Efficient Constructions of Disjunct Matrices with Applications to DNA Library Screening

The study of gene functions requires a DNA library of high quality, such a library is obtained from a large mount of testing and screening. Pooling design is a very helpful tool for reducing the number of tests for DNA library screening. In this paper, we present two Las Vegas algorithms for efficient constructions of d-disjunct and (d ; z)-disjunct matrices respectively. These new constructions can be directly applied to construct error-free and error-tolerant pooling designs.

[1]  Ding-Zhu Du,et al.  New constructions of non-adaptive and error-tolerance pooling designs , 2002, Discret. Math..

[2]  Annalisa De Bonis,et al.  Optimal Two-Stage Algorithms for Group Testing Problems , 2005, SIAM J. Comput..

[3]  Richard C. Singleton,et al.  Nonrandom binary superimposed codes , 1964, IEEE Trans. Inf. Theory.

[4]  L. Hood,et al.  A common language for physical mapping of the human genome. , 1989, Science.

[5]  David C. Torney,et al.  Optimal Pooling Designs with Error Detection , 1994, J. Comb. Theory, Ser. A.

[6]  Weili Wu,et al.  DNA Screening, Pooling Design and Simplicial Complex , 2003, J. Comb. Optim..

[7]  Martin Aigner,et al.  Searching with Lies , 1996, J. Comb. Theory, Ser. A.

[8]  Weili Wu,et al.  New Construction for Transversal Design , 2006, J. Comput. Biol..

[9]  S. Muthukrishnan,et al.  On optimal strategies for searching in presence of errors , 1994, SODA '94.

[10]  Miklós Ruszinkó,et al.  On the Upper Bound of the Size of the R-Cover-Free Families , 1993, Proceedings. IEEE International Symposium on Information Theory.

[11]  Zoltán Füredi On r-Cover-free Families , 1996, J. Comb. Theory, Ser. A.

[12]  D. Du,et al.  Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing , 2006 .

[13]  P. Erdös,et al.  Families of finite sets in which no set is covered by the union ofr others , 1985 .

[14]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[15]  A. Macula Probabilistic nonadaptive group testing in the presence of errors and DNA library screening , 1999 .

[16]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[17]  Arkadii G. D'yachkov,et al.  New constructions of superimposed codes , 2000, IEEE Trans. Inf. Theory.

[18]  Hung-Lin Fu,et al.  A novel use of t-packings to construct d-disjunct matrices , 2006, Discret. Appl. Math..

[19]  Anthony J. Macula,et al.  A simple construction of d-disjunct matrices with certain constant weights , 1996, Discret. Math..

[20]  V. V. Rykov,et al.  Superimposed distance codes , 1989 .

[21]  Anthony J. Macula,et al.  Error-correcting Nonadaptive Group Testing with de-disjunct Matrices , 1997, Discret. Appl. Math..