Pooling Experiments for Consecutive Positives

In this paper, we study the pooling experiments for screening clone maps. Clones are overlapped and placedin a linear order, and hence the clones containing a particular DNA sequence of our interest form a consecutive set (orseveral consecutive subsets) under the linear order. Those clones are called consecutive positives. Pooling experiments areused to identify as many positives as possible by screening as few pools as possible. Stochastic models are introduced toexplain the usefulness of the overlap structure for more efficient pooling experiments even when experimental errors exist. Wedescribe an efficient positive detecting algorithm, called modified Markov chain pool result decoder (MMCPD), for consecutivepositives. We also introduce an efficient algorithm, called random pooling designer (RPD), for estimating the minimal numberof randomly generated pools required for achieving the complete identifiability of pooling experiments when consecutivepositives and experimental errors exist. To our best knowledge, MMCPD is the first probabilistic group testing algorithm fordetecting consecutive positives when experimental errors exist. Interestingly, RPD shows some happy coincidences between ourtheoretical computation results and previously known simulation results. Some simulation results are also reported in hoping ofdemonstrating that MMCPD and RPD may be promising for real settings