Many fault-detection problems fall into the following model: There is a set of n items, some of which are defective. The goal is to identify the defective items by using the minimum number of tests. Each test is on a subset of items and tells whether the subset contains a defective item or not. Let Ma(d, n)(M(d In)) denote the maximum number of tests for an algorithm ot to identify d defectives...

Abstract In this paper we consider a system consisting of a retailer, a supplier with a single processing unit, and a repair center. We assume that the retailer faces a Poisson demand, his ordering cost is zero or negligible, and for his inventory control he applies one-for-one ordering policy, that is, as soon as a demand arrives he orders one unit to the supplier. We also assume that when a d...

Algorithms for the group testing problem when there is no a priori information on the number of defective items are considered. The efficiency criterion used is the competitive ratio, which is the ratio of the number of tests required by an algorithm when there is no a priori information on the number of defective items, to the number of tests required by an optimal algorithm when the number of...

a clinical presentation of a metabolic disorder, often first seen in infants who present with poor feeding, vomiting, tachypnea, acidosis, hyperammonemia, ketosis, ketonuria, irritability, and convulsions or hypotonia and lethargy, findings that are otherwise suggestive of neonatal sepsis diseases with oa isovaleric and propionic acidemias, maple syrup urine disease, medium chain acyl dehydroge...

Abstract In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which goal is high-probability recovery defective set. We show that case $n$ items among $k$ are defective, smallest possible number tests equals $\min \{ C_{k,n} k \log n, n\}$ up to lower-order asymptotic terms, where $C_{k,n}$ a uniformly bounded constant (varying depending on scaling wi...