An Optimum Nested Procedure in Binomial Group Testing

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Abstract
Consider a random sample of n units, each of which has probability p of being defective and probability q = 1 - p of being good. A group test is a simultaneous test on an arbitrary set of units with 2 possible outcomes. The group is good if every unit in it is good; the group is defective if otherwise. The problem is to classify all units in the population by means of a sequence of group tests. The objective is to minimize the expected number of tests. An important class of group testing procedures which have appeared in the literature is the nested class. Sobel and Groll formulated a recursion equation to determine an optimum nested procedure and its expected number of tests. However, it takes O(n2) time for computing. A new formulation is given which can be computed in O(n) time.

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