Hypothesis group testing for disjoint pairs

• Published in: Journal of combinatorial optimization 2008, Vol.15 (1), p.7-16
• Main Authors: Bishop, Morgan A., Macula, Anthony J., Renz, Thomas E., Ufimtsev, Vladimir V.
• Format: Article
• Language: English
• Subjects: Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Theory of Computation
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-007-9081-5

Classical group testing (CGT) is a widely applicable biotechnical technique used to identify a small number of distinguished objects from a population when the presence of any one of these distinguished objects among a group of others produces an observable result. This paper discusses a variant of CGT called group testing for disjoint pairs (GTAP). The difference between the two is that in GTDP, the distinguished items are pairs from, not individual objects in, the population. There are several biological examples of when this abstract model applies. One biological example is DNA hybridization. The presence of pairs of hybridized DNA strands can be detected in a pool of DNA strands. Another situation is the detection of binding interactions between prey and bait proteins. This paper gives a random pooling method, similar in spirit to hypothesis testing, which identifies pairs of objects from a population that collectively have an observable function. This method is simply to apply, achieves good results, is amenable to automation and can be easily modified to compensate for testing errors.