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Group testing is a well-known search problem that consists in detecting of $s$ defective members of a set of $t$ samples by carrying out tests on properly chosen subsets of samples. In classical group testing the goal is to find all…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
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…
The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no…
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…
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…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
The goal of the group testing problem is to identify a set of defective items within a larger set of items, using suitably-designed tests whose outcomes indicate whether any defective item is present. In this paper, we study how the number…
We modify Cheraghchi-Nakos [CN20] and Price-Scarlett's [PS20] fast binary splitting approach to nonadaptive group testing. We show that, to identify a uniformly random subset of $k$ infected persons among a population of $n$, it takes only…
In order to identify the infected individuals of a population, their samples are divided in equally sized groups called pools and a single laboratory test is applied to each pool. Individuals whose samples belong to pools that test negative…
In this paper, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations we obtain the form of…
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,…
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.…
We consider nonadaptive group testing with Bernoulli tests, where each item is placed in each test independently with some fixed probability. We give a tight threshold on the maximum number of tests required to find the defective set under…
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures 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…
When the infection prevalence of a disease is low, Dorfman showed 80 years ago that testing groups of people can prove more efficient than testing people individually. Our goal in this paper is to propose new group testing algorithms that…
The group testing problem consists of determining a small set of defective items from a larger set of items based on tests on groups of items, and is relevant in applications such as medical testing, communication protocols, pattern…
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;…
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…