Error-correcting pooling designs and group testing for consecutive positives

• Main Authors: Yi-tsz Tsai, 蔡一慈
• Other Authors: Huilan Chang
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/39584901398774789345

碩士 === 國立高雄大學 === 應用數學系碩士班 === 102 === Pooling designs are standard experimental tools in many biotechnical applications. Many famous pooling designs have been constructed from mathematical structures by "containing relation". Recently, pooling designs constructed by "intersecting relation" have been proposed by Nan and Guo (2010) and Guo and Wang (2011). Constructing by intersecting relation provides much better error-tolerance capabilities. In this thesis, we study the error-tolerance capabilities of pooling designs constructed by intersecting relation from combinatorial structures proposed by D'yachkov et al. (2007) and Bai et al. (2009). Motivated by application to DNA sequencing, group testing for consecutive positives has been proposed by Balding and Torney(1997) and Colbourn (1999) where n items are linearly ordered and all up to d positive items are consecutive in the order. In this thesis, we study a variation of (k; m; n)-selectors and use this combinatorial object to design a two-stage algorithm for group testing of consecutive positives. Our algorithm takes at most 12log_2 \lceil n/d \rceil +14e + 3d tests to identify all positives and its decoding complexity is O(n/d log n/d + d).