model, where tests are binary…
Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based…
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…
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…
In this paper, we introduce a variation of the group testing problem where each test is specified by an ordered subset of items and returns the first defective item in the specified order or returns null if there are no defectives. We refer…