The Exact Solution to the Two-Stage Group-Testing Problem

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Abstract
In the original two-stage method of group-testing, it is well known that if p is the proportion of infected individuals in the population, then the optimal group size is approximately p −1/2 when p is small. A modified mathematical treatment of the problem is used in this paper to show that for all p < .3 the optimal group size is either 1 + [p −1/2] or 2 + [p −1/2], where [x] denotes the integer part of x, and, when the optimal group size is used, the expected number of tests per individual is between 2p 1/2 – p/2 and 2p 1/2 + 4p 3/2. Other interesting features of the two-stage method, as a function of group size, are also revealed.

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