Born again group testing: Multiaccess communications

A brief summary of the basic notions of group testing is presented together with a brief historical account. One of the early papers on group testing is shown to include a description of the tree-search polling algorithm of Hayes. The classical group testing problem is formulated, including a criterion for optimality of test plans. A restricted class of tests, called nested testing, is described, and a complete description for an optimal nested strategy is given for both a finite number and an infinite number of Bernoulli distributed random variables. A generalization of group testing applicable to the random access communications problem is presented.