Related papers: Smart elements in combinatorial group testing prob…
In combinatorial group testing problems Questioner needs to find a defective element $x\in [n]$ by testing subsets of $[n]$. In [18] the authors introduced a new model, where each element knows the answer for those queries that contain it…
We examine the following version of a classic combinatorial search problem introduced by R\'enyi: Given a finite set $X$ of $n$ elements we want to identify an unknown subset $Y \subset X$ of exactly $d$ elements by testing, by as few as…
We consider the following combinatorial search problem: we are given some excellent elements of $[n]$ and we should find at least one, asking questions of the following type: "Is there an excellent element in $A \subset [n]$?". G.O.H.…
Group testing is an approach aimed at identifying up to $d$ defective items among a total of $n$ elements. This is accomplished by examining subsets to determine if at least one defective item is present. In our study, we focus on the…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
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 context of fault-detection problems, the objective is to identify all defective items among a set of $n$ binary-state items using the minimum number of tests. The {group testing} paradigm, which allows testing a subset of items in a…
We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that…
In group testing, simple binary-output tests are designed to identify a small number $t$ of defective items that are present in a large population of $N$ items. Each test takes as input a group of items and produces a binary output…
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…
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…
Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find…
In the classical combinatorial (adaptive) group testing problem, one is given two integers \(d\) and \(n\), where \(0\le d\le n\), and a population of \(n\) items, exactly \(d\) of which are known to be defective. The question is to devise…
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…
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…
We consider a generalization of group testing where the potentially contaminated sets are the members of a given hypergraph ${\cal F}=(V,E)$. This generalization finds application in contexts where contaminations can be conditioned by some…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
The element distinctness problem is the problem of determining whether the elements of a list are distinct, that is, if $x=(x_1,...,x_N)$ is a list with $N$ elements, we ask whether the elements of $x$ are distinct or not. The solution in a…