On optimal policy in the group testing with incomplete identification
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 n_i 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=\infty. In this note, an optimal solution under policy A for finite N is provided. Keywords: Dynamic programming; Optimal design; Partition problem; Shur-convexity
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2017
- DOI:
- 10.48550/arXiv.1712.03168
- arXiv:
- arXiv:1712.03168
- Bibcode:
- 2017arXiv171203168M
- Keywords:
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- Statistics - Other Statistics;
- 62L99;
- 62P10;
- 90C39
- E-Print:
- Submitted for publication, Revised