Sets pooling designs
type: Item
instance of: scholarly article
title: Sets pooling designs
zbMATH Open document ID: 0932.05018
DOI: 10.1007/BF01609879
author: David C. Torney
published in: Annals of Combinatorics
publication date: 2000-03-13T00:00:00Z
review text: A pooling design is a collection of subsets, called pools, of a finite set \(U\). Conventional pooling designs are used to identify distinguished (positive) elements of \(U\). Provided there are no experimental errors, a pool containing at least one positive object yields a positive assay. The author introduces the notion of positive subset, so that a pool yields a positive assay when it contains a positive subset. Sets pooling designs generalise conventional pooling designs and their introduction is motivated by modern molecular and cellular biology. The feasibility of constructing sets pooling designs is discussed by investigating random, non-adaptive designs in the case all distinguished subsets have the same size. Deterministic and adaptive designs are described, too. An interesting formula is proved for an optimum probability for including an object in a pool.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 62K99
zbMATH DE Number: 1347993
zbMATH Keywords: block design
zbMATH Keywords: group testing
zbMATH Keywords: extremal sets
zbMATH Keywords: asymptotic approximation
zbMATH Keywords: pooling design
zbMATH Keywords: positive subset
zbMATH Keywords: sets pooling designs
zbMATH Keywords: adaptive designs
MaRDI profile type: Publication
cites work: Q3741626
cites work: Q5687002
cites work: Optimal pooling designs with error detection
cites work: Q4873725
cites work: Q5736202
cites work: Families of finite sets in which no set is covered by the union of two others
cites work: Sharper bounds in adpative group testing
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description: scientific article; zbMATH DE number 1347993