Related papers: Efficient and error-tolerant schemes for non-adapt…
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…
In combinatorial group testing problems Questioner needs to find a special element $x \in [n]$ by testing subsets of $[n]$. Tapolcai et al. introduced a new model, where each element knows the answer for those queries that contain it and…
In one-stage or non-adaptive group testing, instead of testing every sample unit individually, they are split, bundled in pools, and simultaneously tested. The results are then decoded to infer the states of the individual items. This…
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 the problem of group testing (pooled testing), first introduced by Dorfman. For non-adaptive testing strategies, we refer to a non-defective item as `intruding' if it only appears in positive tests. Such items cause…
In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of $n$ items and $k$ defectives, we provide an algorithm attaining…
In this note, we present a new adaptive algorithm for generalized group testing, which is asymptotically optimal if $d=o(\log_2|E|)$, $E$ is a set of potentially contaminated sets, $d$ is a maximal size of elements of $E$. Also, we design a…
We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We…
Efficient two-stage group testing algorithms that are particularly suited for rapid and less-expensive DNA library screening and other large scale biological group testing efforts are investigated in this paper. The main focus is on novel…
We study Probabilistic Group Testing of a set of N items each of which is defective with probability p. We focus on the double limit of small defect probability, p<<1, and large number of variables, N>>1, taking either p->0 after…
In a \emph{group testing} scheme, a set of tests is designed to identify a small number $t$ of defective items among a large set (of size $N$) of items. In the non-adaptive scenario the set of tests has to be designed in one-shot. In this…
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…
We consider the problem of quantitative group testing (QGT), where the goal is to recover a sparse binary vector from aggregate subset-sum queries: each query selects a subset of indices and returns the sum of those entries.…
This paper proposes a novel generalization of group testing, called multi-group testing, which relaxes the notion of "testing subset" in group testing to "testing multi-set". The generalization aims to learn more information of each item to…
In many real world problems, features do not act alone but in combination with each other. For example, in genomics, diseases might not be caused by any single mutation but require the presence of multiple mutations. Prior work on feature…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
We study the problem of group testing with a non-adaptive randomized algorithm in the random incidence design (RID) model where each entry in the test is chosen randomly independently from $\{0,1\}$ with a fixed probability $p$. The…
In group testing, the task is to determine the distinguished members of a set of objects L by asking subset queries of the form ``does the subset Q of L contain a distinguished object?'' The primary biological application of group testing…
The use of group testing to locate all instances of disease in a large population of blood samples was first considered seventy years ago. Since then, several methods have been used to approximate the minimum expected number of tests. The…
Semiquantitative group testing (SQGT) is a pooling method in which the test outcomes represent bounded intervals for the number of defectives. Alternatively, it may be viewed as an adder channel with quantized outputs. SQGT represents a…