On optimal policy in the group testing with incomplete identification

Yaakov Malinovsky

Statistics & Probability Letters, 2018, vol. 140, issue C, 44-47

Abstract: Consider a very large (infinite) population of items, where each item independent from the others is defective with probability p, or good with probability q=1−p. The goal is to identify N good items as quickly as possible. The following group testing policy (policy A) is considered: test items together in the groups, if the test outcome of group i of size ni is negative, then accept all items in this group as good, otherwise discard the group. Then, move to the next group and continue until exact N good items are found. The goal is to find an optimal testing configuration, i.e., group sizes, under policy A, such that the expected waiting time to obtain N good items is minimal. Recently, Gusev (2012) found an optimal group testing configuration under the assumptions of constant group size and N=∞. In this note, an optimal solution under policy A for finite N is provided.

Keywords: Dynamic programming; Optimal design; Partition problem; Shur-convexity (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.04.015

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