Combinatorial problems arising from pooling designs for dna library screening
Colbourn (1999) developed some strategy for nonadaptive group testing when the items are linearly ordered and the positive items form a consecutive subset of all items.<br />Müller and Jimbo (2004) improved his strategy by introducing the concept of 2-consecutive positive detectable matrices (...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2004-11-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/169 |
| Summary: | Colbourn (1999) developed some strategy for nonadaptive group testing when the items are linearly ordered and the positive items form a consecutive subset of all items.<br />Müller and Jimbo (2004) improved his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix) requiring that all columns and bitwise OR-sum of each two consecutive columns are pairwise distinct. Such a matrix is called maximal if it has a maximal possible number of columns with respect to some obvious constraints. Using a recursive construction they proved the existence of maximal 2CPD-matrices for any column size <em>m ∈ N </em>except for the case<em> m = 3</em>. Moreover, maximal 2CPD-matrices such that each column is of some fixed constant weight are<br />constructed. This leads to pooling designs, where each item appears in the same number of pools and all pools are of the same size.<br />Secondly, we investigate 2CPD-matrices of some constant column weight <em>τ ∈ N</em>. We give some recursive construction of such matrices having the maximal possible number of columns.<br /> Thirdly, error correction capability of group testing procedures is essential in view of applications such as DNA library screening. We consider a error correcting 2CPD-matrices.<br /> |
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| ISSN: | 0373-3505 2037-5298 |