Related papers: Application-oriented mathematical algorithms for g…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
The group testing problem is concerned with identifying a small set of $k$ infected individuals in a large population of $n$ people. At our disposal is a testing scheme that can test groups of individuals. A test comes back positive if and…
Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…
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…
In the group-testing literature, efficient algorithms have been developed to minimize the number of tests required to identify all minimal "defective" sub-groups embedded within a larger group, using deterministic group splitting with a…
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 at least one defective item is present. This problem is relevant in areas such as medical…
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…
In this work, we consider the sparsity-constrained community-based group testing problem, where the population follows a community structure. In particular, the community consists of $F$ families, each with $M$ members. A number $k_f$ out…
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…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
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…
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…
Imagine you are a teacher attempting to assess a student's level in a particular subject. If you design a test with only hard questions, and the student fails, this mostly proves that the student does not understand the more advanced…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
We consider two closely related problems: anomaly detection in sensor networks and testing for infections in human populations. In both problems, we have $n$ nodes (sensors, humans), and each node exhibits an event of interest (anomaly,…
We propose a mathematical model based on probability theory to optimize COVID-19 testing by a multi-step batch testing approach with variable batch sizes. This model and simulation tool dramatically increase the efficiency and efficacy of…
The original problem of group testing consists in the identification of defective items in a collection, by applying tests on groups of items that detect the presence of at least one defective item in the group. The aim is then to identify…
Detection of defective members of large populations has been widely studied in the statistics community under the name "group testing", a problem which dates back to World War II when it was suggested for syphilis screening. There the main…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…