Related papers: Group Testing with Probabilistic Tests: Theory, De…
We consider non-adaptive threshold group testing for identification of up to $d$ defective items in a set of $n$ items, where a test is positive if it contains at least $2 \leq u \leq d$ defective items, and negative otherwise. The…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and has numerous practical applications. One of the defining features of group testing is…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern…
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…
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…
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…
The problem of distributed matrix-vector product is considered, where the server distributes the task of the computation among $n$ worker nodes, out of which $L$ are compromised (but non-colluding) and may return incorrect results.…
In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m \ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used…
Group testing has recently attracted significant attention from the research community due to its applications in diagnostic virology. An instance of the group testing problem includes a ground set of individuals which includes a small…
We propose a novel infection spread model based on a random connection graph which represents connections between $n$ individuals. Infection spreads via connections between individuals and this results in a probabilistic cluster formation…
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 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 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 to identify infected individuals in a population using a smaller number of tests than individual testing. To achieve this, group testing algorithms commonly assume knowledge of the number of infected individuals;…
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…
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection…
In the group testing problem the aim is to identify a small set of $k\sim n^\theta$ infected individuals out of a population size $n$, $0<\theta<1$. We avail ourselves of a test procedure capable of testing groups of individuals, with the…
Group testing with inhibitors (GTI) introduced by Farach at al. is studied in this paper. There are three types of items, $d$ defectives, $r$ inhibitors and $n-d-r$ normal items in a population of $n$ items. The presence of any inhibitor in…
Group testing is one of the fundamental problems in coding theory and combinatorics in which one is to identify a subset of contaminated items from a given ground set. There has been renewed interest in group testing recently due to its…
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…