Probabilistic nonadaptive group testing in the presence of errors and DNA library screening

We use the subset containment relation to construct a probabilistic nonadaptive group testing design and decoding algorithm that, in the presence of testing errors, identifies many positives in a population. We give a lower bound for the expected portion of positives identified as a function of an upper bound on the number of testing errors.The algorithms contained herein are part of The State University of New York Research Foundation invention C1230-125, Probabilistic and Combinatorial Nonadaptive and Two-Stage Group Testing and DNA Library Screening by A. Macula and K. Anne.