Non-adaptive group testing in the presence of errors
type: Item
instance of: scholarly article
title: Non-adaptive group testing in the presence of errors
zbMATH Open document ID: 0948.62060
DOI: 10.1016/S0166-218X(98)00075-4
published in: Discrete Applied Mathematics
publication date: 1999-06-20T00:00:00Z
review text: In the general group testing problem, the task is to determine the set of distinguished objects in a collection of objects by performing tests on subsets subsets (pools) of the collection. The objective of the group testing problem is to minimize the total worst-case (combinatorial group testing) or average case (probabilistic group testing) cost of the tests. The aim of the present paper is to show how the methods for constructing pooling designs can be used for constructing error tolerant designs. The main contributions include a discussion of useful error models, a unified treatment of known pooling design construction methods, and a new and more general design evaluation methodology. Computable formulas for predicting the average performance are proposed in the presence of errors for pooling designs constructed by several methods, including deterministic and randomized constructions. The use of these formulas is illustrated by an example. The asymptotic behaviour of random \(k\)-sets designs is also discussed. It is shown that the parameters can be chosen to achieve optimal asymptotic behaviour to within a constant factor for reasonable error probabilites. The proposed approach is proved to be useful for evaluating the known options for the design of trivial two-stage pooling designs relevant to real screening problems.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 62K99
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 1268164
zbMATH Keywords: group testing
zbMATH Keywords: error tolerant designs
zbMATH Keywords: pooling design construction methods
zbMATH Keywords: screening problems
author: Emanuel Knill
author: William J. Bruno
author: David C. Torney
MaRDI profile type: Publication
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full work available at URL: s0166-218x(98)00075-4
OpenAlex ID: W2067804144
description: scientific article; zbMATH DE number 1268164